Off-axis illumination direct-to-digital holography

DOEpatents

Thomas, Clarence E.; Price, Jeffery R.; Voelkl, Edgar; Hanson, Gregory R.

2004-06-08

Systems and methods are described for off-axis illumination direct-to-digital holography. A method of recording an off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis, includes: reflecting a reference beam from a reference mirror at a non-normal angle; reflecting an object beam from an object at an angle with respect to an optical axis defined by a focusing lens; focusing the reference beam and the object beam at a focal plane of a digital recorder to form the off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; digitally recording the off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; Fourier analyzing the recorded off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes by transforming axes of the recorded off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes in Fourier space to sit on top of a heterodyne carrier frequency defined as an angle between the reference beam and the object beam; applying a digital filter to cut off signals around an original origin; and then performing an inverse Fourier transform.

Spectral analysis for GNSS coordinate time series using chirp Fourier transform

NASA Astrophysics Data System (ADS)

Feng, Shengtao; Bo, Wanju; Ma, Qingzun; Wang, Zifan

2017-12-01

Spectral analysis for global navigation satellite system (GNSS) coordinate time series provides a principal tool to understand the intrinsic mechanism that affects tectonic movements. Spectral analysis methods such as the fast Fourier transform, Lomb-Scargle spectrum, evolutionary power spectrum, wavelet power spectrum, etc. are used to find periodic characteristics in time series. Among spectral analysis methods, the chirp Fourier transform (CFT) with less stringent requirements is tested with synthetic and actual GNSS coordinate time series, which proves the accuracy and efficiency of the method. With the length of series only limited to even numbers, CFT provides a convenient tool for windowed spectral analysis. The results of ideal synthetic data prove CFT accurate and efficient, while the results of actual data show that CFT is usable to derive periodic information from GNSS coordinate time series.

Fused off-axis object illumination direct-to-digital holography with a plurality of illumination sources

DOEpatents

Price, Jeffery R.; Bingham, Philip R.

2005-11-08

Systems and methods are described for rapid acquisition of fused off-axis illumination direct-to-digital holography. A method of recording a plurality of off-axis object illuminated spatially heterodyne holograms, each of the off-axis object illuminated spatially heterodyne holograms including spatially heterodyne fringes for Fourier analysis, includes digitally recording, with a first illumination source of an interferometer, a first off-axis object illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; and digitally recording, with a second illumination source of the interferometer, a second off-axis object illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis.

Fourier analysis of human soft tissue facial shape: sex differences in normal adults.

PubMed Central

Ferrario, V F; Sforza, C; Schmitz, J H; Miani, A; Taroni, G

1995-01-01

Sexual dimorphism in human facial form involves both size and shape variations of the soft tissue structures. These variations are conventionally appreciated using linear and angular measurements, as well as ratios, taken from photographs or radiographs. Unfortunately this metric approach provides adequate quantitative information about size only, eluding the problems of shape definition. Mathematical methods such as the Fourier series allow a correct quantitative analysis of shape and of its changes. A method for the reconstruction of outlines starting from selected landmarks and for their Fourier analysis has been developed, and applied to analyse sex differences in shape of the soft tissue facial contour in a group of healthy young adults. When standardised for size, no sex differences were found between both cosine and sine coefficients of the Fourier series expansion. This shape similarity was largely overwhelmed by the very evident size differences and it could be measured only using the proper mathematical methods. PMID:8586558

Chemometric Analysis of Multicomponent Biodegradable Plastics by Fourier Transform Infrared Spectrometry: The R-Matrix Method

USDA-ARS?s Scientific Manuscript database

A new chemometric method based on absorbance ratios from Fourier transform infrared spectra was devised to analyze multicomponent biodegradable plastics. The method uses the BeerLambert law to directly compute individual component concentrations and weight losses before and after biodegradation of c...

Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise

NASA Technical Reports Server (NTRS)

SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.

1999-01-01

A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.

Spectral methods for time dependent problems

NASA Technical Reports Server (NTRS)

Tadmor, Eitan

1990-01-01

Spectral approximations are reviewed for time dependent problems. Some basic ingredients from the spectral Fourier and Chebyshev approximations theory are discussed. A brief survey was made of hyperbolic and parabolic time dependent problems which are dealt with by both the energy method and the related Fourier analysis. The ideas presented above are combined in the study of accuracy stability and convergence of the spectral Fourier approximation to time dependent problems.

A laboratory demonstration of high-resolution hard X-ray and gamma-ray imaging using Fourier-transform techniques

NASA Technical Reports Server (NTRS)

Palmer, David; Prince, Thomas A.

1987-01-01

A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard X-ray and gamma-ray imaging, with particular emphasis on possible applications to high-energy astronomy. Considerations for the design of a Fourier-transform imager and the instrumentation used in the laboratory studies is described. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented.

The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.

ERIC Educational Resources Information Center

King, Roy W.; Williams, Kathryn R.

1989-01-01

Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)

Nonadiabatic laser-induced alignment of molecules: Reconstructing ⟨ θ⟩ directly from ⟨ θ2D⟩ by Fourier analysis.

PubMed

Søndergaard, Anders Aspegren; Shepperson, Benjamin; Stapelfeldt, Henrik

2017-07-07

We present an efficient, noise-robust method based on Fourier analysis for reconstructing the three-dimensional measure of the alignment degree, ⟨cos 2 θ⟩, directly from its two-dimensional counterpart, ⟨cos 2 θ 2D ⟩. The method applies to nonadiabatic alignment of linear molecules induced by a linearly polarized, nonresonant laser pulse. Our theoretical analysis shows that the Fourier transform of the time-dependent ⟨cos 2 θ 2D ⟩ trace over one molecular rotational period contains additional frequency components compared to the Fourier transform of ⟨cos 2 θ⟩. These additional frequency components can be identified and removed from the Fourier spectrum of ⟨cos 2 θ 2D ⟩. By rescaling of the remaining frequency components, the Fourier spectrum of ⟨cos 2 θ⟩ is obtained and, finally, ⟨cos 2 θ⟩ is reconstructed through inverse Fourier transformation. The method allows the reconstruction of the ⟨cos 2 θ⟩ trace from a measured ⟨cos 2 θ 2D ⟩ trace, which is the typical observable of many experiments, and thereby provides direct comparison to calculated ⟨cos 2 θ⟩ traces, which is the commonly used alignment metric in theoretical descriptions. We illustrate our method by applying it to the measurement of nonadiabatic alignment of I 2 molecules. In addition, we present an efficient algorithm for calculating the matrix elements of cos 2 θ 2D and any other observable in the symmetric top basis. These matrix elements are required in the rescaling step, and they allow for highly efficient numerical calculation of ⟨cos 2 θ 2D ⟩ and ⟨cos 2 θ⟩ in general.

Fourier Descriptor Analysis and Unification of Voice Range Profile Contours: Method and Applications

ERIC Educational Resources Information Center

Pabon, Peter; Ternstrom, Sten; Lamarche, Anick

2011-01-01

Purpose: To describe a method for unified description, statistical modeling, and comparison of voice range profile (VRP) contours, even from diverse sources. Method: A morphologic modeling technique, which is based on Fourier descriptors (FDs), is applied to the VRP contour. The technique, which essentially involves resampling of the curve of the…

Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method

ERIC Educational Resources Information Center

Ghosh, Supriya; Dixit, Mayank Kumar; Bhattacharyya, S. P.; Tembe, B. L.

2013-01-01

Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…

Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise

NASA Technical Reports Server (NTRS)

Santa Maria, Odilyn L.

1999-01-01

A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary, but possibly harmonizable. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to show helicopter noise as harmonizable. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.

The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon

2018-03-01

In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral decomposition. New method for the best approximation of the square-integrable function by multiple Fourier series summed over the elliptic levels are established. Using the best approximation, the Lebesgue constant corresponding to the elliptic partial sums is estimated. The latter is applied to obtain an estimation for the maximal operator in the classes of Liouville.

Numerical Investigation of Laminar-Turbulent Transition in a Flat Plate Wake

DTIC Science & Technology

1990-03-02

Difference Methods , Oxford University Press. 3 Swarztrauber, P. N. (1977). "The Methods of Cyclic Reduction, Fourier Analysis and The FACR Algorithm for...streamwise and trans- verse directions. For the temporal discretion, a combination of ADI, Crank-Nicolson,Iand Adams-Rashforth methods is employed. The...41 U 5. NUMERICAL METHOD ...... .................... .. 50 3 5.1 Spanwise Spectral Approximation ... .............. ... 50 5.1.1 Fourier

Spatially-Heterodyned Holography

DOEpatents

Thomas, Clarence E [Knoxville, TN; Hanson, Gregory R [Clinton, TN

2006-02-21

A method of recording a spatially low-frequency heterodyne hologram, including spatially heterodyne fringes for Fourier analysis, includes: splitting a laser beam into a reference beam and an object beam; interacting the object beam with an object; focusing the reference beam and the object beam at a focal plane of a digital recorder to form a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis; digital recording the spatially low-frequency heterodyne hologram; Fourier transforming axes of the recorded spatially low-frequency heterodyne hologram including spatially heterodyne fringes in Fourier space to sit on top of a heterodyne carrier frequency defined by an angle between the reference beam and the object beam; cutting off signals around an origin; and performing an inverse Fourier transform.

The hyperbolic chemical bond: Fourier analysis of ground and first excited state potential energy curves of HX (X = H-Ne).

PubMed

Harrison, John A

2008-09-04

RHF/aug-cc-pVnZ, UHF/aug-cc-pVnZ, and QCISD/aug-cc-pVnZ, n = 2-5, potential energy curves of H2 X (1) summation g (+) are analyzed by Fourier transform methods after transformation to a new coordinate system via an inverse hyperbolic cosine coordinate mapping. The Fourier frequency domain spectra are interpreted in terms of underlying mathematical behavior giving rise to distinctive features. There is a clear difference between the underlying mathematical nature of the potential energy curves calculated at the HF and full-CI levels. The method is particularly suited to the analysis of potential energy curves obtained at the highest levels of theory because the Fourier spectra are observed to be of a compact nature, with the envelope of the Fourier frequency coefficients decaying in magnitude in an exponential manner. The finite number of Fourier coefficients required to describe the CI curves allows for an optimum sampling strategy to be developed, corresponding to that required for exponential and geometric convergence. The underlying random numerical noise due to the finite convergence criterion is also a clearly identifiable feature in the Fourier spectrum. The methodology is applied to the analysis of MRCI potential energy curves for the ground and first excited states of HX (X = H-Ne). All potential energy curves exhibit structure in the Fourier spectrum consistent with the existence of resonances. The compact nature of the Fourier spectra following the inverse hyperbolic cosine coordinate mapping is highly suggestive that there is some advantage in viewing the chemical bond as having an underlying hyperbolic nature.

Spectral analysis comparisons of Fourier-theory-based methods and minimum variance (Capon) methods

NASA Astrophysics Data System (ADS)

Garbanzo-Salas, Marcial; Hocking, Wayne. K.

2015-09-01

In recent years, adaptive (data dependent) methods have been introduced into many areas where Fourier spectral analysis has traditionally been used. Although the data-dependent methods are often advanced as being superior to Fourier methods, they do require some finesse in choosing the order of the relevant filters. In performing comparisons, we have found some concerns about the mappings, particularly when related to cases involving many spectral lines or even continuous spectral signals. Using numerical simulations, several comparisons between Fourier transform procedures and minimum variance method (MVM) have been performed. For multiple frequency signals, the MVM resolves most of the frequency content only for filters that have more degrees of freedom than the number of distinct spectral lines in the signal. In the case of Gaussian spectral approximation, MVM will always underestimate the width, and can misappropriate the location of spectral line in some circumstances. Large filters can be used to improve results with multiple frequency signals, but are computationally inefficient. Significant biases can occur when using MVM to study spectral information or echo power from the atmosphere. Artifacts and artificial narrowing of turbulent layers is one such impact.

Broadband turbulent spectra in gamma-ray burst light curves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Putten, Maurice H. P. M.; Guidorzi, Cristiano; Frontera, Filippo, E-mail: mvp@sejong.ac.kr

2014-05-10

Broadband power density spectra offer a window to understanding turbulent behavior in the emission mechanism and, at the highest frequencies, in the putative inner engines powering long gamma-ray bursts (GRBs). We describe a chirp search method alongside Fourier analysis for signal detection in the Poisson noise-dominated, 2 kHz sampled, BeppoSAX light curves. An efficient numerical implementation is described in O(Nnlog n) operations, where N is the number of chirp templates and n is the length of the light-curve time series, suited for embarrassingly parallel processing. For the detection of individual chirps over a 1 s duration, the method is onemore » order of magnitude more sensitive in signal-to-noise ratio than Fourier analysis. The Fourier-chirp spectra of GRB 010408 and GRB 970816 show a continuation of the spectral slope with up to 1 kHz of turbulence identified in low-frequency Fourier analysis. The same continuation is observed in an average spectrum of 42 bright, long GRBs. An outlook on a similar analysis of upcoming gravitational wave data is included.« less

High resolution frequency analysis techniques with application to the redshift experiment

NASA Technical Reports Server (NTRS)

Decher, R.; Teuber, D.

1975-01-01

High resolution frequency analysis methods, with application to the gravitational probe redshift experiment, are discussed. For this experiment a resolution of .00001 Hz is required to measure a slowly varying, low frequency signal of approximately 1 Hz. Major building blocks include fast Fourier transform, discrete Fourier transform, Lagrange interpolation, golden section search, and adaptive matched filter technique. Accuracy, resolution, and computer effort of these methods are investigated, including test runs on an IBM 360/65 computer.

Iterative wave-front reconstruction in the Fourier domain.

PubMed

Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry

2017-05-15

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

A time-frequency analysis method to obtain stable estimates of magnetotelluric response function based on Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Cai, Jianhua

2017-05-01

The time-frequency analysis method represents signal as a function of time and frequency, and it is considered a powerful tool for handling arbitrary non-stationary time series by using instantaneous frequency and instantaneous amplitude. It also provides a possible alternative to the analysis of the non-stationary magnetotelluric (MT) signal. Based on the Hilbert-Huang transform (HHT), a time-frequency analysis method is proposed to obtain stable estimates of the magnetotelluric response function. In contrast to conventional methods, the response function estimation is performed in the time-frequency domain using instantaneous spectra rather than in the frequency domain, which allows for imaging the response parameter content as a function of time and frequency. The theory of the method is presented and the mathematical model and calculation procedure, which are used to estimate response function based on HHT time-frequency spectrum, are discussed. To evaluate the results, response function estimates are compared with estimates from a standard MT data processing method based on the Fourier transform. All results show that apparent resistivities and phases, which are calculated from the HHT time-frequency method, are generally more stable and reliable than those determined from the simple Fourier analysis. The proposed method overcomes the drawbacks of the traditional Fourier methods, and the resulting parameter minimises the estimation bias caused by the non-stationary characteristics of the MT data.

The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings.

PubMed

Komorowski, Dariusz; Pietraszek, Stanislaw

2016-01-01

This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal.

Estimation of phase derivatives using discrete chirp-Fourier-transform-based method.

PubMed

Gorthi, Sai Siva; Rastogi, Pramod

2009-08-15

Estimation of phase derivatives is an important task in many interferometric measurements in optical metrology. This Letter introduces a method based on discrete chirp-Fourier transform for accurate and direct estimation of phase derivatives, even in the presence of noise. The method is introduced in the context of the analysis of reconstructed interference fields in digital holographic interferometry. We present simulation and experimental results demonstrating the utility of the proposed method.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Phase walk analysis of leptokurtic time series.

PubMed

Schreiber, Korbinian; Modest, Heike I; Räth, Christoph

2018-06-01

The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases. The method, being called phase walk analysis, is based on well established measures from random walk analysis, which are now applied to the unwrapped Fourier phases of time series. We provide an analytical description of its functionality and demonstrate its capabilities on systematically controlled leptokurtic noise. Hereby, we investigate the properties of leptokurtic time series and their influence on the Fourier phases of time series. The phase walk analysis is applied to measured and simulated intermittent time series, whose probability density distribution is approximated by power laws. We use the day-to-day returns of the Dow-Jones industrial average, a synthetic time series with tailored nonlinearities mimicing the power law behavior of the Dow-Jones and the acceleration of the wind at an Atlantic offshore site. Testing for nonlinearities by means of surrogates shows that the new method yields strong significances for nonlinear behavior. Due to the drastically decreased computing time as compared to embedding space methods, the number of surrogate realizations can be increased by orders of magnitude. Thereby, the probability distribution of the test statistics can very accurately be derived and parameterized, which allows for much more precise tests on nonlinearities.

Comparison of detrending methods for fluctuation analysis in hydrology

NASA Astrophysics Data System (ADS)

Zhang, Qiang; Zhou, Yu; Singh, Vijay P.; Chen, Yongqin David

2011-03-01

SummaryTrends within a hydrologic time series can significantly influence the scaling results of fluctuation analysis, such as rescaled range (RS) analysis and (multifractal) detrended fluctuation analysis (MF-DFA). Therefore, removal of trends is important in the study of scaling properties of the time series. In this study, three detrending methods, including adaptive detrending algorithm (ADA), Fourier-based method, and average removing technique, were evaluated by analyzing numerically generated series and observed streamflow series with obvious relative regular periodic trend. Results indicated that: (1) the Fourier-based detrending method and ADA were similar in detrending practices, and given proper parameters, these two methods can produce similarly satisfactory results; (2) detrended series by Fourier-based detrending method and ADA lose the fluctuation information at larger time scales, and the location of crossover points is heavily impacted by the chosen parameters of these two methods; and (3) the average removing method has an advantage over the other two methods, i.e., the fluctuation information at larger time scales is kept well-an indication of relatively reliable performance in detrending. In addition, the average removing method performed reasonably well in detrending a time series with regular periods or trends. In this sense, the average removing method should be preferred in the study of scaling properties of the hydrometeorolgical series with relative regular periodic trend using MF-DFA.

Absolute Measurement of Tilts via Fourier Analysis of Interferograms

NASA Technical Reports Server (NTRS)

Toland, Ronald W.

2004-01-01

The Fourier method of interferogram analysis requires the introduction of a constant tilt into the inteferogram to serve as a 'carrier signal' for information on the figure of the surface under test. This tilt is usually removed in the first steps of analysis and ignored thereafter. However, in the problem of aligning optical components and systems, knowledge of part orientation is crucial to proper instrument performance. This paper outlines an algorithm which uses the normally ignored carrier signal in Fourier analysis to compute an absolute tilt (orientation) of the test surface. We also provide a brief outline of how this technique, incorporated in a rotating Twyman-Green interferometer, can be used in alignment and metrology of optical systems.

Absolute Measurement of Tilts via Fourier Analysis of Interferograms

NASA Technical Reports Server (NTRS)

Toland, Ronald W.

2004-01-01

The Fourier method of interferogram analysis requires the introduction of a constant tilt into the interferogram to serve as a carrier signal for information on the figure of the surface under test. This tilt is usually removed in the first steps of analysis and ignored thereafter. However, in the problem of aligning optical components and systems, knowledge of part orientation is crucial to proper instrument performance. This paper outlines an algorithm which uses the normally ignored carrier signal in Fourier analysis to compute an absolute tilt (orientation) of the test surface. We also provide a brief outline of how this technique, incorporated in a rotating Twyman-Green interferometer, can be used in alignment and metrology of optical systems.

Faster processing of multiple spatially-heterodyned direct to digital holograms

DOEpatents

Hanson, Gregory R.; Bingham, Philip R.

2006-10-03

Systems and methods are described for faster processing of multiple spatially-heterodyned direct to digital holograms. A method includes of obtaining multiple spatially-heterodyned holograms, includes: digitally recording a first spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; digitally recording a second spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded first spatially-heterodyned hologram by shifting a first original origin of the recorded first spatially-heterodyned hologram including spatial heterodyne fringes in Fourier space to sit on top of a spatial-heterodyne carrier frequency defined as a first angle between a first reference beam and a first, object beam; applying a first digital filter to cut off signals around the first original origin and performing an inverse Fourier transform on the result; Fourier analyzing the recorded second spatially-heterodyned hologram by shifting a second original origin of the recorded second spatially-heterodyned hologram including spatial heterodyne fringes in Fourier space to sit on top of a spatial-heterodyne carrier frequency defined as a second angle between a second reference beam and a second object beam; and applying a second digital filter to cut off signals around the second original origin and performing an inverse Fourier transform on the result, wherein digitally recording the first spatially-heterodyned hologram is completed before digitally recording the second spatially-heterodyned hologram and a single digital image includes both the first spatially-heterodyned hologram and the second spatially-heterodyned hologram.

Faster processing of multiple spatially-heterodyned direct to digital holograms

DOEpatents

Hanson, Gregory R [Clinton, TN; Bingham, Philip R [Knoxville, TN

2008-09-09

Systems and methods are described for faster processing of multiple spatially-heterodyned direct to digital holograms. A method includes of obtaining multiple spatially-heterodyned holograms, includes: digitally recording a first spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; digitally recording a second spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded first spatially-heterodyned hologram by shifting a first original origin of the recorded first spatially-heterodyned hologram including spatial heterodyne fringes in Fourier space to sit on top of a spatial-heterodyne carrier frequency defined as a first angle between a first reference beam and a first object beam; applying a first digital filter to cut off signals around the first original origin and performing an inverse Fourier transform on the result; Fourier analyzing the recorded second spatially-heterodyned hologram by shifting a second original origin of the recorded second spatially-heterodyned hologram including spatial heterodyne fringes in Fourier space to sit on top of a spatial-heterodyne carrier frequency defined as a second angle between a second reference beam and a second object beam; and applying a second digital filter to cut off signals around the second original origin and performing an inverse Fourier transform on the result, wherein digitally recording the first spatially-heterodyned hologram is completed before digitally recording the second spatially-heterodyned hologram and a single digital image includes both the first spatially-heterodyned hologram and the second spatially-heterodyned hologram.

Fourier Transform Infrared Spectroscopy as a Tool in Analysis of Proteus mirabilis Endotoxins.

PubMed

Żarnowiec, Paulina; Czerwonka, Grzegorz; Kaca, Wiesław

2017-01-01

Fourier transform infrared spectroscopy (FT-IR) was used to scan whole bacterial cells as well as lipopolysaccharides (LPSs, endotoxins) isolated from them. Proteus mirabilis cells, with chemically defined LPSs, served as a model for the ATR FT-IR method. The paper focuses on three steps of infrared spectroscopy: (1) sample preparation, (2) IR scanning, and (3) multivariate analysis of IR data (principal component analysis, PCA).

Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited].

PubMed

Takeda, Mitsuo

2013-01-01

The paper reviews a technique for fringe analysis referred to as Fourier fringe analysis (FFA) or the Fourier transform method, with a particular focus on its application to metrology of extreme physical phenomena. Examples include the measurement of extremely small magnetic fields with subfluxon sensitivity by electron wave interferometry, subnanometer wavefront evaluation of projection optics for extreme UV lithography, the detection of sub-Ångstrom distortion of a crystal lattice, and the measurement of ultrashort optical pulses in the femotsecond to attosecond range, which show how the advantages of FFA are exploited in these cutting edge applications.

Analysis of Franck-Condon factors for CO+ molecule using the Fourier Grid Hamiltonian method

NASA Astrophysics Data System (ADS)

Syiemiong, Arnestar; Swer, Shailes; Jha, Ashok Kumar; Saxena, Atul

2018-04-01

Franck-Condon factors (FCFs) are important parameters and it plays a very important role in determining the intensities of the vibrational bands in electronic transitions. In this paper, we illustrate the Fourier Grid Hamiltonian (FGH) method, a relatively simple method to calculate the FCFs. The FGH is a method used for calculating the vibrational eigenvalues and eigenfunctions of bound electronic states of diatomic molecules. The obtained vibrational wave functions for the ground and the excited states are used to calculate the vibrational overlap integral and then the FCFs. In this computation, we used the Morse potential and Bi-Exponential potential model for constructing and diagonalizing the molecular Hamiltonians. The effects of the change in equilibrium internuclear distance (xe), dissociation energy (De), and the nature of the excited state electronic energy curve on the FCFs have been determined. Here we present our work for the qualitative analysis of Franck-Condon Factorsusing this Fourier Grid Hamiltonian Method.

[Study on Differential Optical Absorption Spectroscopy Data Processing Based on Chirp-Z Transformation].

PubMed

Zheng, Hai-ming; Li, Guang-jie; Wu, Hao

2015-06-01

Differential optical absorption spectroscopy (DOAS) is a commonly used atmospheric pollution monitoring method. Denoising of monitoring spectral data will improve the inversion accuracy. Fourier transform filtering method is effectively capable of filtering out the noise in the spectral data. But the algorithm itself can introduce errors. In this paper, a chirp-z transform method is put forward. By means of the local thinning of Fourier transform spectrum, it can retain the denoising effect of Fourier transform and compensate the error of the algorithm, which will further improve the inversion accuracy. The paper study on the concentration retrieving of SO2 and NO2. The results show that simple division causes bigger error and is not very stable. Chirp-z transform is proved to be more accurate than Fourier transform. Results of the frequency spectrum analysis show that Fourier transform cannot solve the distortion and weakening problems of characteristic absorption spectrum. Chirp-z transform shows ability in fine refactoring of specific frequency spectrum.

Renal geology (quantitative renal stone analysis) by 'Fourier transform infrared spectroscopy'.

PubMed

Singh, Iqbal

2008-01-01

To prospectively determine the precise stone composition (quantitative analysis) by using infrared spectroscopy in patients with urinary stone disease presenting to our clinic. To determine an ideal method for stone analysis suitable for use in a clinical setting. After routine and a detailed metabolic workup of all patients of urolithiasis, stone samples of 50 patients of urolithiasis satisfying the entry criteria were subjected to the Fourier transform infrared spectroscopic analysis after adequate sample homogenization at a single testing center. Calcium oxalate monohydrate and dihydrate stone mixture was most commonly encountered in 35 (71%) followed by calcium phosphate, carbonate apatite, magnesium ammonium hexahydrate and xanthine stones. Fourier transform infrared spectroscopy allows an accurate, reliable quantitative method of stone analysis. It also helps in maintaining a computerized large reference library. Knowledge of precise stone composition may allow the institution of appropriate prophylactic therapy despite the absence of any detectable metabolic abnormalities. This may prevent and or delay stone recurrence.

Measuring sperm movement within the female reproductive tract using Fourier analysis.

PubMed

Nicovich, Philip R; Macartney, Erin L; Whan, Renee M; Crean, Angela J

2015-02-01

The adaptive significance of variation in sperm phenotype is still largely unknown, in part due to the difficulties of observing and measuring sperm movement in its natural, selective environment (i.e., within the female reproductive tract). Computer-assisted sperm analysis systems allow objective and accurate measurement of sperm velocity, but rely on being able to track individual sperm, and are therefore unable to measure sperm movement in species where sperm move in trains or bundles. Here we describe a newly developed computational method for measuring sperm movement using Fourier analysis to estimate sperm tail beat frequency. High-speed time-lapse videos of sperm movement within the female tract of the neriid fly Telostylinus angusticollis were recorded, and a map of beat frequencies generated by converting the periodic signal of an intensity versus time trace at each pixel to the frequency domain using the Fourier transform. We were able to detect small decreases in sperm tail beat frequency over time, indicating the method is sensitive enough to identify consistent differences in sperm movement. Fourier analysis can be applied to a wide range of species and contexts, and should therefore facilitate novel exploration of the causes and consequences of variation in sperm movement.

A Fourier method for the analysis of exponential decay curves.

PubMed

Provencher, S W

1976-01-01

A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions. The Fourier method's usual serious practical limitation of needing high accuracy data over a very wide range is eliminated by the introduction of convergence parameters and a Gaussian taper window. A computer program is described for the analysis of discrete spectra, where the data involves only a sum of exponentials. The program is completely automatic in that the only necessary inputs are the raw data (not necessarily in equal intervals of time); no potentially biased initial guesses concerning either the number or the values of the components are needed. The outputs include the number of components, the amplitudes and time constants together with their estimated errors, and a spectral plot of the solution. The limiting resolving power of the method is studied by analyzing a wide range of simulated two-, three-, and four-component data. The results seem to indicate that the method is applicable over a considerably wider range of conditions than nonlinear least squares or the method of moments.

The application and improvement of Fourier transform spectrometer experiment

NASA Astrophysics Data System (ADS)

Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning

2017-08-01

According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.

Optical Design And Analysis Of Carbon Dioxide Laser Fusion Systems Using Interferometry And Fast Fourier Transform Techniques

NASA Astrophysics Data System (ADS)

Viswanathan, V. K.

1980-11-01

The optical design and analysis of the LASL carbon dioxide laser fusion systems required the use of techniques that are quite different from the currently used method in conventional optical design problems. The necessity for this is explored and the method that has been successfully used at Los Alamos to understand these systems is discussed with examples. This method involves characterization of the various optical components in their mounts by a Zernike polynomial set and using fast Fourier transform techniques to propagate the beam, taking diffraction and other nonlinear effects that occur in these types of systems into account. The various programs used for analysis are briefly discussed.

A new transform for the analysis of complex fractionated atrial electrograms

PubMed Central

2011-01-01

Background Representation of independent biophysical sources using Fourier analysis can be inefficient because the basis is sinusoidal and general. When complex fractionated atrial electrograms (CFAE) are acquired during atrial fibrillation (AF), the electrogram morphology depends on the mix of distinct nonsinusoidal generators. Identification of these generators using efficient methods of representation and comparison would be useful for targeting catheter ablation sites to prevent arrhythmia reinduction. Method A data-driven basis and transform is described which utilizes the ensemble average of signal segments to identify and distinguish CFAE morphologic components and frequencies. Calculation of the dominant frequency (DF) of actual CFAE, and identification of simulated independent generator frequencies and morphologies embedded in CFAE, is done using a total of 216 recordings from 10 paroxysmal and 10 persistent AF patients. The transform is tested versus Fourier analysis to detect spectral components in the presence of phase noise and interference. Correspondence is shown between ensemble basis vectors of highest power and corresponding synthetic drivers embedded in CFAE. Results The ensemble basis is orthogonal, and efficient for representation of CFAE components as compared with Fourier analysis (p ≤ 0.002). When three synthetic drivers with additive phase noise and interference were decomposed, the top three peaks in the ensemble power spectrum corresponded to the driver frequencies more closely as compared with top Fourier power spectrum peaks (p ≤ 0.005). The synthesized drivers with phase noise and interference were extractable from their corresponding ensemble basis with a mean error of less than 10%. Conclusions The new transform is able to efficiently identify CFAE features using DF calculation and by discerning morphologic differences. Unlike the Fourier transform method, it does not distort CFAE signals prior to analysis, and is relatively robust to jitter in periodic events. Thus the ensemble method can provide a useful alternative for quantitative characterization of CFAE during clinical study. PMID:21569421

Applying wavelet transforms to analyse aircraft-measured turbulence and turbulent fluxes in the atmospheric boundary layer over eastern Siberia

NASA Astrophysics Data System (ADS)

Strunin, M. A.; Hiyama, T.

2004-11-01

The wavelet spectral method was applied to aircraft-based measurements of atmospheric turbulence obtained during joint Russian-Japanese research on the atmospheric boundary layer near Yakutsk (eastern Siberia) in April-June 2000. Practical ways to apply Fourier and wavelet methods for aircraft-based turbulence data are described. Comparisons between Fourier and wavelet transform results are shown and they demonstrate, in conjunction with theoretical and experimental restrictions, that the Fourier transform method is not useful for studying non-homogeneous turbulence. The wavelet method is free from many disadvantages of Fourier analysis and can yield more informative results. Comparison of Fourier and Morlet wavelet spectra showed good agreement at high frequencies (small scales). The quality of the wavelet transform and corresponding software was estimated by comparing the original data with restored data constructed with an inverse wavelet transform. A Haar wavelet basis was inappropriate for the turbulence data; the mother wavelet function recommended in this study is the Morlet wavelet. Good agreement was also shown between variances and covariances estimated with different mathematical techniques, i.e. through non-orthogonal wavelet spectra and through eddy correlation methods.

Comparative measurement of collagen bundle orientation by Fourier analysis and semiquantitative evaluation: reliability and agreement in Masson's trichrome, Picrosirius red and confocal microscopy techniques.

PubMed

Marcos-Garcés, V; Harvat, M; Molina Aguilar, P; Ferrández Izquierdo, A; Ruiz-Saurí, A

2017-08-01

Measurement of collagen bundle orientation in histopathological samples is a widely used and useful technique in many research and clinical scenarios. Fourier analysis is the preferred method for performing this measurement, but the most appropriate staining and microscopy technique remains unclear. Some authors advocate the use of Haematoxylin-Eosin (H&E) and confocal microscopy, but there are no studies comparing this technique with other classical collagen stainings. In our study, 46 human skin samples were collected, processed for histological analysis and stained with Masson's trichrome, Picrosirius red and H&E. Five microphotographs of the reticular dermis were taken with a 200× magnification with light microscopy, polarized microscopy and confocal microscopy, respectively. Two independent observers measured collagen bundle orientation with semiautomated Fourier analysis with the Image-Pro Plus 7.0 software and three independent observers performed a semiquantitative evaluation of the same parameter. The average orientation for each case was calculated with the values of the five pictures. We analyzed the interrater reliability, the consistency between Fourier analysis and average semiquantitative evaluation and the consistency between measurements in Masson's trichrome, Picrosirius red and H&E-confocal. Statistical analysis for reliability and agreement was performed with the SPSS 22.0 software and consisted of intraclass correlation coefficient (ICC), Bland-Altman plots and limits of agreement and coefficient of variation. Interrater reliability was almost perfect (ICC > 0.8) with all three histological and microscopy techniques and always superior in Fourier analysis than in average semiquantitative evaluation. Measurements were consistent between Fourier analysis by one observer and average semiquantitative evaluation by three observers, with an almost perfect agreement with Masson's trichrome and Picrosirius red techniques (ICC > 0.8) and a strong agreement with H&E-confocal (0.7 < ICC < 0.8). Comparison of measurements between the three techniques for the same observer showed an almost perfect agreement (ICC > 0.8), better with Fourier analysis than with semiquantitative evaluation (single and average). These results in nonpathological skin samples were also confirmed in a preliminary analysis in eight scleroderma skin samples. Our results show that Masson's trichrome and Picrosirius red are consistent with H&E-confocal for measuring collagen bundle orientation in histological samples and could thus be used indistinctly for this purpose. Fourier analysis is superior to average semiquantitative evaluation and should keep being used as the preferred method. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

Content-based fused off-axis object illumination direct-to-digital holography

DOEpatents

Price, Jeffery R.

2006-05-02

Systems and methods are described for content-based fused off-axis illumination direct-to-digital holography. A method includes calculating an illumination angle with respect to an optical axis defined by a focusing lens as a function of data representing a Fourier analyzed spatially heterodyne hologram; reflecting a reference beam from a reference mirror at a non-normal angle; reflecting an object beam from an object the object beam incident upon the object at the illumination angle; focusing the reference beam and the object beam at a focal plane of a digital recorder to from the content-based off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis; and digitally recording the content based off-axis illuminated spatially heterodyne hologram including spatially heterodyne fringes for Fourier analysis.

Effects of data gaps on Fourier Analysis

NASA Astrophysics Data System (ADS)

Negrea, Catalin; Munteanu, Costel; Echim, Marius

2014-05-01

Fourier Analysis is a vital and widely used tool in all branches of science that require advanced data processing. The method is often used via the Fast Fourier Transform (FFT) implementation readily available in most programming languages. This is a valid approach for data sets with equally spaced data points and no gaps. Such conditions are not always met in real situations where corrections and adjustments to the method are needed. We investigate the intrinsic limitations of four such methods when data gaps are present: 1) linear interpolations and FFT, 2) a direct implementation of the Discrete Fourier Transform, 3) a Z-Transform and 4) the Lomb-Scargle algorithm. Theoretical analysis tools can provide an insight as to the likely problems of such methods and we discuss the likely modifications to the computed spectra. Also, a time series with no data gaps and a constant sampling frequency is altered by introducing several gap configurations and the resulting spectra with the four methods are compared to highlight changes with respect to the original spectrum. Effects on the amplitude and phase of the resulting power spectral densities are analyzed for non-uniformly sampled solar wind data provided by the Venus Express spacecraft. Phase effects are also studied in the context of a sliding window approach. Research supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 313038/STORM, and a grant of the Romanian Ministry of National Education, CNCS - UEFISCDI, project number PN-II-ID-PCE-2012-4-0418.

Determination of the Optimal Fourier Number on the Dynamic Thermal Transmission

NASA Astrophysics Data System (ADS)

Bruzgevičius, P.; Burlingis, A.; Norvaišienė, R.

2016-12-01

This article represents the result of experimental research on transient heat transfer in a multilayered (heterogeneous) wall. Our non-steady thermal transmission simulation is based on a finite-difference calculation method. The value of a Fourier number shows the similarity of thermal variation in conditional layers of an enclosure. Most scientists recommend using no more than a value of 0.5 for the Fourier number when performing calculations on dynamic (transient) heat transfer. The value of the Fourier number is determined in order to acquire reliable calculation results with optimal accuracy. To compare the results of simulation with experimental research, a transient heat transfer calculation spreadsheet was created. Our research has shown that a Fourier number of around 0.5 or even 0.32 is not sufficient ({≈ }17 % of oscillation amplitude) for calculations of transient heat transfer in a multilayered wall. The least distorted calculation results were obtained when the multilayered enclosure was divided into conditional layers with almost equal Fourier number values and when the value of the Fourier number was around 1/6, i.e., approximately 0.17. Statistical deviation analysis using the Statistical Analysis System was applied to assess the accuracy of the spreadsheet calculation and was developed on the basis of our established methodology. The mean and median absolute error as well as their confidence intervals has been estimated by the two methods with optimal accuracy ({F}_{oMDF}= 0.177 and F_{oEPS}= 0.1633 values).

Thermal stabilization of static single-mirror Fourier transform spectrometers

NASA Astrophysics Data System (ADS)

Schardt, Michael; Schwaller, Christian; Tremmel, Anton J.; Koch, Alexander W.

2017-05-01

Fourier transform spectroscopy has become a standard method for spectral analysis of infrared light. With this method, an interferogram is created by two beam interference which is subsequently Fourier-transformed. Most Fourier transform spectrometers used today provide the interferogram in the temporal domain. In contrast, static Fourier transform spectrometers generate interferograms in the spatial domain. One example of this type of spectrometer is the static single-mirror Fourier transform spectrometer which offers a high etendue in combination with a simple, miniaturized optics design. As no moving parts are required, it also features a high vibration resistance and high measurement rates. However, it is susceptible to temperature variations. In this paper, we therefore discuss the main sources for temperature-induced errors in static single-mirror Fourier transform spectrometers: changes in the refractive index of the optical components used, variations of the detector sensitivity, and thermal expansion of the housing. As these errors manifest themselves in temperature-dependent wavenumber shifts and intensity shifts, they prevent static single-mirror Fourier transform spectrometers from delivering long-term stable spectra. To eliminate these shifts, we additionally present a work concept for the thermal stabilization of the spectrometer. With this stabilization, static single-mirror Fourier transform spectrometers are made suitable for infrared process spectroscopy under harsh thermal environmental conditions. As the static single-mirror Fourier transform spectrometer uses the so-called source-doubling principle, many of the mentioned findings are transferable to other designs of static Fourier transform spectrometers based on the same principle.

Pulse analysis of acoustic emission signals. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Houghton, J. R.

1976-01-01

A method for the signature analysis of pulses in the frequency domain and the time domain is presented. Fourier spectrum, Fourier transfer function, shock spectrum and shock spectrum ratio are examined in the frequency domain analysis, and pulse shape deconvolution is developed for use in the time domain analysis. To demonstrate the relative sensitivity of each of the methods to small changes in the pulse shape, signatures of computer modeled systems with analytical pulses are presented. Optimization techniques are developed and used to indicate the best design parameters values for deconvolution of the pulse shape. Several experiments are presented that test the pulse signature analysis methods on different acoustic emission sources. These include acoustic emissions associated with: (1) crack propagation, (2) ball dropping on a plate, (3) spark discharge and (4) defective and good ball bearings.

A Fast Fourier transform stochastic analysis of the contaminant transport problem

USGS Publications Warehouse

Deng, F.W.; Cushman, J.H.; Delleur, J.W.

1993-01-01

A three-dimensional stochastic analysis of the contaminant transport problem is developed in the spirit of Naff (1990). The new derivation is more general and simpler than previous analysis. The fast Fourier transformation is used extensively to obtain numerical estimates of the mean concentration and various spatial moments. Data from both the Borden and Cape Cod experiments are used to test the methodology. Results are comparable to results obtained by other methods, and to the experiments themselves.

Radial artery pulse waveform analysis based on curve fitting using discrete Fourier series.

PubMed

Jiang, Zhixing; Zhang, David; Lu, Guangming

2018-04-19

Radial artery pulse diagnosis has been playing an important role in traditional Chinese medicine (TCM). For its non-invasion and convenience, the pulse diagnosis has great significance in diseases analysis of modern medicine. The practitioners sense the pulse waveforms in patients' wrist to make diagnoses based on their non-objective personal experience. With the researches of pulse acquisition platforms and computerized analysis methods, the objective study on pulse diagnosis can help the TCM to keep up with the development of modern medicine. In this paper, we propose a new method to extract feature from pulse waveform based on discrete Fourier series (DFS). It regards the waveform as one kind of signal that consists of a series of sub-components represented by sine and cosine (SC) signals with different frequencies and amplitudes. After the pulse signals are collected and preprocessed, we fit the average waveform for each sample using discrete Fourier series by least squares. The feature vector is comprised by the coefficients of discrete Fourier series function. Compared with the fitting method using Gaussian mixture function, the fitting errors of proposed method are smaller, which indicate that our method can represent the original signal better. The classification performance of proposed feature is superior to the other features extracted from waveform, liking auto-regression model and Gaussian mixture model. The coefficients of optimized DFS function, who is used to fit the arterial pressure waveforms, can obtain better performance in modeling the waveforms and holds more potential information for distinguishing different psychological states. Copyright © 2018 Elsevier B.V. All rights reserved.

Chiral Analysis of Isopulegol by Fourier Transform Molecular Rotational Spectroscopy

NASA Astrophysics Data System (ADS)

Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks

2016-06-01

Chiral analysis on molecules with multiple chiral centers can be performed using pulsed-jet Fourier transform rotational spectroscopy. This analysis includes quantitative measurement of diastereomer products and, with the three wave mixing methods developed by Patterson, Schnell, and Doyle (Nature 497, 475-477 (2013)), quantitative determination of the enantiomeric excess of each diastereomer. The high resolution features enable to perform the analysis directly on complex samples without the need for chromatographic separation. Isopulegol has been chosen to show the capabilities of Fourier transform rotational spectroscopy for chiral analysis. Broadband rotational spectroscopy produces spectra with signal-to-noise ratio exceeding 1000:1. The ability to identify low-abundance (0.1-1%) diastereomers in the sample will be described. Methods to rapidly identify rotational spectra from isotopologues at natural abundance will be shown and the molecular structures obtained from this analysis will be compared to theory. The role that quantum chemistry calculations play in identifying structural minima and estimating their spectroscopic properties to aid spectral analysis will be described. Finally, the implementation of three wave mixing techniques to measure the enantiomeric excess of each diastereomer and determine the absolute configuration of the enantiomer in excess will be described.

A method to identify differential expression profiles of time-course gene data with Fourier transformation.

PubMed

Kim, Jaehee; Ogden, Robert Todd; Kim, Haseong

2013-10-18

Time course gene expression experiments are an increasingly popular method for exploring biological processes. Temporal gene expression profiles provide an important characterization of gene function, as biological systems are both developmental and dynamic. With such data it is possible to study gene expression changes over time and thereby to detect differential genes. Much of the early work on analyzing time series expression data relied on methods developed originally for static data and thus there is a need for improved methodology. Since time series expression is a temporal process, its unique features such as autocorrelation between successive points should be incorporated into the analysis. This work aims to identify genes that show different gene expression profiles across time. We propose a statistical procedure to discover gene groups with similar profiles using a nonparametric representation that accounts for the autocorrelation in the data. In particular, we first represent each profile in terms of a Fourier basis, and then we screen out genes that are not differentially expressed based on the Fourier coefficients. Finally, we cluster the remaining gene profiles using a model-based approach in the Fourier domain. We evaluate the screening results in terms of sensitivity, specificity, FDR and FNR, compare with the Gaussian process regression screening in a simulation study and illustrate the results by application to yeast cell-cycle microarray expression data with alpha-factor synchronization.The key elements of the proposed methodology: (i) representation of gene profiles in the Fourier domain; (ii) automatic screening of genes based on the Fourier coefficients and taking into account autocorrelation in the data, while controlling the false discovery rate (FDR); (iii) model-based clustering of the remaining gene profiles. Using this method, we identified a set of cell-cycle-regulated time-course yeast genes. The proposed method is general and can be potentially used to identify genes which have the same patterns or biological processes, and help facing the present and forthcoming challenges of data analysis in functional genomics.

Abel inversion using fast Fourier transforms.

PubMed

Kalal, M; Nugent, K A

1988-05-15

A fast Fourier transform based Abel inversion technique is proposed. The method is faster than previously used techniques, potentially very accurate (even for a relatively small number of points), and capable of handling large data sets. The technique is discussed in the context of its use with 2-D digital interferogram analysis algorithms. Several examples are given.

Clustering change patterns using Fourier transformation with time-course gene expression data.

PubMed

Kim, Jaehee

2011-01-01

To understand the behavior of genes, it is important to explore how the patterns of gene expression change over a period of time because biologically related gene groups can share the same change patterns. In this study, the problem of finding similar change patterns is induced to clustering with the derivative Fourier coefficients. This work is aimed at discovering gene groups with similar change patterns which share similar biological properties. We developed a statistical model using derivative Fourier coefficients to identify similar change patterns of gene expression. We used a model-based method to cluster the Fourier series estimation of derivatives. We applied our model to cluster change patterns of yeast cell cycle microarray expression data with alpha-factor synchronization. It showed that, as the method clusters with the probability-neighboring data, the model-based clustering with our proposed model yielded biologically interpretable results. We expect that our proposed Fourier analysis with suitably chosen smoothing parameters could serve as a useful tool in classifying genes and interpreting possible biological change patterns.

An Accurate and Stable FFT-based Method for Pricing Options under Exp-Lévy Processes

NASA Astrophysics Data System (ADS)

Ding, Deng; Chong U, Sio

2010-05-01

An accurate and stable method for pricing European options in exp-Lévy models is presented. The main idea of this new method is combining the quadrature technique and the Carr-Madan Fast Fourier Transform methods. The theoretical analysis shows that the overall complexity of this new method is still O(N log N) with N grid points as the fast Fourier transform methods. Numerical experiments for different exp-Lévy processes also show that the numerical algorithm proposed by this new method has an accuracy and stability for the small strike prices K. That develops and improves the Carr-Madan method.

Investigation to realize a computationally efficient implementation of the high-order instantaneous-moments-based fringe analysis method

NASA Astrophysics Data System (ADS)

Gorthi, Sai Siva; Rajshekhar, Gannavarpu; Rastogi, Pramod

2010-06-01

Recently, a high-order instantaneous moments (HIM)-operator-based method was proposed for accurate phase estimation in digital holographic interferometry. The method relies on piece-wise polynomial approximation of phase and subsequent evaluation of the polynomial coefficients from the HIM operator using single-tone frequency estimation. The work presents a comparative analysis of the performance of different single-tone frequency estimation techniques, like Fourier transform followed by optimization, estimation of signal parameters by rotational invariance technique (ESPRIT), multiple signal classification (MUSIC), and iterative frequency estimation by interpolation on Fourier coefficients (IFEIF) in HIM-operator-based methods for phase estimation. Simulation and experimental results demonstrate the potential of the IFEIF technique with respect to computational efficiency and estimation accuracy.

FPGA-based multi-channel fluorescence lifetime analysis of Fourier multiplexed frequency-sweeping lifetime imaging

PubMed Central

Zhao, Ming; Li, Yu; Peng, Leilei

2014-01-01

We report a fast non-iterative lifetime data analysis method for the Fourier multiplexed frequency-sweeping confocal FLIM (Fm-FLIM) system [ Opt. Express22, 10221 ( 2014)24921725]. The new method, named R-method, allows fast multi-channel lifetime image analysis in the system’s FPGA data processing board. Experimental tests proved that the performance of the R-method is equivalent to that of single-exponential iterative fitting, and its sensitivity is well suited for time-lapse FLIM-FRET imaging of live cells, for example cyclic adenosine monophosphate (cAMP) level imaging with GFP-Epac-mCherry sensors. With the R-method and its FPGA implementation, multi-channel lifetime images can now be generated in real time on the multi-channel frequency-sweeping FLIM system, and live readout of FRET sensors can be performed during time-lapse imaging. PMID:25321778

Clustering of change patterns using Fourier coefficients.

PubMed

Kim, Jaehee; Kim, Haseong

2008-01-15

To understand the behavior of genes, it is important to explore how the patterns of gene expression change over a time period because biologically related gene groups can share the same change patterns. Many clustering algorithms have been proposed to group observation data. However, because of the complexity of the underlying functions there have not been many studies on grouping data based on change patterns. In this study, the problem of finding similar change patterns is induced to clustering with the derivative Fourier coefficients. The sample Fourier coefficients not only provide information about the underlying functions, but also reduce the dimension. In addition, as their limiting distribution is a multivariate normal, a model-based clustering method incorporating statistical properties would be appropriate. This work is aimed at discovering gene groups with similar change patterns that share similar biological properties. We developed a statistical model using derivative Fourier coefficients to identify similar change patterns of gene expression. We used a model-based method to cluster the Fourier series estimation of derivatives. The model-based method is advantageous over other methods in our proposed model because the sample Fourier coefficients asymptotically follow the multivariate normal distribution. Change patterns are automatically estimated with the Fourier representation in our model. Our model was tested in simulations and on real gene data sets. The simulation results showed that the model-based clustering method with the sample Fourier coefficients has a lower clustering error rate than K-means clustering. Even when the number of repeated time points was small, the same results were obtained. We also applied our model to cluster change patterns of yeast cell cycle microarray expression data with alpha-factor synchronization. It showed that, as the method clusters with the probability-neighboring data, the model-based clustering with our proposed model yielded biologically interpretable results. We expect that our proposed Fourier analysis with suitably chosen smoothing parameters could serve as a useful tool in classifying genes and interpreting possible biological change patterns. The R program is available upon the request.

Fourier analysis: from cloaking to imaging

NASA Astrophysics Data System (ADS)

Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping

2016-04-01

Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.

Recording multiple spatially-heterodyned direct to digital holograms in one digital image

DOEpatents

Hanson, Gregory R [Clinton, TN; Bingham, Philip R [Knoxville, TN

2008-03-25

Systems and methods are described for recording multiple spatially-heterodyned direct to digital holograms in one digital image. A method includes digitally recording, at a first reference beam-object beam angle, a first spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded first spatially-heterodyned hologram by shifting a first original origin of the recorded first spatially-heterodyned hologram to sit on top of a first spatial-heterodyne carrier frequency defined by the first reference beam-object beam angle; digitally recording, at a second reference beam-object beam angle, a second spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis; Fourier analyzing the recorded second spatially-heterodyned hologram by shifting a second original origin of the recorded second spatially-heterodyned hologram to sit on top of a second spatial-heterodyne carrier frequency defined by the second reference beam-object beam angle; applying a first digital filter to cut off signals around the first original origin and define a first result; performing a first inverse Fourier transform on the first result; applying a second digital filter to cut off signals around the second original origin and define a second result; and performing a second inverse Fourier transform on the second result, wherein the first reference beam-object beam angle is not equal to the second reference beam-object beam angle and a single digital image includes both the first spatially-heterodyned hologram and the second spatially-heterodyned hologram.

Discrete Fourier Transform Analysis in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H.

2009-01-01

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Bladed wheels damage detection through Non-Harmonic Fourier Analysis improved algorithm

NASA Astrophysics Data System (ADS)

Neri, P.

2017-05-01

Recent papers introduced the Non-Harmonic Fourier Analysis for bladed wheels damage detection. This technique showed its potential in estimating the frequency of sinusoidal signals even when the acquisition time is short with respect to the vibration period, provided that some hypothesis are fulfilled. Anyway, previously proposed algorithms showed severe limitations in cracks detection at their early stage. The present paper proposes an improved algorithm which allows to detect a blade vibration frequency shift due to a crack whose size is really small compared to the blade width. Such a technique could be implemented for condition-based maintenance, allowing to use non-contact methods for vibration measurements. A stator-fixed laser sensor could monitor all the blades as they pass in front of the spot, giving precious information about the wheel health. This configuration determines an acquisition time for each blade which become shorter as the machine rotational speed increases. In this situation, traditional Discrete Fourier Transform analysis results in poor frequency resolution, being not suitable for small frequency shift detection. Non-Harmonic Fourier Analysis instead showed high reliability in vibration frequency estimation even with data samples collected in a short time range. A description of the improved algorithm is provided in the paper, along with a comparison with the previous one. Finally, a validation of the method is presented, based on finite element simulations results.

Strategies for efficient resolution analysis in full-waveform inversion

NASA Astrophysics Data System (ADS)

Fichtner, A.; van Leeuwen, T.; Trampert, J.

2016-12-01

Full-waveform inversion is developing into a standard method in the seismological toolbox. It combines numerical wave propagation for heterogeneous media with adjoint techniques in order to improve tomographic resolution. However, resolution becomes increasingly difficult to quantify because of the enormous computational requirements. Here we present two families of methods that can be used for efficient resolution analysis in full-waveform inversion. They are based on the targeted extraction of resolution proxies from the Hessian matrix, which is too large to store and to compute explicitly. Fourier methods rest on the application of the Hessian to Earth models with harmonic oscillations. This yields the Fourier spectrum of the Hessian for few selected wave numbers, from which we can extract properties of the tomographic point-spread function for any point in space. Random probing methods use uncorrelated, random test models instead of harmonic oscillations. Auto-correlating the Hessian-model applications for sufficiently many test models also characterises the point-spread function. Both Fourier and random probing methods provide a rich collection of resolution proxies. These include position- and direction-dependent resolution lengths, and the volume of point-spread functions as indicator of amplitude recovery and inter-parameter trade-offs. The computational requirements of these methods are equivalent to approximately 7 conjugate-gradient iterations in full-waveform inversion. This is significantly less than the optimisation itself, which may require tens to hundreds of iterations to reach convergence. In addition to the theoretical foundations of the Fourier and random probing methods, we show various illustrative examples from real-data full-waveform inversion for crustal and mantle structure.

Methodology for processing pressure traces used as inputs for combustion analyses in diesel engines

NASA Astrophysics Data System (ADS)

Rašić, Davor; Vihar, Rok; Žvar Baškovič, Urban; Katrašnik, Tomaž

2017-05-01

This study proposes a novel methodology for designing an optimum equiripple finite impulse response (FIR) filter for processing in-cylinder pressure traces of a diesel internal combustion engine, which serve as inputs for high-precision combustion analyses. The proposed automated workflow is based on an innovative approach of determining the transition band frequencies and optimum filter order. The methodology is based on discrete Fourier transform analysis, which is the first step to estimate the location of the pass-band and stop-band frequencies. The second step uses short-time Fourier transform analysis to refine the estimated aforementioned frequencies. These pass-band and stop-band frequencies are further used to determine the most appropriate FIR filter order. The most widely used existing methods for estimating the FIR filter order are not effective in suppressing the oscillations in the rate- of-heat-release (ROHR) trace, thus hindering the accuracy of combustion analyses. To address this problem, an innovative method for determining the order of an FIR filter is proposed in this study. This method is based on the minimization of the integral of normalized signal-to-noise differences between the stop-band frequency and the Nyquist frequency. Developed filters were validated using spectral analysis and calculation of the ROHR. The validation results showed that the filters designed using the proposed innovative method were superior compared with those using the existing methods for all analyzed cases. Highlights • Pressure traces of a diesel engine were processed by finite impulse response (FIR) filters with different orders • Transition band frequencies were determined with an innovative method based on discrete Fourier transform and short-time Fourier transform • Spectral analyses showed deficiencies of existing methods in determining the FIR filter order • A new method of determining the FIR filter order for processing pressure traces was proposed • The efficiency of the new method was demonstrated by spectral analyses and calculations of rate-of-heat-release traces

An alternative approach to characterize nonlinear site effects

USGS Publications Warehouse

Zhang, R.R.; Hartzell, S.; Liang, J.; Hu, Y.

2005-01-01

This paper examines the rationale of a method of nonstationary processing and analysis, referred to as the Hilbert-Huang transform (HHT), for its application to a recording-based approach in quantifying influences of soil nonlinearity in site response. In particular, this paper first summarizes symptoms of soil nonlinearity shown in earthquake recordings, reviews the Fourier-based approach to characterizing nonlinearity, and offers justifications for the HHT in addressing nonlinearity issues. This study then uses the HHT method to analyze synthetic data and recordings from the 1964 Niigata and 2001 Nisqually earthquakes. In doing so, the HHT-based site response is defined as the ratio of marginal Hilbert amplitude spectra, alternative to the Fourier-based response that is the ratio of Fourier amplitude spectra. With the Fourier-based approach in studies of site response as a reference, this study shows that the alternative HHT-based approach is effective in characterizing soil nonlinearity and nonlinear site response.

Method of estimating pulse response using an impedance spectrum

DOEpatents

Morrison, John L; Morrison, William H; Christophersen, Jon P; Motloch, Chester G

2014-10-21

Electrochemical Impedance Spectrum data are used to predict pulse performance of an energy storage device. The impedance spectrum may be obtained in-situ. A simulation waveform includes a pulse wave with a period greater than or equal to the lowest frequency used in the impedance measurement. Fourier series coefficients of the pulse train can be obtained. The number of harmonic constituents in the Fourier series are selected so as to appropriately resolve the response, but the maximum frequency should be less than or equal to the highest frequency used in the impedance measurement. Using a current pulse as an example, the Fourier coefficients of the pulse are multiplied by the impedance spectrum at corresponding frequencies to obtain Fourier coefficients of the voltage response to the desired pulse. The Fourier coefficients of the response are then summed and reassembled to obtain the overall time domain estimate of the voltage using the Fourier series analysis.

Thermal Stress Analysis of a Continuous and Pulsed End-Pumped Nd:YAG Rod Crystal Using Non-Classic Conduction Heat Transfer Theory

NASA Astrophysics Data System (ADS)

Mojahedi, Mahdi; Shekoohinejad, Hamidreza

2018-02-01

In this paper, temperature distribution in the continuous and pulsed end-pumped Nd:YAG rod crystal is determined using nonclassical and classical heat conduction theories. In order to find the temperature distribution in crystal, heat transfer differential equations of crystal with consideration of boundary conditions are derived based on non-Fourier's model and temperature distribution of the crystal is achieved by an analytical method. Then, by transferring non-Fourier differential equations to matrix equations, using finite element method, temperature and stress of every point of crystal are calculated in the time domain. According to the results, a comparison between classical and nonclassical theories is represented to investigate rupture power values. In continuous end pumping with equal input powers, non-Fourier theory predicts greater temperature and stress compared to Fourier theory. It also shows that with an increase in relaxation time, crystal rupture power decreases. Despite of these results, in single rectangular pulsed end-pumping condition, with an equal input power, Fourier theory indicates higher temperature and stress rather than non-Fourier theory. It is also observed that, when the relaxation time increases, maximum amounts of temperature and stress decrease.

The Delicate Analysis of Short-Term Load Forecasting

NASA Astrophysics Data System (ADS)

Song, Changwei; Zheng, Yuan

2017-05-01

This paper proposes a new method for short-term load forecasting based on the similar day method, correlation coefficient and Fast Fourier Transform (FFT) to achieve the precision analysis of load variation from three aspects (typical day, correlation coefficient, spectral analysis) and three dimensions (time dimension, industry dimensions, the main factors influencing the load characteristic such as national policies, regional economic, holidays, electricity and so on). First, the branch algorithm one-class-SVM is adopted to selection the typical day. Second, correlation coefficient method is used to obtain the direction and strength of the linear relationship between two random variables, which can reflect the influence caused by the customer macro policy and the scale of production to the electricity price. Third, Fourier transform residual error correction model is proposed to reflect the nature of load extracting from the residual error. Finally, simulation result indicates the validity and engineering practicability of the proposed method.

INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections

NASA Astrophysics Data System (ADS)

Caliari, Marco; Zuccher, Simone

2017-04-01

Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of arbitrary points are quite rare, especially in MATLAB language. Here we employ the Nonequispaced Fast Fourier Transform (NFFT, by J. Keiner, S. Kunis, and D. Potts), a C library designed for this purpose, and provide a Matlab® and GNU Octave interface that makes NFFT easily available to the Numerical Analysis community. We test the effectiveness of our package in the framework of quantum vortex reconnections, where pseudospectral Fourier methods are commonly used and local high resolution is required in the post-processing stage. We show that the efficient evaluation of a truncated Fourier series at arbitrary points provides excellent results at a computational cost much smaller than carrying out a numerical simulation of the problem on a sufficiently fine regular grid that can reproduce comparable details of the reconnecting vortices.

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.

PubMed

Wang, Yubo; Veluvolu, Kalyana C

2017-06-14

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

Intelligent Automatic Classification of True and Counterfeit Notes Based on Spectrum Analysis

NASA Astrophysics Data System (ADS)

Matsunaga, Shohei; Omatu, Sigeru; Kosaka, Toshohisa

The purpose of this paper is to classify bank notes into “true” or “counterfeit” ones faster and more precisely compared with a conventional method. We note that thin lines are represented by direct lines in the images of true notes while they are represented in the counterfeit notes by dotted lines. This is due to properties of dot printers or scanner levels. To use the properties, we propose two method to classify a note into true or counterfeited one by checking whether there exist thin lines or dotted lines of the note. First, we use Fourier transform of the note to find quantity of features for classification and we classify a note into true or counterfeit one by using the features by Fourier transform. Then we propose a classification method by using wavelet transform in place of Fourier transform. Finally, some classification results are illustrated to show the effectiveness of the proposed methods.

Fourier-domain Mobility Spectrum Analysis (FMSA) for Characterizing Semiconductors with Multi-Electron/Hole Species

NASA Astrophysics Data System (ADS)

Cui, Boya; Kielb, Edward; Luo, Jiajun; Tang, Yang; Grayson, Matthew

Superlattices and narrow gap semiconductors often host multiple conducting species, such as electrons and holes, requiring a mobility spectral analysis (MSA) method to separate contributions to the conductivity. Here, a least-squares MSA method is introduced: the QR-algorithm Fourier-domain MSA (FMSA). Like other MSA methods, the FMSA sorts the conductivity contributions of different carrier species from magnetotransport measurements, arriving at a best fit to the experimentally measured longitudinal and Hall conductivities σxx and σxy, respectively. This method distinguishes itself from other methods by using the so-called QR-algorithm of linear algebra to achieve rapid convergence of the mobility spectrum as the solution to an eigenvalue problem, and by alternately solving this problem in both the mobility domain and its Fourier reciprocal-space. The result accurately fits a mobility range spanning nearly four orders of magnitude (μ = 300 to 1,000,000 cm2/V .s). This method resolves the mobility spectra as well as, or better than, competing MSA methods while also achieving high computational efficiency, requiring less than 30 second on average to converge to a solution on a standard desktop computer. Acknowledgement: Funded by AFOSR FA9550-15-1-0377 and AFOSR FA9550-15-1-0247.

Determination of uronic acids in isolated hemicelluloses from kenaf using diffuse reflectance infrared fourier transform spectroscopy (DRIFTS) and the curve-fitting deconvolution method.

PubMed

Batsoulis, A N; Nacos, M K; Pappas, C S; Tarantilis, P A; Mavromoustakos, T; Polissiou, M G

2004-02-01

Hemicellulose samples were isolated from kenaf (Hibiscus cannabinus L.). Hemicellulosic fractions usually contain a variable percentage of uronic acids. The uronic acid content (expressed in polygalacturonic acid) of the isolated hemicelluloses was determined by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and the curve-fitting deconvolution method. A linear relationship between uronic acids content and the sum of the peak areas at 1745, 1715, and 1600 cm(-1) was established with a high correlation coefficient (0.98). The deconvolution analysis using the curve-fitting method allowed the elimination of spectral interferences from other cell wall components. The above method was compared with an established spectrophotometric method and was found equivalent for accuracy and repeatability (t-test, F-test). This method is applicable in analysis of natural or synthetic mixtures and/or crude substances. The proposed method is simple, rapid, and nondestructive for the samples.

Frequency analysis via the method of moment functionals

NASA Technical Reports Server (NTRS)

Pearson, A. E.; Pan, J. Q.

1990-01-01

Several variants are presented of a linear-in-parameters least squares formulation for determining the transfer function of a stable linear system at specified frequencies given a finite set of Fourier series coefficients calculated from transient nonstationary input-output data. The basis of the technique is Shinbrot's classical method of moment functionals using complex Fourier based modulating functions to convert a differential equation model on a finite time interval into an algebraic equation which depends linearly on frequency-related parameters.

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Weighted network analysis of high-frequency cross-correlation measures

NASA Astrophysics Data System (ADS)

Iori, Giulia; Precup, Ovidiu V.

2007-03-01

In this paper we implement a Fourier method to estimate high-frequency correlation matrices from small data sets. The Fourier estimates are shown to be considerably less noisy than the standard Pearson correlation measures and thus capable of detecting subtle changes in correlation matrices with just a month of data. The evolution of correlation at different time scales is analyzed from the full correlation matrix and its minimum spanning tree representation. The analysis is performed by implementing measures from the theory of random weighted networks.

A new finite element formulation for computational fluid dynamics. IX - Fourier analysis of space-time Galerkin/least-squares algorithms

NASA Technical Reports Server (NTRS)

Shakib, Farzin; Hughes, Thomas J. R.

1991-01-01

A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.

New Substrate-Guided Method of Predicting Slow Conducting Isthmuses of Ventricular Tachycardia: Preliminary Analysis to the Combined Use of Voltage Limit Adjustment and Fast-Fourier Transform Analysis.

PubMed

Kuroki, Kenji; Nogami, Akihiko; Igarashi, Miyako; Masuda, Keita; Kowase, Shinya; Kurosaki, Kenji; Komatsu, Yuki; Naruse, Yoshihisa; Machino, Takeshi; Yamasaki, Hiro; Xu, Dongzhu; Murakoshi, Nobuyuki; Sekiguchi, Yukio; Aonuma, Kazutaka

2018-04-01

Several conducting channels of ventricular tachycardia (VT) can be identified using voltage limit adjustment (VLA) of substrate mapping. However, the sensitivity or specificity to predict a VT isthmus is not high by using VLA alone. This study aimed to evaluate the efficacy of the combined use of VLA and fast-Fourier transform analysis to predict VT isthmuses. VLA and fast-Fourier transform analyses of local ventricular bipolar electrograms during sinus rhythm were performed in 9 postinfarction patients who underwent catheter ablation for a total of 13 monomorphic VTs. Relatively higher voltage areas on an electroanatomical map were defined as high voltage channels (HVCs), and relatively higher fast-Fourier transform areas were defined as high-frequency channels (HFCs). HVCs were classified into full or partial HVCs (the entire or >30% of HVC can be detectable, respectively). Twelve full HVCs were identified in 7 of 9 patients. HFCs were located on 7 of 12 full HVCs. Five VT isthmuses (71%) were included in the 7 full HVC+/HFC+ sites, whereas no VT isthmus was found in the 5 full HVC+/HFC- sites. HFCs were identical to 9 of 16 partial HVCs. Eight VT isthmuses (89%) were included in the 9 partial HVC+/HFC+ sites, whereas no VT isthmus was found in the 7 partial HVC+/HFC- sites. All HVC+/HFC+ sites predicted VT isthmus with a sensitivity of 100% and a specificity of 80%. Combined use of VLA and fast-Fourier transform analysis may be a useful method to detect VT isthmuses. © 2018 American Heart Association, Inc.

Spatial-heterodyne interferometry for transmission (SHIFT) measurements

DOEpatents

Bingham, Philip R.; Hanson, Gregory R.; Tobin, Ken W.

2006-10-10

Systems and methods are described for spatial-heterodyne interferometry for transmission (SHIFT) measurements. A method includes digitally recording a spatially-heterodyned hologram including spatial heterodyne fringes for Fourier analysis using a reference beam, and an object beam that is transmitted through an object that is at least partially translucent; Fourier analyzing the digitally recorded spatially-heterodyned hologram, by shifting an original origin of the digitally recorded spatially-heterodyned hologram to sit on top of a spatial-heterodyne carrier frequency defined by an angle between the reference beam and the object beam, to define an analyzed image; digitally filtering the analyzed image to cut off signals around the original origin to define a result; and performing an inverse Fourier transform on the result.

Algorithm, applications and evaluation for protein comparison by Ramanujan Fourier transform.

PubMed

Zhao, Jian; Wang, Jiasong; Hua, Wei; Ouyang, Pingkai

2015-12-01

The amino acid sequence of a protein determines its chemical properties, chain conformation and biological functions. Protein sequence comparison is of great importance to identify similarities of protein structures and infer their functions. Many properties of a protein correspond to the low-frequency signals within the sequence. Low frequency modes in protein sequences are linked to the secondary structures, membrane protein types, and sub-cellular localizations of the proteins. In this paper, we present Ramanujan Fourier transform (RFT) with a fast algorithm to analyze the low-frequency signals of protein sequences. The RFT method is applied to similarity analysis of protein sequences with the Resonant Recognition Model (RRM). The results show that the proposed fast RFT method on protein comparison is more efficient than commonly used discrete Fourier transform (DFT). RFT can detect common frequencies as significant feature for specific protein families, and the RFT spectrum heat-map of protein sequences demonstrates the information conservation in the sequence comparison. The proposed method offers a new tool for pattern recognition, feature extraction and structural analysis on protein sequences. Copyright © 2015 Elsevier Ltd. All rights reserved.

Polarization-phase tomography of biological fluids polycrystalline structure

NASA Astrophysics Data System (ADS)

Dubolazov, A. V.; Vanchuliak, O. Ya.; Garazdiuk, M.; Sidor, M. I.; Motrich, A. V.; Kostiuk, S. V.

2013-12-01

Our research is aimed at designing an experimental method of Fourier's laser polarization phasometry of the layers of human effusion for an express diagnostics during surgery and a differentiation of the degree of severity (acute - gangrenous) appendectomy by means of statistical, correlation and fractal analysis of the coherent scattered field. A model of generalized optical anisotropy of polycrystal networks of albumin and globulin of the effusion of appendicitis has been suggested and the method of Fourier's phasometry of linear (a phase shift between the orthogonal components of the laser wave amplitude) and circular (the angle of rotation of the polarization plane) birefringence with a spatial-frequency selection of the coordinate distributions for the differentiation of acute and gangrenous conditions have been analytically substantiated. Comparative studies of the efficacy of the methods of direct mapping of phase distributions and Fourier's phasometry of a laser radiation field transformed by the dendritic and spherolitic networks of albumin and globulin of the layers of effusion of appendicitis on the basis of complex statistical, correlation and fractal analysis of the structure of phase maps.

Fourier-based integration of quasi-periodic gait accelerations for drift-free displacement estimation using inertial sensors.

PubMed

Sabatini, Angelo Maria; Ligorio, Gabriele; Mannini, Andrea

2015-11-23

In biomechanical studies Optical Motion Capture Systems (OMCS) are considered the gold standard for determining the orientation and the position (pose) of an object in a global reference frame. However, the use of OMCS can be difficult, which has prompted research on alternative sensing technologies, such as body-worn inertial sensors. We developed a drift-free method to estimate the three-dimensional (3D) displacement of a body part during cyclical motions using body-worn inertial sensors. We performed the Fourier analysis of the stride-by-stride estimates of the linear acceleration, which were obtained by transposing the specific forces measured by the tri-axial accelerometer into the global frame using a quaternion-based orientation estimation algorithm and detecting when each stride began using a gait-segmentation algorithm. The time integration was performed analytically using the Fourier series coefficients; the inverse Fourier series was then taken for reconstructing the displacement over each single stride. The displacement traces were concatenated and spline-interpolated to obtain the entire trace. The method was applied to estimate the motion of the lower trunk of healthy subjects that walked on a treadmill and it was validated using OMCS reference 3D displacement data; different approaches were tested for transposing the measured specific force into the global frame, segmenting the gait and performing time integration (numerically and analytically). The width of the limits of agreements were computed between each tested method and the OMCS reference method for each anatomical direction: Medio-Lateral (ML), VerTical (VT) and Antero-Posterior (AP); using the proposed method, it was observed that the vertical component of displacement (VT) was within ±4 mm (±1.96 standard deviation) of OMCS data and each component of horizontal displacement (ML and AP) was within ±9 mm of OMCS data. Fourier harmonic analysis was applied to model stride-by-stride linear accelerations during walking and to perform their analytical integration. Our results showed that analytical integration based on Fourier series coefficients was a useful approach to accurately estimate 3D displacement from noisy acceleration data.

A method to identify differential expression profiles of time-course gene data with Fourier transformation

PubMed Central

2013-01-01

Background Time course gene expression experiments are an increasingly popular method for exploring biological processes. Temporal gene expression profiles provide an important characterization of gene function, as biological systems are both developmental and dynamic. With such data it is possible to study gene expression changes over time and thereby to detect differential genes. Much of the early work on analyzing time series expression data relied on methods developed originally for static data and thus there is a need for improved methodology. Since time series expression is a temporal process, its unique features such as autocorrelation between successive points should be incorporated into the analysis. Results This work aims to identify genes that show different gene expression profiles across time. We propose a statistical procedure to discover gene groups with similar profiles using a nonparametric representation that accounts for the autocorrelation in the data. In particular, we first represent each profile in terms of a Fourier basis, and then we screen out genes that are not differentially expressed based on the Fourier coefficients. Finally, we cluster the remaining gene profiles using a model-based approach in the Fourier domain. We evaluate the screening results in terms of sensitivity, specificity, FDR and FNR, compare with the Gaussian process regression screening in a simulation study and illustrate the results by application to yeast cell-cycle microarray expression data with alpha-factor synchronization. The key elements of the proposed methodology: (i) representation of gene profiles in the Fourier domain; (ii) automatic screening of genes based on the Fourier coefficients and taking into account autocorrelation in the data, while controlling the false discovery rate (FDR); (iii) model-based clustering of the remaining gene profiles. Conclusions Using this method, we identified a set of cell-cycle-regulated time-course yeast genes. The proposed method is general and can be potentially used to identify genes which have the same patterns or biological processes, and help facing the present and forthcoming challenges of data analysis in functional genomics. PMID:24134721

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

ERIC Educational Resources Information Center

Grimm, C. A.

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

Fan beam image reconstruction with generalized Fourier slice theorem.

PubMed

Zhao, Shuangren; Yang, Kang; Yang, Kevin

2014-01-01

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.

A New Green Method for the Quantitative Analysis of Enrofloxacin by Fourier-Transform Infrared Spectroscopy.

PubMed

Rebouças, Camila Tavares; Kogawa, Ana Carolina; Salgado, Hérida Regina Nunes

2018-05-18

Background: A green analytical chemistry method was developed for quantification of enrofloxacin in tablets. The drug, a second-generation fluoroquinolone, was first introduced in veterinary medicine for the treatment of various bacterial species. Objective: This study proposed to develop, validate, and apply a reliable, low-cost, fast, and simple IR spectroscopy method for quantitative routine determination of enrofloxacin in tablets. Methods: The method was completely validated according to the International Conference on Harmonisation guidelines, showing accuracy, precision, selectivity, robustness, and linearity. Results: It was linear over the concentration range of 1.0-3.0 mg with correlation coefficients >0.9999 and LOD and LOQ of 0.12 and 0.36 mg, respectively. Conclusions: Now that this IR method has met performance qualifications, it can be adopted and applied for the analysis of enrofloxacin tablets for production process control. The validated method can also be utilized to quantify enrofloxacin in tablets and thus is an environmentally friendly alternative for the routine analysis of enrofloxacin in quality control. Highlights: A new green method for the quantitative analysis of enrofloxacin by Fourier-Transform Infrared spectroscopy was validated. It is a fast, clean and low-cost alternative for the evaluation of enrofloxacin tablets.

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

NASA Astrophysics Data System (ADS)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Accurate evaluation of sensitivity for calibration between a LiDAR and a panoramic camera used for remote sensing

NASA Astrophysics Data System (ADS)

García-Moreno, Angel-Iván; González-Barbosa, José-Joel; Ramírez-Pedraza, Alfonso; Hurtado-Ramos, Juan B.; Ornelas-Rodriguez, Francisco-Javier

2016-04-01

Computer-based reconstruction models can be used to approximate urban environments. These models are usually based on several mathematical approximations and the usage of different sensors, which implies dependency on many variables. The sensitivity analysis presented in this paper is used to weigh the relative importance of each uncertainty contributor into the calibration of a panoramic camera-LiDAR system. Both sensors are used for three-dimensional urban reconstruction. Simulated and experimental tests were conducted. For the simulated tests we analyze and compare the calibration parameters using the Monte Carlo and Latin hypercube sampling techniques. Sensitivity analysis for each variable involved into the calibration was computed by the Sobol method, which is based on the analysis of the variance breakdown, and the Fourier amplitude sensitivity test method, which is based on Fourier's analysis. Sensitivity analysis is an essential tool in simulation modeling and for performing error propagation assessments.

Quantitative comparison of tympanic membrane displacements using two optical methods to recover the optical phase

NASA Astrophysics Data System (ADS)

Santiago-Lona, Cynthia V.; Hernández-Montes, María del Socorro; Mendoza-Santoyo, Fernando; Esquivel-Tejeda, Jesús

2018-02-01

The study and quantification of the tympanic membrane (TM) displacements add important information to advance the knowledge about the hearing process. A comparative statistical analysis between two commonly used demodulation methods employed to recover the optical phase in digital holographic interferometry, namely the fast Fourier transform and phase-shifting interferometry, is presented as applied to study thin tissues such as the TM. The resulting experimental TM surface displacement data are used to contrast both methods through the analysis of variance and F tests. Data are gathered when the TMs are excited with continuous sound stimuli at levels 86, 89 and 93 dB SPL for the frequencies of 800, 1300 and 2500 Hz under the same experimental conditions. The statistical analysis shows repeatability in z-direction displacements with a standard deviation of 0.086, 0.098 and 0.080 μm using the Fourier method, and 0.080, 0.104 and 0.055 μm with the phase-shifting method at a 95% confidence level for all frequencies. The precision and accuracy are evaluated by means of the coefficient of variation; the results with the Fourier method are 0.06143, 0.06125, 0.06154 and 0.06154, 0.06118, 0.06111 with phase-shifting. The relative error between both methods is 7.143, 6.250 and 30.769%. On comparing the measured displacements, the results indicate that there is no statistically significant difference between both methods for frequencies at 800 and 1300 Hz; however, errors and other statistics increase at 2500 Hz.

Live face detection based on the analysis of Fourier spectra

NASA Astrophysics Data System (ADS)

Li, Jiangwei; Wang, Yunhong; Tan, Tieniu; Jain, Anil K.

2004-08-01

Biometrics is a rapidly developing technology that is to identify a person based on his or her physiological or behavioral characteristics. To ensure the correction of authentication, the biometric system must be able to detect and reject the use of a copy of a biometric instead of the live biometric. This function is usually termed "liveness detection". This paper describes a new method for live face detection. Using structure and movement information of live face, an effective live face detection algorithm is presented. Compared to existing approaches, which concentrate on the measurement of 3D depth information, this method is based on the analysis of Fourier spectra of a single face image or face image sequences. Experimental results show that the proposed method has an encouraging performance.

Time-frequency analysis of band-limited EEG with BMFLC and Kalman filter for BCI applications

PubMed Central

2013-01-01

Background Time-Frequency analysis of electroencephalogram (EEG) during different mental tasks received significant attention. As EEG is non-stationary, time-frequency analysis is essential to analyze brain states during different mental tasks. Further, the time-frequency information of EEG signal can be used as a feature for classification in brain-computer interface (BCI) applications. Methods To accurately model the EEG, band-limited multiple Fourier linear combiner (BMFLC), a linear combination of truncated multiple Fourier series models is employed. A state-space model for BMFLC in combination with Kalman filter/smoother is developed to obtain accurate adaptive estimation. By virtue of construction, BMFLC with Kalman filter/smoother provides accurate time-frequency decomposition of the bandlimited signal. Results The proposed method is computationally fast and is suitable for real-time BCI applications. To evaluate the proposed algorithm, a comparison with short-time Fourier transform (STFT) and continuous wavelet transform (CWT) for both synthesized and real EEG data is performed in this paper. The proposed method is applied to BCI Competition data IV for ERD detection in comparison with existing methods. Conclusions Results show that the proposed algorithm can provide optimal time-frequency resolution as compared to STFT and CWT. For ERD detection, BMFLC-KF outperforms STFT and BMFLC-KS in real-time applicability with low computational requirement. PMID:24274109

Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

PubMed

Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie

2015-10-20

In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.

Spectral analysis method and sample generation for real time visualization of speech

NASA Astrophysics Data System (ADS)

Hobohm, Klaus

A method for translating speech signals into optical models, characterized by high sound discrimination and learnability and designed to provide to deaf persons a feedback towards control of their way of speaking, is presented. Important properties of speech production and perception processes and organs involved in these mechanisms are recalled in order to define requirements for speech visualization. It is established that the spectral representation of time, frequency and amplitude resolution of hearing must be fair and continuous variations of acoustic parameters of speech signal must be depicted by a continuous variation of images. A color table was developed for dynamic illustration and sonograms were generated with five spectral analysis methods such as Fourier transformations and linear prediction coding. For evaluating sonogram quality, test persons had to recognize consonant/vocal/consonant words and an optimized analysis method was achieved with a fast Fourier transformation and a postprocessor. A hardware concept of a real time speech visualization system, based on multiprocessor technology in a personal computer, is presented.

Characterization of non-polar aromatic hydrocarbons in crude oil using atmospheric pressure laser ionization and Fourier transform ion cyclotron resonance mass spectrometry (APLI FT-ICR MS).

PubMed

Schrader, Wolfgang; Panda, Saroj K; Brockmann, Klaus J; Benter, Thorsten

2008-07-01

We report on the successful application of the recently introduced atmospheric pressure laser ionization (APLI) method as a novel tool for the analysis of crude oil and its components. Using Fourier transform ion cyclotron resonance mass spectrometry, unambiguous determination of key compounds in this complex matrix with unprecedented sensitivity is presented.

Pulse analysis of acoustic emission signals

NASA Technical Reports Server (NTRS)

Houghton, J. R.; Packman, P. F.

1977-01-01

A method for the signature analysis of pulses in the frequency domain and the time domain is presented. Fourier spectrum, Fourier transfer function, shock spectrum and shock spectrum ratio were examined in the frequency domain analysis and pulse shape deconvolution was developed for use in the time domain analysis. Comparisons of the relative performance of each analysis technique are made for the characterization of acoustic emission pulses recorded by a measuring system. To demonstrate the relative sensitivity of each of the methods to small changes in the pulse shape, signatures of computer modeled systems with analytical pulses are presented. Optimization techniques are developed and used to indicate the best design parameter values for deconvolution of the pulse shape. Several experiments are presented that test the pulse signature analysis methods on different acoustic emission sources. These include acoustic emission associated with (a) crack propagation, (b) ball dropping on a plate, (c) spark discharge, and (d) defective and good ball bearings. Deconvolution of the first few micro-seconds of the pulse train is shown to be the region in which the significant signatures of the acoustic emission event are to be found.

Pulse analysis of acoustic emission signals

NASA Technical Reports Server (NTRS)

Houghton, J. R.; Packman, P. F.

1977-01-01

A method for the signature analysis of pulses in the frequency domain and the time domain is presented. Fourier spectrum, Fourier transfer function, shock spectrum and shock spectrum ratio were examined in the frequency domain analysis, and pulse shape deconvolution was developed for use in the time domain analysis. Comparisons of the relative performance of each analysis technique are made for the characterization of acoustic emission pulses recorded by a measuring system. To demonstrate the relative sensitivity of each of the methods to small changes in the pulse shape, signatures of computer modeled systems with analytical pulses are presented. Optimization techniques are developed and used to indicate the best design parameters values for deconvolution of the pulse shape. Several experiments are presented that test the pulse signature analysis methods on different acoustic emission sources. These include acoustic emissions associated with: (1) crack propagation, (2) ball dropping on a plate, (3) spark discharge and (4) defective and good ball bearings. Deconvolution of the first few micro-seconds of the pulse train are shown to be the region in which the significant signatures of the acoustic emission event are to be found.

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.

PubMed

Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda

2017-09-13

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

Modelling fourier regression for time series data- a case study: modelling inflation in foods sector in Indonesia

NASA Astrophysics Data System (ADS)

Prahutama, Alan; Suparti; Wahyu Utami, Tiani

2018-03-01

Regression analysis is an analysis to model the relationship between response variables and predictor variables. The parametric approach to the regression model is very strict with the assumption, but nonparametric regression model isn’t need assumption of model. Time series data is the data of a variable that is observed based on a certain time, so if the time series data wanted to be modeled by regression, then we should determined the response and predictor variables first. Determination of the response variable in time series is variable in t-th (yt), while the predictor variable is a significant lag. In nonparametric regression modeling, one developing approach is to use the Fourier series approach. One of the advantages of nonparametric regression approach using Fourier series is able to overcome data having trigonometric distribution. In modeling using Fourier series needs parameter of K. To determine the number of K can be used Generalized Cross Validation method. In inflation modeling for the transportation sector, communication and financial services using Fourier series yields an optimal K of 120 parameters with R-square 99%. Whereas if it was modeled by multiple linear regression yield R-square 90%.

Quantization of an electromagnetic field in two-dimensional photonic structures based on the scattering matrix formalism ( S-quantization)

NASA Astrophysics Data System (ADS)

Ivanov, K. A.; Nikolaev, V. V.; Gubaydullin, A. R.; Kaliteevski, M. A.

2017-10-01

Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures ( S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate difficulties that arise in the analysis of the Purcell effect because of the divergence of the integral describing the effective volume of the mode in open systems.

Fault detection of gearbox using time-frequency method

NASA Astrophysics Data System (ADS)

Widodo, A.; Satrijo, Dj.; Prahasto, T.; Haryanto, I.

2017-04-01

This research deals with fault detection and diagnosis of gearbox by using vibration signature. In this work, fault detection and diagnosis are approached by employing time-frequency method, and then the results are compared with cepstrum analysis. Experimental work has been conducted for data acquisition of vibration signal thru self-designed gearbox test rig. This test-rig is able to demonstrate normal and faulty gearbox i.e., wears and tooth breakage. Three accelerometers were used for vibration signal acquisition from gearbox, and optical tachometer was used for shaft rotation speed measurement. The results show that frequency domain analysis using fast-fourier transform was less sensitive to wears and tooth breakage condition. However, the method of short-time fourier transform was able to monitor the faults in gearbox. Wavelet Transform (WT) method also showed good performance in gearbox fault detection using vibration signal after employing time synchronous averaging (TSA).

Analysis of Coherent Phonon Signals by Sparsity-promoting Dynamic Mode Decomposition

NASA Astrophysics Data System (ADS)

Murata, Shin; Aihara, Shingo; Tokuda, Satoru; Iwamitsu, Kazunori; Mizoguchi, Kohji; Akai, Ichiro; Okada, Masato

2018-05-01

We propose a method to decompose normal modes in a coherent phonon (CP) signal by sparsity-promoting dynamic mode decomposition. While the CP signals can be modeled as the sum of finite number of damped oscillators, the conventional method such as Fourier transform adopts continuous bases in a frequency domain. Thus, the uncertainty of frequency appears and it is difficult to estimate the initial phase. Moreover, measurement artifacts are imposed on the CP signal and deforms the Fourier spectrum. In contrast, the proposed method can separate the signal from the artifact precisely and can successfully estimate physical properties of the normal modes.

Runoff potentiality of a watershed through SCS and functional data analysis technique.

PubMed

Adham, M I; Shirazi, S M; Othman, F; Rahman, S; Yusop, Z; Ismail, Z

2014-01-01

Runoff potentiality of a watershed was assessed based on identifying curve number (CN), soil conservation service (SCS), and functional data analysis (FDA) techniques. Daily discrete rainfall data were collected from weather stations in the study area and analyzed through lowess method for smoothing curve. As runoff data represents a periodic pattern in each watershed, Fourier series was introduced to fit the smooth curve of eight watersheds. Seven terms of Fourier series were introduced for the watersheds 5 and 8, while 8 terms of Fourier series were used for the rest of the watersheds for the best fit of data. Bootstrapping smooth curve analysis reveals that watersheds 1, 2, 3, 6, 7, and 8 are with monthly mean runoffs of 29, 24, 22, 23, 26, and 27 mm, respectively, and these watersheds would likely contribute to surface runoff in the study area. The purpose of this study was to transform runoff data into a smooth curve for representing the surface runoff pattern and mean runoff of each watershed through statistical method. This study provides information of runoff potentiality of each watershed and also provides input data for hydrological modeling.

Runoff Potentiality of a Watershed through SCS and Functional Data Analysis Technique

PubMed Central

Adham, M. I.; Shirazi, S. M.; Othman, F.; Rahman, S.; Yusop, Z.; Ismail, Z.

2014-01-01

Runoff potentiality of a watershed was assessed based on identifying curve number (CN), soil conservation service (SCS), and functional data analysis (FDA) techniques. Daily discrete rainfall data were collected from weather stations in the study area and analyzed through lowess method for smoothing curve. As runoff data represents a periodic pattern in each watershed, Fourier series was introduced to fit the smooth curve of eight watersheds. Seven terms of Fourier series were introduced for the watersheds 5 and 8, while 8 terms of Fourier series were used for the rest of the watersheds for the best fit of data. Bootstrapping smooth curve analysis reveals that watersheds 1, 2, 3, 6, 7, and 8 are with monthly mean runoffs of 29, 24, 22, 23, 26, and 27 mm, respectively, and these watersheds would likely contribute to surface runoff in the study area. The purpose of this study was to transform runoff data into a smooth curve for representing the surface runoff pattern and mean runoff of each watershed through statistical method. This study provides information of runoff potentiality of each watershed and also provides input data for hydrological modeling. PMID:25152911

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR

PubMed Central

Mobli, Mehdi; Hoch, Jeffrey C.

2017-01-01

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR. PMID:25456315

Boosting Sensitivity in Liquid Chromatography–Fourier Transform Ion Cyclotron Resonance–Tandem Mass Spectrometry for Product Ion Analysis of Monoterpene Indole Alkaloids

PubMed Central

Nakabayashi, Ryo; Tsugawa, Hiroshi; Kitajima, Mariko; Takayama, Hiromitsu; Saito, Kazuki

2015-01-01

In metabolomics, the analysis of product ions in tandem mass spectrometry (MS/MS) is noteworthy to chemically assign structural information. However, the development of relevant analytical methods are less advanced. Here, we developed a method to boost sensitivity in liquid chromatography–Fourier transform ion cyclotron resonance–tandem mass spectrometry analysis (MS/MS boost analysis). To verify the MS/MS boost analysis, both quercetin and uniformly labeled 13C quercetin were analyzed, revealing that the origin of the product ions is not the instrument, but the analyzed compounds resulting in sensitive product ions. Next, we applied this method to the analysis of monoterpene indole alkaloids (MIAs). The comparative analyses of MIAs having indole basic skeleton (ajmalicine, catharanthine, hirsuteine, and hirsutine) and oxindole skeleton (formosanine, isoformosanine, pteropodine, isopteropodine, rhynchophylline, isorhynchophylline, and mitraphylline) identified 86 and 73 common monoisotopic ions, respectively. The comparative analyses of the three pairs of stereoisomers showed more than 170 common monoisotopic ions in each pair. This method was also applied to the targeted analysis of MIAs in Catharanthus roseus and Uncaria rhynchophylla to profile indole and oxindole compounds using the product ions. This analysis is suitable for chemically assigning features of the metabolite groups, which contributes to targeted metabolome analysis. PMID:26734034

Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.

PubMed

Caple, Jodi; Byrd, John; Stephan, Carl N

2017-11-01

The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.

A comb-sampling method for enhanced mass analysis in linear electrostatic ion traps.

PubMed

Greenwood, J B; Kelly, O; Calvert, C R; Duffy, M J; King, R B; Belshaw, L; Graham, L; Alexander, J D; Williams, I D; Bryan, W A; Turcu, I C E; Cacho, C M; Springate, E

2011-04-01

In this paper an algorithm for extracting spectral information from signals containing a series of narrow periodic impulses is presented. Such signals can typically be acquired by pickup detectors from the image-charge of ion bunches oscillating in a linear electrostatic ion trap, where frequency analysis provides a scheme for high-resolution mass spectrometry. To provide an improved technique for such frequency analysis, we introduce the CHIMERA algorithm (Comb-sampling for High-resolution IMpulse-train frequency ExtRAaction). This algorithm utilizes a comb function to generate frequency coefficients, rather than using sinusoids via a Fourier transform, since the comb provides a superior match to the data. This new technique is developed theoretically, applied to synthetic data, and then used to perform high resolution mass spectrometry on real data from an ion trap. If the ions are generated at a localized point in time and space, and the data is simultaneously acquired with multiple pickup rings, the method is shown to be a significant improvement on Fourier analysis. The mass spectra generated typically have an order of magnitude higher resolution compared with that obtained from fundamental Fourier frequencies, and are absent of large contributions from harmonic frequency components. © 2011 American Institute of Physics

An evaluation of random analysis methods for the determination of panel damping

NASA Technical Reports Server (NTRS)

Bhat, W. V.; Wilby, J. F.

1972-01-01

An analysis is made of steady-state and non-steady-state methods for the measurement of panel damping. Particular emphasis is placed on the use of random process techniques in conjunction with digital data reduction methods. The steady-state methods considered use the response power spectral density, response autocorrelation, excitation-response crosspower spectral density, or single-sided Fourier transform (SSFT) of the response autocorrelation function. Non-steady-state methods are associated mainly with the use of rapid frequency sweep excitation. Problems associated with the practical application of each method are evaluated with specific reference to the case of a panel exposed to a turbulent airflow, and two methods, the power spectral density and the single-sided Fourier transform methods, are selected as being the most suitable. These two methods are demonstrated experimentally, and it is shown that the power spectral density method is satisfactory under most conditions, provided that appropriate corrections are applied to account for filter bandwidth and background noise errors. Thus, the response power spectral density method is recommended for the measurement of the damping of panels exposed to a moving airflow.

A VLSI architecture for simplified arithmetic Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.

1992-01-01

The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.

Hilbert-Huang Transform: A Spectral Analysis Tool Applied to Sunspot Number and Total Solar Irradiance Variations, as well as Near-Surface Atmospheric Variables

NASA Astrophysics Data System (ADS)

Barnhart, B. L.; Eichinger, W. E.; Prueger, J. H.

2010-12-01

Hilbert-Huang transform (HHT) is a relatively new data analysis tool which is used to analyze nonstationary and nonlinear time series data. It consists of an algorithm, called empirical mode decomposition (EMD), which extracts the cyclic components embedded within time series data, as well as Hilbert spectral analysis (HSA) which displays the time and frequency dependent energy contributions from each component in the form of a spectrogram. The method can be considered a generalized form of Fourier analysis which can describe the intrinsic cycles of data with basis functions whose amplitudes and phases may vary with time. The HHT will be introduced and compared to current spectral analysis tools such as Fourier analysis, short-time Fourier analysis, wavelet analysis and Wigner-Ville distributions. A number of applications are also presented which demonstrate the strengths and limitations of the tool, including analyzing sunspot number variability and total solar irradiance proxies as well as global averaged temperature and carbon dioxide concentration. Also, near-surface atmospheric quantities such as temperature and wind velocity are analyzed to demonstrate the nonstationarity of the atmosphere.

Quantitative determination of dimethicone in commercial tablets and capsules by Fourier transform infrared spectroscopy and antifoaming activity test.

PubMed

Torrado, G; García-Arieta, A; de los Ríos, F; Menéndez, J C; Torrado, S

1999-03-01

Fourier transform infrared (FTIR) spectroscopy and antifoaming activity test have been employed for the quantitative analysis of dimethicone. Linearity, accuracy and precision are presented for both methods. These methods have been also used to compare different dimethicone-containing proprietary medicines. FTIR spectroscopy has shown to be adequate for quantitation of dimethicone in commercial tablets and capsules in order to comply with USP requirements. The antifoaming activity test is able to detect incompatibilities between dimethicone and other constituents. The presence of certain enzymes in some medicinal products increases the defoaming properties of these formulations.

A Method to Compute the Force Signature of a Body Impacting on a Linear Elastic Structure Using Fourier Analysis

DTIC Science & Technology

1982-09-17

FK * 1PK (2) The convolution of two transforms in time domain is the inverse transform of the product in frequency domain. Thus Rp(s) - Fgc() Ipg(*) (3...its inverse transform by: R,(r)- R,(a.)e’’ do. (5)2w In order to nuke use f a very accurate numerical method to ompute Fourier "ke and coil...taorm. When the inverse transform it tken by using Eq. (15), the cosine transform, because it converges faster than the sine transform refu-ft the

Quantification of fibre polymerization through Fourier space image analysis

PubMed Central

Nekouzadeh, Ali; Genin, Guy M.

2011-01-01

Quantification of changes in the total length of randomly oriented and possibly curved lines appearing in an image is a necessity in a wide variety of biological applications. Here, we present an automated approach based upon Fourier space analysis. Scaled, band-pass filtered power spectral densities of greyscale images are integrated to provide a quantitative measurement of the total length of lines of a particular range of thicknesses appearing in an image. A procedure is presented to correct for changes in image intensity. The method is most accurate for two-dimensional processes with fibres that do not occlude one another. PMID:24959096

[Application of Fourier transform infrared spectroscopy in identification of wine spoilage].

PubMed

Zhao, Xian-De; Dong, Da-Ming; Zheng, Wen-Gang; Jiao, Lei-Zi; Lang, Yun

2014-10-01

In the present work, fresh and spoiled wine samples from three wines produced by different companies were studied u- sing Fourier transform infrared (FTIR) spectroscopy. We analyzed the physicochemical property change in the process of spoil- age, and then, gave out the attribution of some main FTIR absorption peaks. A novel determination method was explored based on the comparisons of some absorbance ratios at different wavebands although the absorbance ratios in this method were relative. Through the compare of the wine spectra before and after spoiled, the authors found that they were informative at the bands of 3,020~2,790, 1,760~1,620 and 1,550~800 cm(-1). In order to find the relation between these informative spectral bands and the wine deterioration and achieve the discriminant analysis, chemometrics methods were introduced. Principal compounds analysis (PCA) and soft independent modeling of class analogy (SIMCA) were used for classifying different-quality wines. And partial least squares discriminant analysis (PLS-DA) was applied to identify spoiled wines and good wines. Results showed that FTIR technique combined with chemometrics methods could effectively distinguish spoiled wines from fresh samples. The effect of classification at the wave band of 1 550-800 cm(-1) was the best. The recognition rate of SIMCA and PLSDA were respectively 94% and 100%. This study demonstrates that Fourier transform infrared spectroscopy is an effective tool for monitoring red wine's spoilage and provides theoretical support for developing early-warning equipments.

The Fourier analysis of biological transients.

PubMed

Harris, C M

1998-08-31

With modern computing technology the digital implementation of the Fourier transform is widely available, mostly in the form of the fast Fourier transform (FFT). Although the FFT has become almost synonymous with the Fourier transform, it is a fast numerical technique for computing the discrete Fourier transform (DFT) of a finite sequence of sampled data. The DFT is not directly equivalent to the continuous Fourier transform of the underlying biological signal, which becomes important when analyzing biological transients. Although this distinction is well known by some, for many it leads to confusion in how to interpret the FFT of biological data, and in how to precondition data so as to yield a more accurate Fourier transform using the FFT. We review here the fundamentals of Fourier analysis with emphasis on the analysis of transient signals. As an example of a transient, we consider the human saccade to illustrate the pitfalls and advantages of various Fourier analyses.

Stokes polarimetry using analysis of the nonlinear voltage-retardance relationship for liquid-crystal variable retarders

DOE Office of Scientific and Technical Information (OSTI.GOV)

López-Téllez, J. M., E-mail: jmlopez@comunidad.unam.mx; Bruce, N. C.

2014-03-15

We present a method for using liquid-crystal variable retarders (LCVR’s) with continually varying voltage to measure the Stokes vector of a light beam. The LCVR's are usually employed with fixed retardance values due to the nonlinear voltage-retardance behavior that they show. The nonlinear voltage-retardance relationship is first measured and then a linear fit of the known retardance terms to the detected signal is performed. We use known waveplates (half-wave and quarter-wave) as devices to provide controlled polarization states to the Stokes polarimeter and we use the measured Stokes parameters as functions of the orientation of the axes of the waveplatesmore » as an indication of the quality of the polarimeter. Results are compared to a Fourier analysis method that does not take into account the nonlinear voltage-retardance relationship and also to a Fourier analysis method that uses experimental voltage values to give a linear retardance function with time. Also, we present results of simulations for comparison.« less

Segment density profiles of polyelectrolyte brushes determined by Fourier transform ellipsometry

NASA Astrophysics Data System (ADS)

Biesalski, Markus; Rühe, Jürgen; Johannsmann, Diethelm

1999-10-01

We describe a method for the explicit determination of the segment density profile φ(z) of surface-attached polymer brushes with multiple angle of incidence null-ellipsometry. Because the refractive index contrast between the brush layer and the solvent is weak, multiple reflections are of minor influence and the ellipsometric spectrum is closely related to the Fourier transform of the refractive index profile, thereby allowing for explicit inversion of the ellipsometric data. We chose surface-attached monolayers of polymethacrylic acid (PMAA), a weak polyelectrolyte, as a model system and determined the segment density profile of this system as a function of the pH value of the surrounding medium by the Fourier method. Complementary to the Fourier analysis, fits with error functions are given as well. The brushes were prepared on the bases of high refractive index prisms with the "grafting-from" technique. In water, the brushes swell by more than a factor of 30. The swelling increases with increasing pH because of a growing fraction of dissociated acidic groups leading to a larger electrostatic repulsion.

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levnajić, Zoran; Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, California 93106; Mezić, Igor

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone,more » and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.« less

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.

PubMed

Levnajić, Zoran; Mezić, Igor

2015-05-01

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.

A Comparison of Analytical and Data Preprocessing Methods for Spectral Fingerprinting

PubMed Central

LUTHRIA, DEVANAND L.; MUKHOPADHYAY, SUDARSAN; LIN, LONG-ZE; HARNLY, JAMES M.

2013-01-01

Spectral fingerprinting, as a method of discriminating between plant cultivars and growing treatments for a common set of broccoli samples, was compared for six analytical instruments. Spectra were acquired for finely powdered solid samples using Fourier transform infrared (FT-IR) and Fourier transform near-infrared (NIR) spectrometry. Spectra were also acquired for unfractionated aqueous methanol extracts of the powders using molecular absorption in the ultraviolet (UV) and visible (VIS) regions and mass spectrometry with negative (MS−) and positive (MS+) ionization. The spectra were analyzed using nested one-way analysis of variance (ANOVA) and principal component analysis (PCA) to statistically evaluate the quality of discrimination. All six methods showed statistically significant differences between the cultivars and treatments. The significance of the statistical tests was improved by the judicious selection of spectral regions (IR and NIR), masses (MS+ and MS−), and derivatives (IR, NIR, UV, and VIS). PMID:21352644

Face recognition system using multiple face model of hybrid Fourier feature under uncontrolled illumination variation.

PubMed

Hwang, Wonjun; Wang, Haitao; Kim, Hyunwoo; Kee, Seok-Cheol; Kim, Junmo

2011-04-01

The authors present a robust face recognition system for large-scale data sets taken under uncontrolled illumination variations. The proposed face recognition system consists of a novel illumination-insensitive preprocessing method, a hybrid Fourier-based facial feature extraction, and a score fusion scheme. First, in the preprocessing stage, a face image is transformed into an illumination-insensitive image, called an "integral normalized gradient image," by normalizing and integrating the smoothed gradients of a facial image. Then, for feature extraction of complementary classifiers, multiple face models based upon hybrid Fourier features are applied. The hybrid Fourier features are extracted from different Fourier domains in different frequency bandwidths, and then each feature is individually classified by linear discriminant analysis. In addition, multiple face models are generated by plural normalized face images that have different eye distances. Finally, to combine scores from multiple complementary classifiers, a log likelihood ratio-based score fusion scheme is applied. The proposed system using the face recognition grand challenge (FRGC) experimental protocols is evaluated; FRGC is a large available data set. Experimental results on the FRGC version 2.0 data sets have shown that the proposed method shows an average of 81.49% verification rate on 2-D face images under various environmental variations such as illumination changes, expression changes, and time elapses.

Functional feature embedded space mapping of fMRI data.

PubMed

Hu, Jin; Tian, Jie; Yang, Lei

2006-01-01

We have proposed a new method for fMRI data analysis which is called Functional Feature Embedded Space Mapping (FFESM). Our work mainly focuses on the experimental design with periodic stimuli which can be described by a number of Fourier coefficients in the frequency domain. A nonlinear dimension reduction technique Isomap is applied to the high dimensional features obtained from frequency domain of the fMRI data for the first time. Finally, the presence of activated time series is identified by the clustering method in which the information theoretic criterion of minimum description length (MDL) is used to estimate the number of clusters. The feasibility of our algorithm is demonstrated by real human experiments. Although we focus on analyzing periodic fMRI data, the approach can be extended to analyze non-periodic fMRI data (event-related fMRI) by replacing the Fourier analysis with a wavelet analysis.

Double Fourier analysis for Emotion Identification in Voiced Speech

NASA Astrophysics Data System (ADS)

Sierra-Sosa, D.; Bastidas, M.; Ortiz P., D.; Quintero, O. L.

2016-04-01

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented.

Accurate determination of the diffusion coefficient of proteins by Fourier analysis with whole column imaging detection.

PubMed

Zarabadi, Atefeh S; Pawliszyn, Janusz

2015-02-17

Analysis in the frequency domain is considered a powerful tool to elicit precise information from spectroscopic signals. In this study, the Fourier transformation technique is employed to determine the diffusion coefficient (D) of a number of proteins in the frequency domain. Analytical approaches are investigated for determination of D from both experimental and data treatment viewpoints. The diffusion process is modeled to calculate diffusion coefficients based on the Fourier transformation solution to Fick's law equation, and its results are compared to time domain results. The simulations characterize optimum spatial and temporal conditions and demonstrate the noise tolerance of the method. The proposed model is validated by its application for the electropherograms from the diffusion path of a set of proteins. Real-time dynamic scanning is conducted to monitor dispersion by employing whole column imaging detection technology in combination with capillary isoelectric focusing (CIEF) and the imaging plug flow (iPF) experiment. These experimental techniques provide different peak shapes, which are utilized to demonstrate the Fourier transformation ability in extracting diffusion coefficients out of irregular shape signals. Experimental results confirmed that the Fourier transformation procedure substantially enhanced the accuracy of the determined values compared to those obtained in the time domain.

Determination of layer ordering using sliding-window Fourier transform of x-ray reflectivity data

NASA Astrophysics Data System (ADS)

Smigiel, E.; Knoll, A.; Broll, N.; Cornet, A.

1998-01-01

X-ray reflectometry allows the determination of the thickness, density and roughness of thin layers on a substrate from several Angstroms to some hundred nanometres. The thickness is determined by simulation with trial-and-error methods after extracting initial values of the layer thicknesses from the result of a classical Fast Fourier Transform (FFT) of the reflectivity data. However, the order information of the layers is lost during classical FFT. The order of the layers has then to be known a priori. In this paper, it will be shown that the order of the layers can be obtained by a sliding-window Fourier transform, the so-called Gabor representation. This joint time-frequency analysis allows the direct determination of the order of the layers and, therefore, the use of a more appropriate starting model for refining simulations. A simulated and a measured example show the interest of this method.

Nucleic Acid analysis by fourier transform ion cyclotron resonance mass spectrometry at the beginning of the twenty-first century.

PubMed

Frahm, J L; Muddiman, D C

2005-01-01

Mass spectrometers measure an intrinsic property (i.e., mass) of a molecule, which makes it an ideal platform for nucleic acid analysis. Importantly, the unparalleled capabilities of Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry further extend its usefulness for nucleic acid analysis. The beginning of the twenty-first century has been marked with notable advances in the field of FT-ICR mass spectrometry analysis of nucleic acids. Some of these accomplishments include fundamental studies of nucleic acid properties, improvements in sample clean up and preparation, better methods to obtain higher mass measurement accuracy, analysis of noncovalent complexes, tandem mass spectrometry, and characterization of peptide nucleic acids. This diverse range of studies will be presented herein.

Automated Bayesian model development for frequency detection in biological time series.

PubMed

Granqvist, Emma; Oldroyd, Giles E D; Morris, Richard J

2011-06-24

A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure.

Automated Bayesian model development for frequency detection in biological time series

PubMed Central

2011-01-01

Background A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. Results In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Conclusions Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time series often deviate significantly from the requirements of optimality for Fourier transformation. In this paper we present an alternative approach based on Bayesian inference. We show the value of placing spectral analysis in the framework of Bayesian inference and demonstrate how model comparison can automate this procedure. PMID:21702910

An optical Fourier transform coprocessor with direct phase determination.

PubMed

Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D

2017-10-20

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

Non-invasive characterization of colorants by portable diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy and chemometrics

NASA Astrophysics Data System (ADS)

Manfredi, Marcello; Barberis, Elettra; Aceto, Maurizio; Marengo, Emilio

2017-06-01

During the last years the need for non-invasive and non-destructive analytical methods brought to the development and application of new instrumentation and analytical methods for the in-situ analysis of cultural heritage objects. In this work we present the application of a portable diffuse reflectance infrared Fourier transform (DRIFT) method for the non-invasive characterization of colorants prepared according to ancient recipes and using egg white and Gum Arabic as binders. Approximately 50 colorants were analyzed with the DRIFT spectroscopy: we were able to identify and discriminate the most used yellow (i.e. yellow ochres, Lead-tin Yellow, Orpiment, etc.), red (i.e. red ochres, Hematite) and blue (i.e. Lapis Lazuli, Azurite, indigo) colorants, creating a complete DRIFT spectral library. The Principal Component Analysis-Discriminant Analysis (PCA-DA) was then employed for the colorants classification according to the chemical/mineralogical composition. The DRIFT analysis was also performed on a gouache painting of the artist Sutherland; and the colorants used by the painter were identified directly in-situ and in a non-invasive manner.

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeong, Yongjin; Park, Jinsu; Lee, Hyun Chul

2015-12-01

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also notedmore » that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.« less

Holographic maps of quasiparticle interference

NASA Astrophysics Data System (ADS)

Dalla Torre, Emanuele G.; He, Yang; Demler, Eugene

2016-11-01

The analysis of Fourier-transformed scanning tunnelling microscopy images with subatomic resolution is a common tool for studying the properties of quasiparticle excitations in strongly correlated materials. Although Fourier amplitudes are generally complex valued, earlier analysis primarily focused on their absolute values. Their complex phases were often deemed random, and thus irrelevant, due to the unknown positions of the impurities in the sample. Here we show how to factor out these random phases by analysing overlaps between Fourier amplitudes that differ by reciprocal lattice vectors. The resulting holographic maps provide important and previously unknown information about the electronic structures. When applied to superconducting cuprates, our method solves a long-standing puzzle of the dichotomy between equivalent wavevectors. We show that d-wave Wannier functions of the conduction band provide a natural explanation for experimental results that were interpreted as evidence for competing unconventional charge modulations. Our work opens a new pathway to identify the nature of electronic states in scanning tunnelling microscopy.

Topics in Chemical Instrumentation.

ERIC Educational Resources Information Center

Settle, Frank A. Jr., Ed.

1989-01-01

Using Fourier transformation methods in nuclear resonance has made possible increased sensitivity in chemical analysis. This article describes data acquisition, data processing, and the frequency spectrum as they relate to this technique. (CW)

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR.

PubMed

Mobli, Mehdi; Hoch, Jeffrey C

2014-11-01

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR. Copyright © 2014 Elsevier B.V. All rights reserved.

Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2018-02-01

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4 π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 2^{30} {≈ } 10^9. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.

Application of otolith shape analysis for stock discrimination and species identification of five goby species (Perciformes: Gobiidae) in the northern Chinese coastal waters

NASA Astrophysics Data System (ADS)

Yu, Xin; Cao, Liang; Liu, Jinhu; Zhao, Bo; Shan, Xiujuan; Dou, Shuozeng

2014-09-01

We tested the use of otolith shape analysis to discriminate between species and stocks of five goby species ( Ctenotrypauchen chinensis, Odontamblyopus lacepedii, Amblychaeturichthys hexanema, Chaeturichthys stigmatias, and Acanthogobius hasta) found in northern Chinese coastal waters. The five species were well differentiated with high overall classification success using shape indices (83.7%), elliptic Fourier coefficients (98.6%), or the combination of both methods (94.9%). However, shape analysis alone was only moderately successful at discriminating among the four stocks (Liaodong Bay, LD; Bohai Bay, BH; Huanghe (Yellow) River estuary HRE, and Jiaozhou Bay, JZ stocks) of A. hasta (50%-54%) and C. stigmatias (65.7%-75.8%). For these two species, shape analysis was moderately successful at discriminating the HRE or JZ stocks from other stocks, but failed to effectively identify the LD and BH stocks. A large number of otoliths were misclassified between the HRE and JZ stocks, which are geographically well separated. The classification success for stock discrimination was higher using elliptic Fourier coefficients alone (70.2%) or in combination with shape indices (75.8%) than using only shape indices (65.7%) in C. stigmatias whereas there was little difference among the three methods for A. hasta. Our results supported the common belief that otolith shape analysis is generally more effective for interspecific identification than intraspecific discrimination. Moreover, compared with shape indices analysis, Fourier analysis improves classification success during inter- and intra-species discrimination by otolith shape analysis, although this did not necessarily always occur in all fish species.

Innovative design method of automobile profile based on Fourier descriptor

NASA Astrophysics Data System (ADS)

Gao, Shuyong; Fu, Chaoxing; Xia, Fan; Shen, Wei

2017-10-01

Aiming at the innovation of the contours of automobile side, this paper presents an innovative design method of vehicle side profile based on Fourier descriptor. The design flow of this design method is: pre-processing, coordinate extraction, standardization, discrete Fourier transform, simplified Fourier descriptor, exchange descriptor innovation, inverse Fourier transform to get the outline of innovative design. Innovative concepts of the innovative methods of gene exchange among species and the innovative methods of gene exchange among different species are presented, and the contours of the innovative design are obtained separately. A three-dimensional model of a car is obtained by referring to the profile curve which is obtained by exchanging xenogeneic genes. The feasibility of the method proposed in this paper is verified by various aspects.

An empirical evaluation of three vibrational spectroscopic methods for detection of aflatoxins in maize.

PubMed

Lee, Kyung-Min; Davis, Jessica; Herrman, Timothy J; Murray, Seth C; Deng, Youjun

2015-04-15

Three commercially available vibrational spectroscopic techniques, including Raman, Fourier transform near infrared reflectance (FT-NIR), and Fourier transform infrared (FTIR) were evaluated to help users determine the spectroscopic method best suitable for aflatoxin analysis in maize (Zea mays L.) grain based on their relative efficiency and predictive ability. Spectral differences of Raman and FTIR spectra were more marked and pronounced among aflatoxin contamination groups than those of FT-NIR spectra. From the observations and findings in our current and previous studies, Raman and FTIR spectroscopic methods are superior to FT-NIR method in terms of predictive power and model performance for aflatoxin analysis and they are equally effective and accurate in predicting aflatoxin concentration in maize. The present study is considered as the first attempt to assess how spectroscopic techniques with different physical processes can influence and improve accuracy and reliability for rapid screening of aflatoxin contaminated maize samples. Copyright © 2014 Elsevier Ltd. All rights reserved.

Multiresolution Analysis by Infinitely Differentiable Compactly Supported Functions

DTIC Science & Technology

1992-09-01

Math. Surveys 45:1 (1990), 87-120. [I] (;. Strang and G. Fix, A Fourier analysis of the finite element variational method. C.I.M.F. I 1 Ciclo 1971, in Constructi’c Aspects of Functional Analyszs ed. G. Geymonat 1973, 793-840. 10

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. G.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

PubMed

van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B

2015-12-01

Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.

Plane wave diffraction by a finite plate with impedance boundary conditions.

PubMed

Nawaz, Rab; Ayub, Muhammad; Javaid, Akmal

2014-01-01

In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier transform and the modified stationary phase method. Detailed graphical analysis was also made for various physical parameters we were interested in.

A New Method for Nonlinear and Nonstationary Time Series Analysis and Its Application to the Earthquake and Building Response Records

NASA Technical Reports Server (NTRS)

Huang, Norden E.

1999-01-01

A new method for analyzing nonlinear and nonstationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum, Example of application of this method to earthquake and building response will be given. The results indicate those low frequency components, totally missed by the Fourier analysis, are clearly identified by the new method. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.

Infrared Analysis Using Tissue Paper.

ERIC Educational Resources Information Center

Owen, Noel L.; Wood, Steven G.

1987-01-01

Described is a quick, easy, and cheap, but effective method of obtaining infrared spectra of solids and nonvolatile liquids by Fourier transform infrared spectroscopy. The technique uses tissue paper as a support matrix. (RH)

Fourier descriptor analysis and unification of voice range profile contours: method and applications.

PubMed

Pabon, Peter; Ternström, Sten; Lamarche, Anick

2011-06-01

To describe a method for unified description, statistical modeling, and comparison of voice range profile (VRP) contours, even from diverse sources. A morphologic modeling technique, which is based on Fourier descriptors (FDs), is applied to the VRP contour. The technique, which essentially involves resampling of the curve of the contour, is assessed and also is compared to density-based VRP averaging methods that use the overlap count. VRP contours can be usefully described and compared using FDs. The method also permits the visualization of the local covariation along the contour average. For example, the FD-based analysis shows that the population variance for ensembles of VRP contours is usually smallest at the upper left part of the VRP. To illustrate the method's advantages and possible further application, graphs are given that compare the averaged contours from different authors and recording devices--for normal, trained, and untrained male and female voices as well as for child voices. The proposed technique allows any VRP shape to be brought to the same uniform base. On this uniform base, VRP contours or contour elements coming from a variety of sources may be placed within the same graph for comparison and for statistical analysis.

Criteria for confirming sequence periodicity identified by Fourier transform analysis: application to GCR2, a candidate plant GPCR?

PubMed

Illingworth, Christopher J R; Parkes, Kevin E; Snell, Christopher R; Mullineaux, Philip M; Reynolds, Christopher A

2008-03-01

Methods to determine periodicity in protein sequences are useful for inferring function. Fourier transformation is one approach but care is required to ensure the periodicity is genuine. Here we have shown that empirically-derived statistical tables can be used as a measure of significance. Genuine protein sequences data rather than randomly generated sequences were used as the statistical backdrop. The method has been applied to G-protein coupled receptor (GPCR) sequences, by Fourier transformation of hydrophobicity values, codon frequencies and the extent of over-representation of codon pairs; the latter being related to translational step times. Genuine periodicity was observed in the hydrophobicity whereas the apparent periodicity (as inferred from previously reported measures) in the translation step times was not validated statistically. GCR2 has recently been proposed as the plant GPCR receptor for the hormone abscisic acid. It has homology to the Lanthionine synthetase C-like family of proteins, an observation confirmed by fold recognition. Application of the Fourier transform algorithm to the GCR2 family revealed strongly predicted seven fold periodicity in hydrophobicity, suggesting why GCR2 has been reported to be a GPCR, despite negative indications in most transmembrane prediction algorithms. The underlying multiple sequence alignment, also required for the Fourier transform analysis of periodicity, indicated that the hydrophobic regions around the 7 GXXG motifs commence near the C-terminal end of each of the 7 inner helices of the alpha-toroid and continue to the N-terminal region of the helix. The results clearly explain why GCR2 has been understandably but erroneously predicted to be a GPCR.

Edge-augmented Fourier partial sums with applications to Magnetic Resonance Imaging (MRI)

NASA Astrophysics Data System (ADS)

Larriva-Latt, Jade; Morrison, Angela; Radgowski, Alison; Tobin, Joseph; Iwen, Mark; Viswanathan, Aditya

2017-08-01

Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the Gibbs phenomenon - with associated oscillatory artifacts in the vicinity of edges and an overall reduced order of convergence in the approximation. This paper proposes an edge-augmented Fourier reconstruction procedure which uses only the first few Fourier coefficients of an underlying piecewise-smooth function to accurately estimate jump information and then incorporate it into a Fourier partial sum approximation. We provide both theoretical and empirical results showing the improved accuracy of the proposed method, as well as comparisons demonstrating superior performance over existing state-of-the-art sparse optimization-based methods.

Extracting Micro-Doppler Radar Signatures from Rotating Targets Using Fourier-Bessel Transform and Time-Frequency Analysis

DTIC Science & Technology

2014-10-16

Time-Frequency analysis, Short-Time Fourier Transform, Wigner Ville Distribution, Fourier Bessel Transform, Fractional Fourier Transform. I...INTRODUCTION Most widely used time-frequency transforms are short-time Fourier Transform (STFT) and Wigner Ville distribution (WVD). In STFT, time and...frequency resolutions are limited by the size of window function used in calculating STFT. For mono-component signals, WVD gives the best time and frequency

Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Liao, Feng; Zhang, Luming; Wang, Shanshan

2018-02-01

In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

NASA Technical Reports Server (NTRS)

Gatewood, B. E.

1971-01-01

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

Occupant Motion Sensors

DOT National Transportation Integrated Search

1971-03-01

An analysis was made of methods for measuring vehicle occupant motion during crash or impact conditions. The purpose of the measurements is to evaluate restraint performance using human, anthropometric dummy, or animal occupants. A detailed Fourier f...

SPHARA--a generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: application to EEG.

PubMed

Graichen, Uwe; Eichardt, Roland; Fiedler, Patrique; Strohmeier, Daniel; Zanow, Frank; Haueisen, Jens

2015-01-01

Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.

Propagation characteristics of optical fiber structures with arbitrary shape and index variation

NASA Technical Reports Server (NTRS)

Manshadi, F.

1990-01-01

The application of the scalar wave-fast Fourier transform (SW-FFT) technique to the computation of the propagation characteristics of some complex optical fiber structures is presented. The SW-FFT technique is based on the numerical solution of the scalar wave equation by a forward-marching fast Fourier transform method. This solution yields the spatial configuration of the fields as well as its modal characteristics in and around the guiding structure. The following are treated by the SW-FFT method: analysis of coupled optical fibers and computation of their odd and even modes and coupling length; the solution of tapered optical waveguides (transitions) and the study of the effect of the slope of the taper on mode conversion; and the analysis of branching optical fibers and demonstration of their mode-filtering and/or power-dividing properties.

Research on FBG-based longitudinal-acousto-optic modulator with Fourier mode coupling method.

PubMed

Li, Zhuoxuan; Pei, Li; Liu, Chao; Ning, Tigang; Yu, Shaowei

2012-10-20

Fourier mode coupling model was first applied to achieve the spectra property of a fiber Bragg grating (FBG)-based longitudinal-acousto-optic modulator. Compared with traditional analysis algorithms, such as the transfer matrix method, the Fourier mode coupling model could improve the computing efficiency up to 100 times with a guarantee of accuracy. In this paper, based on the theoretical analysis of this model, the spectra characteristics of the modulator in different frequencies and acoustically induced strains were numerically simulated. In the experiment, a uniform FBG was modulated by acoustic wave (AW) at 12 different frequencies. In particular, the modulator responses at 563 and 885.5 KHz with three different lead zirconate titanate (PZT) loads applied were plotted for illustration, and the linear fitting of experimental data demonstrated a good match with the simulation result. The acoustic excitation of the longitudinal wave is obtained using a conic silica horn attached to the surface of a shear-mode PZT plate paralleled to the fiber axis. This way of generating longitudinal AW with a transversal PZT may shed light on the optimal structural design for the FBG-based longitudinal-acousto-optic modulator.

Digital double random amplitude image encryption method based on the symmetry property of the parametric discrete Fourier transform

NASA Astrophysics Data System (ADS)

Bekkouche, Toufik; Bouguezel, Saad

2018-03-01

We propose a real-to-real image encryption method. It is a double random amplitude encryption method based on the parametric discrete Fourier transform coupled with chaotic maps to perform the scrambling. The main idea behind this method is the introduction of a complex-to-real conversion by exploiting the inherent symmetry property of the transform in the case of real-valued sequences. This conversion allows the encrypted image to be real-valued instead of being a complex-valued image as in all existing double random phase encryption methods. The advantage is to store or transmit only one image instead of two images (real and imaginary parts). Computer simulation results and comparisons with the existing double random amplitude encryption methods are provided for peak signal-to-noise ratio, correlation coefficient, histogram analysis, and key sensitivity.

Improved full analytical polygon-based method using Fourier analysis of the three-dimensional affine transformation.

PubMed

Pan, Yijie; Wang, Yongtian; Liu, Juan; Li, Xin; Jia, Jia

2014-03-01

Previous research [Appl. Opt.52, A290 (2013)] has revealed that Fourier analysis of three-dimensional affine transformation theory can be used to improve the computation speed of the traditional polygon-based method. In this paper, we continue our research and propose an improved full analytical polygon-based method developed upon this theory. Vertex vectors of primitive and arbitrary triangles and the pseudo-inverse matrix were used to obtain an affine transformation matrix representing the spatial relationship between the two triangles. With this relationship and the primitive spectrum, we analytically obtained the spectrum of the arbitrary triangle. This algorithm discards low-level angular dependent computations. In order to add diffusive reflection to each arbitrary surface, we also propose a whole matrix computation approach that takes advantage of the affine transformation matrix and uses matrix multiplication to calculate shifting parameters of similar sub-polygons. The proposed method improves hologram computation speed for the conventional full analytical approach. Optical experimental results are demonstrated which prove that the proposed method can effectively reconstruct three-dimensional scenes.

Acoustic Analysis of Chinese Fricatives and Affricates.

ERIC Educational Resources Information Center

Svantesson, Jan-Olof

1986-01-01

Develops a method of analyzing and describing the acoustic properties of fricatives, which consists of making frequency spectra using the Fast Fourier Transform and then analyzing the spectra in terms of critical bands. The six fricatives of Chinese are analyzed by this method, and comparison with other languages is made. (SED)

Fourier transform methods in local gravity modeling

NASA Technical Reports Server (NTRS)

Harrison, J. C.; Dickinson, M.

1989-01-01

New algorithms were derived for computing terrain corrections, all components of the attraction of the topography at the topographic surface and the gradients of these attractions. These algoriithms utilize fast Fourier transforms, but, in contrast to methods currently in use, all divergences of the integrals are removed during the analysis. Sequential methods employing a smooth intermediate reference surface were developed to avoid the very large transforms necessary when making computations at high resolution over a wide area. A new method for the numerical solution of Molodensky's problem was developed to mitigate the convergence difficulties that occur at short wavelengths with methods based on a Taylor series expansion. A trial field on a level surface is continued analytically to the topographic surface, and compared with that predicted from gravity observations. The difference is used to compute a correction to the trial field and the process iterated. Special techniques are employed to speed convergence and prevent oscillations. Three different spectral methods for fitting a point-mass set to a gravity field given on a regular grid at constant elevation are described. Two of the methods differ in the way that the spectrum of the point-mass set, which extends to infinite wave number, is matched to that of the gravity field which is band-limited. The third method is essentially a space-domain technique in which Fourier methods are used to solve a set of simultaneous equations.

[Identification of different Citrus sinensis (L.) Osbeck trees varieties using Fourier transform infrared spectroscopy and hierarchical cluster analysis].

PubMed

Yi, Shi-Lai; Deng, Lie; He, Shao-Lan; Shi, You-Ming; Zheng, Yong-Qiang; Lu, Qiang; Xie, Rang-Jin; Wei, Xian-Guoi; Li, Song-Wei; Jian, Shui-Xian

2012-11-01

Researched on diversity of the spring leaf samples of seven different Citrus sinensis (L.) Osbeck varieties by Fourier transform infrared (FTIR) spectroscopy technology, the results showed that the Fourier transform infrared spectra of seven varieties leaves was composited by the absorption band of cellulose and polysaccharide mainly, the wave number of characteristics absorption peaks were similar at their FTIR spectra. However, there were some differences in shape of peaks and relatively absorption intensity. The conspicuous difference was presented at the region between 1 500 and 700 cm(-1) by second derivative spectra. Through the hierarchical cluster analysis (HCA) of second derivative spectra between 1 500 and 700 cm(-1), the results showed that the clustering of the different varieties of Citrus sinensis (L.) Osbeck varieties was classification according to genetic relationship. The results showed that FTIR spectroscopy combined with hierarchical cluster analysis could be used to identify and classify of citrus varieties rapidly, it was an extension method to study on early leaves of varieties orange seedlings.

Analysis of the Long Period Terms of Local and Global Data of UT1-AT

NASA Astrophysics Data System (ADS)

Stavinschi, Magdalena; Souchay, Jean; Donea, Alina-Catalina

In our analysis of UTO and UTI, the long period terms 18.6y, 13.9y, 12.5y, 11.1y, 9.2y have been emphasized. To be sure that the results are trustworthy, different methods (Scargle for data unevenly distributed,the classical least square method and Fourier analysis) have been used for the data recorded as well at the Bucharest Observatory and the data of IERS.

A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levenhagen, R. S., E-mail: ronaldo.levenhagen@gmail.com

Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In thismore » work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).« less

A novel method for automated grid generation of ice shapes for local-flow analysis

NASA Astrophysics Data System (ADS)

Ogretim, Egemen; Huebsch, Wade W.

2004-02-01

Modelling a complex geometry, such as ice roughness, plays a key role for the computational flow analysis over rough surfaces. This paper presents two enhancement ideas in modelling roughness geometry for local flow analysis over an aerodynamic surface. The first enhancement is use of the leading-edge region of an airfoil as a perturbation to the parabola surface. The reasons for using a parabola as the base geometry are: it resembles the airfoil leading edge in the vicinity of its apex and it allows the use of a lower apparent Reynolds number. The second enhancement makes use of the Fourier analysis for modelling complex ice roughness on the leading edge of airfoils. This method of modelling provides an analytical expression, which describes the roughness geometry and the corresponding derivatives. The factors affecting the performance of the Fourier analysis were also investigated. It was shown that the number of sine-cosine terms and the number of control points are of importance. Finally, these enhancements are incorporated into an automated grid generation method over the airfoil ice accretion surface. The validations for both enhancements demonstrate that they can improve the current capability of grid generation and computational flow field analysis around airfoils with ice roughness.

Online frequency estimation with applications to engine and generator sets

NASA Astrophysics Data System (ADS)

Manngård, Mikael; Böling, Jari M.

2017-07-01

Frequency and spectral analysis based on the discrete Fourier transform is a fundamental task in signal processing and machine diagnostics. This paper aims at presenting computationally efficient methods for real-time estimation of stationary and time-varying frequency components in signals. A brief survey of the sliding time window discrete Fourier transform and Goertzel filter is presented, and two filter banks consisting of: (i) sliding time window Goertzel filters (ii) infinite impulse response narrow bandpass filters are proposed for estimating instantaneous frequencies. The proposed methods show excellent results on both simulation studies and on a case study using angular speed data measurements of the crankshaft of a marine diesel engine-generator set.

Discrete Fourier transforms of nonuniformly spaced data

NASA Technical Reports Server (NTRS)

Swan, P. R.

1982-01-01

Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.

Antenna pattern correction for the Nimbus-7 SMMR

NASA Technical Reports Server (NTRS)

Milman, A. S.

1986-01-01

This paper describes the philosophy and method used to develop the antenna pattern correction (APC) algorithm that was used on the data from the Scanning Multichannel Microwave Radiometer (SMMR) on Nimbus-7. There are limitations on what can be accomplished with such a procedure; these limitations are explored with the aid of Fourier analysis, even though the algorithm used on the SMMR data does not perform any Fourier transforms. The resulting analysis showed that, for the SMMR instrument, no useful improvement could be made in the data in terms of reduction of side lobes, but the quality of the sea surface temperature retrievals could be improved considerably by matching the antenna beamwidths at the different frequencies.

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

PubMed

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp.

PubMed

Barlow, Euan; Mulholland, Anthony J

2011-11-01

The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios.

Molecular structure, vibrational spectral assignments (FT-IR and FT-RAMAN), NMR, NBO, HOMO-LUMO and NLO properties of O-methoxybenzaldehyde based on DFT calculations

NASA Astrophysics Data System (ADS)

Vennila, P.; Govindaraju, M.; Venkatesh, G.; Kamal, C.

2016-05-01

Fourier transform - Infra red (FT-IR) and Fourier transform - Raman (FT-Raman) spectroscopic techniques have been carried out to analyze O-methoxy benzaldehyde (OMB) molecule. The fundamental vibrational frequencies and intensity of vibrational bands were evaluated using density functional theory (DFT). The vibrational analysis of stable isomer of OMB has been carried out by FT-IR and FT-Raman in combination with theoretical method simultaneously. The first-order hyperpolarizability and the anisotropy polarizability invariant were computed by DFT method. The atomic charges, hardness, softness, ionization potential, electronegativity, HOMO-LUMO energies, and electrophilicity index have been calculated. The 13C and 1H Nuclear magnetic resonance (NMR) have also been obtained by GIAO method. Molecular electronic potential (MEP) has been calculated by the DFT calculation method. Electronic excitation energies, oscillator strength and excited states characteristics were computed by the closed-shell singlet calculation method.

Diffuse Reflectance Infrared Fourier Transform Spectroscopy for the Determination of Asbestos Species in Bulk Building Materials

PubMed Central

Accardo, Grazia; Cioffi, Raffaeke; Colangelo, Francesco; d’Angelo, Raffaele; De Stefano, Luca; Paglietti, Fderica

2014-01-01

Diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy is a well-known technique for thin film characterization. Since all asbestos species exhibit intense adsorptions peaks in the 4000–400 cm−1 region of the infrared spectrum, a quantitative analysis of asbestos in bulk samples by DRIFT is possible. In this work, different quantitative analytical procedures have been used to quantify chrysotile content in bulk materials produced by building requalification: partial least squares (PLS) chemometrics, the Linear Calibration Curve Method (LCM) and the Method of Additions (MoA). Each method has its own pros and cons, but all give affordable results for material characterization: the amount of asbestos (around 10%, weight by weight) can be determined with precision and accuracy (errors less than 0.1). PMID:28788467

Quantitative multi-color FRET measurements by Fourier lifetime excitation-emission matrix spectroscopy.

PubMed

Zhao, Ming; Huang, Run; Peng, Leilei

2012-11-19

Förster resonant energy transfer (FRET) is extensively used to probe macromolecular interactions and conformation changes. The established FRET lifetime analysis method measures the FRET process through its effect on the donor lifetime. In this paper we present a method that directly probes the time-resolved FRET signal with frequency domain Fourier lifetime excitation-emission matrix (FLEEM) measurements. FLEEM separates fluorescent signals by their different phonon energy pathways from excitation to emission. The FRET process generates a unique signal channel that is initiated by donor excitation but ends with acceptor emission. Time-resolved analysis of the FRET EEM channel allows direct measurements on the FRET process, unaffected by free fluorophores that might be present in the sample. Together with time-resolved analysis on non-FRET channels, i.e. donor and acceptor EEM channels, time resolved EEM analysis allows precise quantification of FRET in the presence of free fluorophores. The method is extended to three-color FRET processes, where quantification with traditional methods remains challenging because of the significantly increased complexity in the three-way FRET interactions. We demonstrate the time-resolved EEM analysis method with quantification of three-color FRET in incompletely hybridized triple-labeled DNA oligonucleotides. Quantitative measurements of the three-color FRET process in triple-labeled dsDNA are obtained in the presence of free single-labeled ssDNA and double-labeled dsDNA. The results establish a quantification method for studying multi-color FRET between multiple macromolecules in biochemical equilibrium.

Quantitative multi-color FRET measurements by Fourier lifetime excitation-emission matrix spectroscopy

PubMed Central

Zhao, Ming; Huang, Run; Peng, Leilei

2012-01-01

Förster resonant energy transfer (FRET) is extensively used to probe macromolecular interactions and conformation changes. The established FRET lifetime analysis method measures the FRET process through its effect on the donor lifetime. In this paper we present a method that directly probes the time-resolved FRET signal with frequency domain Fourier lifetime excitation-emission matrix (FLEEM) measurements. FLEEM separates fluorescent signals by their different phonon energy pathways from excitation to emission. The FRET process generates a unique signal channel that is initiated by donor excitation but ends with acceptor emission. Time-resolved analysis of the FRET EEM channel allows direct measurements on the FRET process, unaffected by free fluorophores that might be present in the sample. Together with time-resolved analysis on non-FRET channels, i.e. donor and acceptor EEM channels, time resolved EEM analysis allows precise quantification of FRET in the presence of free fluorophores. The method is extended to three-color FRET processes, where quantification with traditional methods remains challenging because of the significantly increased complexity in the three-way FRET interactions. We demonstrate the time-resolved EEM analysis method with quantification of three-color FRET in incompletely hybridized triple-labeled DNA oligonucleotides. Quantitative measurements of the three-color FRET process in triple-labeled dsDNA are obtained in the presence of free single-labeled ssDNA and double-labeled dsDNA. The results establish a quantification method for studying multi-color FRET between multiple macromolecules in biochemical equilibrium. PMID:23187535

On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1980-01-01

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

Differentiation of live and dead salmonella cells using fourier transform infrared (FTIR) spectroscopy and principle component analysis (PCA) technique

USDA-ARS?s Scientific Manuscript database

Various technologies have been developed for pathogen detection using optical, electrochemical, biochemical and physical properties. Conventional microbiological methods need time from days to week to get the result. Though this method is very sensitive and accurate, a rapid detection of pathogens i...

Quantitative analysis of red wine tannins using Fourier-transform mid-infrared spectrometry.

PubMed

Fernandez, Katherina; Agosin, Eduardo

2007-09-05

Tannin content and composition are critical quality components of red wines. No spectroscopic method assessing these phenols in wine has been described so far. We report here a new method using Fourier transform mid-infrared (FT-MIR) spectroscopy and chemometric techniques for the quantitative analysis of red wine tannins. Calibration models were developed using protein precipitation and phloroglucinolysis as analytical reference methods. After spectra preprocessing, six different predictive partial least-squares (PLS) models were evaluated, including the use of interval selection procedures such as iPLS and CSMWPLS. PLS regression with full-range (650-4000 cm(-1)), second derivative of the spectra and phloroglucinolysis as the reference method gave the most accurate determination for tannin concentration (RMSEC = 2.6%, RMSEP = 9.4%, r = 0.995). The prediction of the mean degree of polymerization (mDP) of the tannins also gave a reasonable prediction (RMSEC = 6.7%, RMSEP = 10.3%, r = 0.958). These results represent the first step in the development of a spectroscopic methodology for the quantification of several phenolic compounds that are critical for wine quality.

[Application of Fourier transform profilometry in 3D-surface reconstruction].

PubMed

Shi, Bi'er; Lu, Kuan; Wang, Yingting; Li, Zhen'an; Bai, Jing

2011-08-01

With the improvement of system frame and reconstruction methods in fluorescent molecules tomography (FMT), the FMT technology has been widely used as an important experimental tool in biomedical research. It is necessary to get the 3D-surface profile of the experimental object as the boundary constraints of FMT reconstruction algorithms. We proposed a new 3D-surface reconstruction method based on Fourier transform profilometry (FTP) method under the blue-purple light condition. The slice images were reconstructed using proper image processing methods, frequency spectrum analysis and filtering. The results of experiment showed that the method properly reconstructed the 3D-surface of objects and has the mm-level accuracy. Compared to other methods, this one is simple and fast. Besides its well-reconstructed, the proposed method could help monitor the behavior of the object during the experiment to ensure the correspondence of the imaging process. Furthermore, the method chooses blue-purple light section as its light source to avoid the interference towards fluorescence imaging.

2D signature for detection and identification of drugs

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Varentsova, Svetlana A.; Shen, Jingling; Zhang, Cunlin; Zhou, Qingli; Shi, Yulei

2011-06-01

The method of spectral dynamics analysis (SDA-method) is used for obtaining the2D THz signature of drugs. This signature is used for the detection and identification of drugs with similar Fourier spectra by transmitted THz signal. We discuss the efficiency of SDA method for the identification problem of pure methamphetamine (MA), methylenedioxyamphetamine (MDA), 3, 4-methylenedioxymethamphetamine (MDMA) and Ketamine.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA.

PubMed

Scargle, Jeffrey D; Way, M J; Gazis, P R

2017-04-10

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA

PubMed Central

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys. PMID:29628519

Structure in the 3D Galaxy Distribution: III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

NASA Astrophysics Data System (ADS)

Liu, X.; Banerjee, J. R.

2017-03-01

A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

Using Musical Intervals to Demonstrate Superposition of Waves and Fourier Analysis

ERIC Educational Resources Information Center

LoPresto, Michael C.

2013-01-01

What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.

The Use of ATR-FTIR in Conjunction with Thermal Analysis Methods for Efficient Identification of Polymer Samples: A Qualitative Multiinstrument Instrumental Analysis Laboratory Experiment

ERIC Educational Resources Information Center

Dickson-Karn, Nicole M.

2017-01-01

A multi-instrument approach has been applied to the efficient identification of polymers in an upper-division undergraduate instrumental analysis laboratory course. Attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) is used in conjunction with differential scanning calorimetry (DSC) to identify 18 polymer samples and…

The application of an optical Fourier spectrum analyzer on detecting defects in mass-produced satellite photographs

NASA Technical Reports Server (NTRS)

Athale, R.; Lee, S. H.

1976-01-01

Various defects in mass-produced pictures transmitted to earth from a satellite are investigated. It is found that the following defects are readily detectable via Fourier spectrum analysis: (1) bit slip, (2) breakup causing loss of image, and (3) disabled track at the top of the imagery. The scratches made on the film during mass production, which are difficult to detect by visual observation, also show themselves readily in Fourier spectrum analysis. A relation is established between the number of scratches, their width and depth and the intensity of their Fourier spectra. Other defects that are found to be equally suitable for Fourier spectrum analysis or visual (image analysis) detection are synchronous loss without blurring of image, and density variation in gray scale. However, the Fourier spectrum analysis is found to be unsuitable for detection of such defects as pin holes, annotation error, synchronous loss with blurring of images, and missing image in the beginning of the work order. The design of an automated, real time system, which will reject defective films, is treated.

Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for wave propagation

NASA Astrophysics Data System (ADS)

Pagán Muñoz, Raúl; Hornikx, Maarten

2017-11-01

The Fourier Pseudospectral time-domain (Fourier PSTD) method was shown to be an efficient way of modelling acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly staircase-like boundary shapes. This paper presents a hybrid approach to solve the LEE, coupling Fourier PSTD with a nodal Discontinuous Galerkin (DG) method. DG exhibits almost no restrictions with respect to geometrical complexity or boundary conditions. The aim of this novel method is to allow the computation of complex geometries and to be a step towards the implementation of frequency dependent boundary conditions by using the benefits of DG at the boundaries, while keeping the efficient Fourier PSTD in the bulk of the domain. The hybridization approach is based on conformal meshes to avoid spatial interpolation of the DG solutions when transferring values from DG to Fourier PSTD, while the data transfer from Fourier PSTD to DG is done utilizing spectral interpolation of the Fourier PSTD solutions. The accuracy of the hybrid approach is presented for one- and two-dimensional acoustic problems and the main sources of error are investigated. It is concluded that the hybrid methodology does not introduce significant errors compared to the Fourier PSTD stand-alone solver. An example of a cylinder scattering problem is presented and accurate results have been obtained when using the proposed approach. Finally, no instabilities were found during long-time calculation using the current hybrid methodology on a two-dimensional domain.

SPHARA - A Generalized Spatial Fourier Analysis for Multi-Sensor Systems with Non-Uniformly Arranged Sensors: Application to EEG

PubMed Central

Graichen, Uwe; Eichardt, Roland; Fiedler, Patrique; Strohmeier, Daniel; Zanow, Frank; Haueisen, Jens

2015-01-01

Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications. PMID:25885290

ESTER HYDROLYSIS RATE CONSTANT PREDICTION FROM INFRARED INTERFEROGRAMS

EPA Science Inventory

A method for predicting reactivity parameters of organic chemicals from spectroscopic data is being developed to assist in assessing the environmental fate of pollutants. he prototype system, which employs multiple linear regression analysis using selected points from the Fourier...

An improved model for whole genome phylogenetic analysis by Fourier transform.

PubMed

Yin, Changchuan; Yau, Stephen S-T

2015-10-07

DNA sequence similarity comparison is one of the major steps in computational phylogenetic studies. The sequence comparison of closely related DNA sequences and genomes is usually performed by multiple sequence alignments (MSA). While the MSA method is accurate for some types of sequences, it may produce incorrect results when DNA sequences undergone rearrangements as in many bacterial and viral genomes. It is also limited by its computational complexity for comparing large volumes of data. Previously, we proposed an alignment-free method that exploits the full information contents of DNA sequences by Discrete Fourier Transform (DFT), but still with some limitations. Here, we present a significantly improved method for the similarity comparison of DNA sequences by DFT. In this method, we map DNA sequences into 2-dimensional (2D) numerical sequences and then apply DFT to transform the 2D numerical sequences into frequency domain. In the 2D mapping, the nucleotide composition of a DNA sequence is a determinant factor and the 2D mapping reduces the nucleotide composition bias in distance measure, and thus improving the similarity measure of DNA sequences. To compare the DFT power spectra of DNA sequences with different lengths, we propose an improved even scaling algorithm to extend shorter DFT power spectra to the longest length of the underlying sequences. After the DFT power spectra are evenly scaled, the spectra are in the same dimensionality of the Fourier frequency space, then the Euclidean distances of full Fourier power spectra of the DNA sequences are used as the dissimilarity metrics. The improved DFT method, with increased computational performance by 2D numerical representation, can be applicable to any DNA sequences of different length ranges. We assess the accuracy of the improved DFT similarity measure in hierarchical clustering of different DNA sequences including simulated and real datasets. The method yields accurate and reliable phylogenetic trees and demonstrates that the improved DFT dissimilarity measure is an efficient and effective similarity measure of DNA sequences. Due to its high efficiency and accuracy, the proposed DFT similarity measure is successfully applied on phylogenetic analysis for individual genes and large whole bacterial genomes. Copyright © 2015 Elsevier Ltd. All rights reserved.

Evaluation of removal of the size effect using data scaling and elliptic Fourier descriptors in otolith shape analysis, exemplified by the discrimination of two yellow croaker stocks along the Chinese coast

NASA Astrophysics Data System (ADS)

Zhao, Bo; Liu, Jinhu; Song, Junjie; Cao, Liang; Dou, Shuozeng

2017-11-01

Removal of the length effect in otolith shape analysis for stock identification using length scaling is an important issue; however, few studies have attempted to investigate the effectiveness or weakness of this methodology in application. The aim of this study was to evaluate whether commonly used size scaling methods and normalized elliptic Fourier descriptors (NEFDs) could effectively remove the size effect of fish in stock discrimination. To achieve this goal, length groups from two known geographical stocks of yellow croaker, Larimichthys polyactis, along the Chinese coast (five groups from the Changjiang River estuary of the East China Sea and three groups from the Bohai Sea) were subjected to otolith shape analysis. The results indicated that the variation of otolith shape caused by intra-stock fish length might exceed that due to inter-stock geographical separation, even when otolith shape variables are standardized with length scaling methods. This variation could easily result in misleading stock discrimination through otolith shape analysis. Therefore, conclusions about fish stock structure should be carefully drawn from otolith shape analysis because the observed discrimination may primarily be due to length effects, rather than differences among stocks. The application of multiple methods, such as otoliths shape analysis combined with elemental fingering, tagging or genetic analysis, is recommended for sock identification.

A new hybrid double divisor ratio spectra method for the analysis of ternary mixtures

NASA Astrophysics Data System (ADS)

Youssef, Rasha M.; Maher, Hadir M.

2008-10-01

A new spectrophotometric method was developed for the simultaneous determination of ternary mixtures, without prior separation steps. This method is based on convolution of the double divisor ratio spectra, obtained by dividing the absorption spectrum of the ternary mixture by a standard spectrum of two of the three compounds in the mixture, using combined trigonometric Fourier functions. The magnitude of the Fourier function coefficients, at either maximum or minimum points, is related to the concentration of each drug in the mixture. The mathematical explanation of the procedure is illustrated. The method was applied for the assay of a model mixture consisting of isoniazid (ISN), rifampicin (RIF) and pyrazinamide (PYZ) in synthetic mixtures, commercial tablets and human urine samples. The developed method was compared with the double divisor ratio spectra derivative method (DDRD) and derivative ratio spectra-zero-crossing method (DRSZ). Linearity, validation, accuracy, precision, limits of detection, limits of quantitation, and other aspects of analytical validation are included in the text.

Fourier Transform Infrared Spectroscopy (FTIR) and Multivariate Analysis for Identification of Different Vegetable Oils Used in Biodiesel Production

PubMed Central

Mueller, Daniela; Ferrão, Marco Flôres; Marder, Luciano; da Costa, Adilson Ben; de Cássia de Souza Schneider, Rosana

2013-01-01

The main objective of this study was to use infrared spectroscopy to identify vegetable oils used as raw material for biodiesel production and apply multivariate analysis to the data. Six different vegetable oil sources—canola, cotton, corn, palm, sunflower and soybeans—were used to produce biodiesel batches. The spectra were acquired by Fourier transform infrared spectroscopy using a universal attenuated total reflectance sensor (FTIR-UATR). For the multivariate analysis principal component analysis (PCA), hierarchical cluster analysis (HCA), interval principal component analysis (iPCA) and soft independent modeling of class analogy (SIMCA) were used. The results indicate that is possible to develop a methodology to identify vegetable oils used as raw material in the production of biodiesel by FTIR-UATR applying multivariate analysis. It was also observed that the iPCA found the best spectral range for separation of biodiesel batches using FTIR-UATR data, and with this result, the SIMCA method classified 100% of the soybean biodiesel samples. PMID:23539030

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

NASA Astrophysics Data System (ADS)

Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning

2017-09-01

Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

NASA Technical Reports Server (NTRS)

Corral, Roque; Jimenez, Javier

1992-01-01

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

Quantitative analysis of virgin coconut oil in cream cosmetics preparations using fourier transform infrared (FTIR) spectroscopy.

PubMed

Rohman, A; Man, Yb Che; Sismindari

2009-10-01

Today, virgin coconut oil (VCO) is becoming valuable oil and is receiving an attractive topic for researchers because of its several biological activities. In cosmetics industry, VCO is excellent material which functions as a skin moisturizer and softener. Therefore, it is important to develop a quantitative analytical method offering a fast and reliable technique. Fourier transform infrared (FTIR) spectroscopy with sample handling technique of attenuated total reflectance (ATR) can be successfully used to analyze VCO quantitatively in cream cosmetic preparations. A multivariate analysis using calibration of partial least square (PLS) model revealed the good relationship between actual value and FTIR-predicted value of VCO with coefficient of determination (R2) of 0.998.

Analysis of Digital Communication Signals and Extraction of Parameters.

DTIC Science & Technology

1994-12-01

Fast Fourier Transform (FFT). The correlation methods utilize modified time-frequency distributions , where one of these is based on the Wigner - Ville ... Distribution ( WVD ). Gaussian white noise is added to the signal to simulate various signal-to-noise ratios (SNRs).

Figures of merit for detectors in digital radiography. II. Finite number of secondaries and structured backgrounds.

PubMed

Pineda, Angel R; Barrett, Harrison H

2004-02-01

The current paradigm for evaluating detectors in digital radiography relies on Fourier methods. Fourier methods rely on a shift-invariant and statistically stationary description of the imaging system. The theoretical justification for the use of Fourier methods is based on a uniform background fluence and an infinite detector. In practice, the background fluence is not uniform and detector size is finite. We study the effect of stochastic blurring and structured backgrounds on the correlation between Fourier-based figures of merit and Hotelling detectability. A stochastic model of the blurring leads to behavior similar to what is observed by adding electronic noise to the deterministic blurring model. Background structure does away with the shift invariance. Anatomical variation makes the covariance matrix of the data less amenable to Fourier methods by introducing long-range correlations. It is desirable to have figures of merit that can account for all the sources of variation, some of which are not stationary. For such cases, we show that the commonly used figures of merit based on the discrete Fourier transform can provide an inaccurate estimate of Hotelling detectability.

Fourier transform magnitudes are unique pattern recognition templates.

PubMed

Gardenier, P H; McCallum, B C; Bates, R H

1986-01-01

Fourier transform magnitudes are commonly used in the generation of templates in pattern recognition applications. We report on recent advances in Fourier phase retrieval which are relevant to pattern recognition. We emphasise in particular that the intrinsic form of a finite, positive image is, in general, uniquely related to the magnitude of its Fourier transform. We state conditions under which the Fourier phase can be reconstructed from samples of the Fourier magnitude, and describe a method of achieving this. Computational examples of restoration of Fourier phase (and hence, by Fourier transformation, the intrinsic form of the image) from samples of the Fourier magnitude are also presented.

Wavelet Filter Banks for Super-Resolution SAR Imaging

NASA Technical Reports Server (NTRS)

Sheybani, Ehsan O.; Deshpande, Manohar; Memarsadeghi, Nargess

2011-01-01

This paper discusses Innovative wavelet-based filter banks designed to enhance the analysis of super resolution Synthetic Aperture Radar (SAR) images using parametric spectral methods and signal classification algorithms, SAR finds applications In many of NASA's earth science fields such as deformation, ecosystem structure, and dynamics of Ice, snow and cold land processes, and surface water and ocean topography. Traditionally, standard methods such as Fast-Fourier Transform (FFT) and Inverse Fast-Fourier Transform (IFFT) have been used to extract Images from SAR radar data, Due to non-parametric features of these methods and their resolution limitations and observation time dependence, use of spectral estimation and signal pre- and post-processing techniques based on wavelets to process SAR radar data has been proposed. Multi-resolution wavelet transforms and advanced spectral estimation techniques have proven to offer efficient solutions to this problem.

Support vector machine based classification of fast Fourier transform spectroscopy of proteins

NASA Astrophysics Data System (ADS)

Lazarevic, Aleksandar; Pokrajac, Dragoljub; Marcano, Aristides; Melikechi, Noureddine

2009-02-01

Fast Fourier transform spectroscopy has proved to be a powerful method for study of the secondary structure of proteins since peak positions and their relative amplitude are affected by the number of hydrogen bridges that sustain this secondary structure. However, to our best knowledge, the method has not been used yet for identification of proteins within a complex matrix like a blood sample. The principal reason is the apparent similarity of protein infrared spectra with actual differences usually masked by the solvent contribution and other interactions. In this paper, we propose a novel machine learning based method that uses protein spectra for classification and identification of such proteins within a given sample. The proposed method uses principal component analysis (PCA) to identify most important linear combinations of original spectral components and then employs support vector machine (SVM) classification model applied on such identified combinations to categorize proteins into one of given groups. Our experiments have been performed on the set of four different proteins, namely: Bovine Serum Albumin, Leptin, Insulin-like Growth Factor 2 and Osteopontin. Our proposed method of applying principal component analysis along with support vector machines exhibits excellent classification accuracy when identifying proteins using their infrared spectra.

Application of several methods for determining transfer functions and frequency response of aircraft from flight data

NASA Technical Reports Server (NTRS)

Eggleston, John M; Mathews, Charles W

1954-01-01

In the process of analyzing the longitudinal frequency-response characteristics of aircraft, information on some of the methods of analysis has been obtained by the Langley Aeronautical Laboratory of the National Advisory Committee for Aeronautics. In the investigation of these methods, the practical applications and limitations were stressed. In general, the methods considered may be classed as: (1) analysis of sinusoidal response, (2) analysis of transient response as to harmonic content through determination of the Fourier integral by manual or machine methods, and (3) analysis of the transient through the use of least-squares solutions of the coefficients of an assumed equation for either the transient time response or frequency response (sometimes referred to as curve-fitting methods). (author)

Quantitative analysis of active compounds in pharmaceutical preparations by use of attenuated total-reflection Fourier transform mid-infrared spectrophotometry and the internal standard method.

PubMed

Sastre Toraño, J; van Hattum, S H

2001-10-01

A new method is presented for the quantitative analysis of compounds in pharmaceutical preparations Fourier transform (FT) mid-infrared (MIR) spectroscopy with an attenuated total reflection (ATR) module. Reduction of the quantity of overlapping absorption bands, by interaction of the compound of interest with an appropriate solvent, and the employment of an internal standard (IS), makes MIR suitable for quantitative analysis. Vigabatrin, as active compound in vigabatrin 100-mg capsules, was used as a model compound for the development of the method. Vigabatrin was extracted from the capsule content with water after addition of a sodium thiosulfate IS solution. The extract was concentrated by volume reduction and applied to the FTMIR-ATR module. Concentrations of unknown samples were calculated from the ratio of the vigabatrin band area (1321-1610 cm(-1)) and the IS band area (883-1215 cm(-1)) using a calibration standard. The ratio of the area of the vigabatrin peak to that of the IS was linear with the concentration in the range of interest (90-110 mg, in twofold; n=2). The accuracy of the method in this range was 99.7-100.5% (n=5) with a variability of 0.4-1.3% (n=5). The comparison of the presented method with an HPLC assay showed similar results; the analysis of five vigabatrin 100-mg capsules resulted in a mean concentration of 102 mg with a variation of 2% with both methods.

An L1-norm phase constraint for half-Fourier compressed sensing in 3D MR imaging.

PubMed

Li, Guobin; Hennig, Jürgen; Raithel, Esther; Büchert, Martin; Paul, Dominik; Korvink, Jan G; Zaitsev, Maxim

2015-10-01

In most half-Fourier imaging methods, explicit phase replacement is used. In combination with parallel imaging, or compressed sensing, half-Fourier reconstruction is usually performed in a separate step. The purpose of this paper is to report that integration of half-Fourier reconstruction into iterative reconstruction minimizes reconstruction errors. The L1-norm phase constraint for half-Fourier imaging proposed in this work is compared with the L2-norm variant of the same algorithm, with several typical half-Fourier reconstruction methods. Half-Fourier imaging with the proposed phase constraint can be seamlessly combined with parallel imaging and compressed sensing to achieve high acceleration factors. In simulations and in in-vivo experiments half-Fourier imaging with the proposed L1-norm phase constraint enables superior performance both reconstruction of image details and with regard to robustness against phase estimation errors. The performance and feasibility of half-Fourier imaging with the proposed L1-norm phase constraint is reported. Its seamless combination with parallel imaging and compressed sensing enables use of greater acceleration in 3D MR imaging.

Higuchi Dimension of Digital Images

PubMed Central

Ahammer, Helmut

2011-01-01

There exist several methods for calculating the fractal dimension of objects represented as 2D digital images. For example, Box counting, Minkowski dilation or Fourier analysis can be employed. However, there appear to be some limitations. It is not possible to calculate only the fractal dimension of an irregular region of interest in an image or to perform the calculations in a particular direction along a line on an arbitrary angle through the image. The calculations must be made for the whole image. In this paper, a new method to overcome these limitations is proposed. 2D images are appropriately prepared in order to apply 1D signal analyses, originally developed to investigate nonlinear time series. The Higuchi dimension of these 1D signals is calculated using Higuchi's algorithm, and it is shown that both regions of interests and directional dependencies can be evaluated independently of the whole picture. A thorough validation of the proposed technique and a comparison of the new method to the Fourier dimension, a common two dimensional method for digital images, are given. The main result is that Higuchi's algorithm allows a direction dependent as well as direction independent analysis. Actual values for the fractal dimensions are reliable and an effective treatment of regions of interests is possible. Moreover, the proposed method is not restricted to Higuchi's algorithm, as any 1D method of analysis, can be applied. PMID:21931854

Application of Fourier transform infrared spectroscopy with chemometrics on postmortem interval estimation based on pericardial fluids.

PubMed

Zhang, Ji; Li, Bing; Wang, Qi; Wei, Xin; Feng, Weibo; Chen, Yijiu; Huang, Ping; Wang, Zhenyuan

2017-12-21

Postmortem interval (PMI) evaluation remains a challenge in the forensic community due to the lack of efficient methods. Studies have focused on chemical analysis of biofluids for PMI estimation; however, no reports using spectroscopic methods in pericardial fluid (PF) are available. In this study, Fourier transform infrared (FTIR) spectroscopy with attenuated total reflectance (ATR) accessory was applied to collect comprehensive biochemical information from rabbit PF at different PMIs. The PMI-dependent spectral signature was determined by two-dimensional (2D) correlation analysis. The partial least square (PLS) and nu-support vector machine (nu-SVM) models were then established based on the acquired spectral dataset. Spectral variables associated with amide I, amide II, COO - , C-H bending, and C-O or C-OH vibrations arising from proteins, polypeptides, amino acids and carbohydrates, respectively, were susceptible to PMI in 2D correlation analysis. Moreover, the nu-SVM model appeared to achieve a more satisfactory prediction than the PLS model in calibration; the reliability of both models was determined in an external validation set. The study shows the possibility of application of ATR-FTIR methods in postmortem interval estimation using PF samples.

Identification of pulmonary edema in forensic autopsy cases of fatal anaphylactic shock using Fourier transform infrared microspectroscopy.

PubMed

Lin, Hancheng; Luo, Yiwen; Wang, Lei; Deng, Kaifei; Sun, Qiran; Fang, Ruoxi; Wei, Xin; Zha, Shuai; Wang, Zhenyuan; Huang, Ping

2018-03-01

Anaphylaxis is a rapid allergic reaction that may cause sudden death. Currently, postmortem diagnosis of anaphylactic shock is sometimes difficult and often achieved through exclusion. The aim of our study was to investigate whether Fourier transform infrared (FTIR) microspectroscopy combined with pattern recognition methods would be complementary to traditional methods and provide a more accurate postmortem diagnosis of fatal anaphylactic shock. First, the results of spectral peak area analysis showed that the pulmonary edema fluid of the fatal anaphylactic shock group was richer in protein components than the control group, which included mechanical asphyxia, brain injury, and acute cardiac death. Subsequently, principle component analysis (PCA) was performed and showed that the anaphylactic shock group contained more turn and α-helix protein structures as well as less tyrosine-rich proteins than the control group. Ultimately, a partial least-square discriminant analysis (PLS-DA) model combined with a variables selection method called the genetic algorithm (GA) was built and demonstrated good separation between these two groups. This pilot study demonstrates that FTIR microspectroscopy has the potential to be an effective aid for postmortem diagnosis of fatal anaphylactic shock.

Fourier transform infrared spectroscopy combined with chemometrics for discrimination of Curcuma longa, Curcuma xanthorrhiza and Zingiber cassumunar

NASA Astrophysics Data System (ADS)

Rohaeti, Eti; Rafi, Mohamad; Syafitri, Utami Dyah; Heryanto, Rudi

2015-02-01

Turmeric (Curcuma longa), java turmeric (Curcuma xanthorrhiza) and cassumunar ginger (Zingiber cassumunar) are widely used in traditional Indonesian medicines (jamu). They have similar color for their rhizome and possess some similar uses, so it is possible to substitute one for the other. The identification and discrimination of these closely-related plants is a crucial task to ensure the quality of the raw materials. Therefore, an analytical method which is rapid, simple and accurate for discriminating these species using Fourier transform infrared spectroscopy (FTIR) combined with some chemometrics methods was developed. FTIR spectra were acquired in the mid-IR region (4000-400 cm-1). Standard normal variate, first and second order derivative spectra were compared for the spectral data. Principal component analysis (PCA) and canonical variate analysis (CVA) were used for the classification of the three species. Samples could be discriminated by visual analysis of the FTIR spectra by using their marker bands. Discrimination of the three species was also possible through the combination of the pre-processed FTIR spectra with PCA and CVA, in which CVA gave clearer discrimination. Subsequently, the developed method could be used for the identification and discrimination of the three closely-related plant species.

Computationally efficient method for Fourier transform of highly chirped pulses for laser and parametric amplifier modeling.

PubMed

Andrianov, Alexey; Szabo, Aron; Sergeev, Alexander; Kim, Arkady; Chvykov, Vladimir; Kalashnikov, Mikhail

2016-11-14

We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.

Fourier transform infrared spectroscopy for analysis of kidney stones.

PubMed

Khan, Aysha Habib; Imran, Sheharbano; Talati, Jamsheer; Jafri, Lena

2018-01-01

To compare the results of a chemical method of kidney stone analysis with the results of Fourier transform infrared (FT-IR) spectroscopy. Kidney stones collected between June and October 2015 were simultaneously analyzed by chemical and FT-IR methods. Kidney stones (n=449) were collected from patients from 1 to 81 years old. Most stones were from adults, with only 11.5% from children (aged 3-16 years) and 1.5% from children aged <2 years. The male to female ratio was 4.6. In adults, the calcium oxalate stone type, calcium oxalate monohydrate (COM, n=224), was the most common crystal, followed by uric acid and calcium oxalate dihydrate (COD, n=83). In children, the most frequently occurring type was predominantly COD (n=21), followed by COM (n=11), ammonium urate (n=10), carbonate apatite (n=6), uric acid (n=4), and cystine (n=1). Core composition in 22 stones showed ammonium urate (n=2), COM (n=2), and carbonate apatite (n=1) in five stones, while uric acid crystals were detected (n=13) by FT-IR. While chemical analysis identified 3 stones as uric acid and the rest as calcium oxalate only. Agreement between the two methods was moderate, with a kappa statistic of 0.57 (95% confidence interval, 0.5-0.64). Disagreement was noted in the analysis of 77 stones. FT-IR analysis of kidney stones can overcome many limitations associated with chemical analysis.

Dating a tropical ice core by time-frequency analysis of ion concentration depth profiles

NASA Astrophysics Data System (ADS)

Gay, M.; De Angelis, M.; Lacoume, J.-L.

2014-09-01

Ice core dating is a key parameter for the interpretation of the ice archives. However, the relationship between ice depth and ice age generally cannot be easily established and requires the combination of numerous investigations and/or modelling efforts. This paper presents a new approach to ice core dating based on time-frequency analysis of chemical profiles at a site where seasonal patterns may be significantly distorted by sporadic events of regional importance, specifically at the summit area of Nevado Illimani (6350 m a.s.l.), located in the eastern Bolivian Andes (16°37' S, 67°46' W). We used ion concentration depth profiles collected along a 100 m deep ice core. The results of Fourier time-frequency and wavelet transforms were first compared. Both methods were applied to a nitrate concentration depth profile. The resulting chronologies were checked by comparison with the multi-proxy year-by-year dating published by de Angelis et al. (2003) and with volcanic tie points. With this first experiment, we demonstrated the efficiency of Fourier time-frequency analysis when tracking the nitrate natural variability. In addition, we were able to show spectrum aliasing due to under-sampling below 70 m. In this article, we propose a method of de-aliasing which significantly improves the core dating in comparison with annual layer manual counting. Fourier time-frequency analysis was applied to concentration depth profiles of seven other ions, providing information on the suitability of each of them for the dating of tropical Andean ice cores.

Fourier Deconvolution Methods for Resolution Enhancement in Continuous-Wave EPR Spectroscopy.

PubMed

Reed, George H; Poyner, Russell R

2015-01-01

An overview of resolution enhancement of conventional, field-swept, continuous-wave electron paramagnetic resonance spectra using Fourier transform-based deconvolution methods is presented. Basic steps that are involved in resolution enhancement of calculated spectra using an implementation based on complex discrete Fourier transform algorithms are illustrated. Advantages and limitations of the method are discussed. An application to an experimentally obtained spectrum is provided to illustrate the power of the method for resolving overlapped transitions. © 2015 Elsevier Inc. All rights reserved.

Methods and Applications of Time Series Analysis. Part I. Regression, Trends, Smoothing, and Differencing.

DTIC Science & Technology

1980-07-01

FUNCTION ( t) CENTERED AT C WITH PERIOD n -nr 0 soTIME t FIGURE 3.4S RECTAPOOLAR PORN )=C FUNCTION g t) CENTERED AT 0 WITH PERIOD n n n 52n tI y I (h...of a typical family in Kabiria (a city in Northern Algeria) over the time period Jan.-Feb. 1975 through Nov.-Dec. 1977. We would like to obtain a...values of y .. .. ... -75- Table 4.2 The Average Bi-Monthly Expenses of a Family in Kabiria and Their Fourier Representation Fourier Coefficients x k

Mid-Latitude Temperatures at 87 km: Results From Multi-Instrument Fourier Analysis

NASA Technical Reports Server (NTRS)

Drob, Douglas P.; Picone, J. M.; Eckermann, Stephen D.; She, C . Y.; Kafkalidis, J. F.; Ortland, D. A.; Niciejewski, R. J.; Killeen, T. L.

2000-01-01

Using a novel Fourier fitting method we combine two years of mid-latitude temperature measurements at 87 km from the High Resolution Doppler Imager, the Colorado State University lidar, and the Peach Mountain Interferometer. After accounting for calibration bias, significant local-time variations on the order of 10 K were observed. Stationary planetary waves with amplitudes up to 10 K were observed during winter, with weaker wave amplitudes occurring during other seasons. Because of calibration biases among these instruments, we could estimate the annual mean temperature to no better than 193.5 plus or minus 8.5 K.

Elliptical Fourier descriptors of outline and morphological analysis in caudal view of foramen magnum of the tropical raccoon (Procyon cancrivorus) (Linnaeus, 1758).

PubMed

Samuel, O M; Casanova, P M; Olopade, J O

2018-03-01

To evaluate sexual-size dimorphism and attempt at categorization of inter-individual shapes of foramen magnum outlines using Fourier descriptors which allow for shape outline evaluations with a resultant specimen character definition. Individual characterization and quantification of foramen magnum shapes in direct caudal view based on elliptical Fourier technique was applied to 46 tropical raccoon skulls (26 females, 20 males). Incremental number of harmonics demonstrates morphological contributions of such descriptors with their relations to specific anatomical constructions established. The initial harmonics (1st to 3rd) described the general foramen shapes while the second (4th to 12th) demonstrated fine morphological details. Sexual-size dimorphism was observed in females (87.1%) and 91.7% in males, normalization of size produces 75% in females and 83% in males. With respect to foramen magnum dimorphism analysis, the result obtained through elliptic Fourier analysis was comparatively better in detail information of outline contours than earlier classical methods. The first four effective principal components defined 70.63% of its shape properties while the rest (22.51%) constituted fine details of morphology. Both size and shape seems important in sexual dimorphisms in this species, this investigation suggest clinical implications, taxonomic and anthropologic perspectives in foramen characterization magnum characterization and further postulates an increased possibility of volume reduction cerebellar protrusion, ontogenic magnum shape irregularities in the sample population with neurologic consequences especially among females. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

Adaptive synchrosqueezing based on a quilted short-time Fourier transform

NASA Astrophysics Data System (ADS)

Berrian, Alexander; Saito, Naoki

2017-08-01

In recent years, the synchrosqueezing transform (SST) has gained popularity as a method for the analysis of signals that can be broken down into multiple components determined by instantaneous amplitudes and phases. One such version of SST, based on the short-time Fourier transform (STFT), enables the sharpening of instantaneous frequency (IF) information derived from the STFT, as well as the separation of amplitude-phase components corresponding to distinct IF curves. However, this SST is limited by the time-frequency resolution of the underlying window function, and may not resolve signals exhibiting diverse time-frequency behaviors with sufficient accuracy. In this work, we develop a framework for an SST based on a "quilted" short-time Fourier transform (SST-QSTFT), which allows adaptation to signal behavior in separate time-frequency regions through the use of multiple windows. This motivates us to introduce a discrete reassignment frequency formula based on a finite difference of the phase spectrum, ensuring computational accuracy for a wider variety of windows. We develop a theoretical framework for the SST-QSTFT in both the continuous and the discrete settings, and describe an algorithm for the automatic selection of optimal windows depending on the region of interest. Using synthetic data, we demonstrate the superior numerical performance of SST-QSTFT relative to other SST methods in a noisy context. Finally, we apply SST-QSTFT to audio recordings of animal calls to demonstrate the potential of our method for the analysis of real bioacoustic signals.

Validating data analysis of broadband laser ranging

NASA Astrophysics Data System (ADS)

Rhodes, M.; Catenacci, J.; Howard, M.; La Lone, B.; Kostinski, N.; Perry, D.; Bennett, C.; Patterson, J.

2018-03-01

Broadband laser ranging combines spectral interferometry and a dispersive Fourier transform to achieve high-repetition-rate measurements of the position of a moving surface. Telecommunications fiber is a convenient tool for generating the large linear dispersions required for a dispersive Fourier transform, but standard fiber also has higher-order dispersion that distorts the Fourier transform. Imperfections in the dispersive Fourier transform significantly complicate the ranging signal and must be dealt with to make high-precision measurements. We describe in detail an analysis process for interpreting ranging data when standard telecommunications fiber is used to perform an imperfect dispersive Fourier transform. This analysis process is experimentally validated over a 27-cm scan of static positions, showing an accuracy of 50 μm and a root-mean-square precision of 4.7 μm.

Comparative analysis of imaging configurations and objectives for Fourier microscopy.

PubMed

Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid

2015-11-01

Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.

A Fourier analysis for a fast simulation algorithm. [for switching converters

NASA Technical Reports Server (NTRS)

King, Roger J.

1988-01-01

This paper presents a derivation of compact expressions for the Fourier series analysis of the steady-state solution of a typical switching converter. The modeling procedure for the simulation and the steady-state solution is described, and some desirable traits for its matrix exponential subroutine are discussed. The Fourier analysis algorithm was tested on a phase-controlled parallel-loaded resonant converter, providing an experimental confirmation.

Inverse modeling of the overpressure distribution in an extension fracture with an arbitrary aperture variation: application to non-feeder dikes in the Miyake-jima Volcano, Japan

NASA Astrophysics Data System (ADS)

Kusumoto, Shigekazu; Geshi, Nobuo; Gudmundsson, Agust

2010-05-01

We derived a solution for the overpressure distribution acting on the walls (surfaces) of an extension fracture (a hydrofracture) with an arbitrary opening-displacement (or aperture) variation. In the proposed model, we assume that the overpressure distribution can be described by Fourier cosine series. We at first present a solution for the forward model giving the fracture aperture when it is opened by an irregular overpressure variation obtained using the Fourier cosine series. Next, by changing the form of the solution for the forward model, we obtain a matrix equation that can be used to estimate the Fourier coefficients to obtain the overpressure distribution from the fracture aperture variation. As simple examples of this inverse analysis, we estimate the overpressure conditions from crack apertures given analytically for two cases, namely, 1) the overpressure in the crack is constant, and 2) the overpressure variation in the crack varies linearly from its center. The estimated overpressure distributions were found to be correct, although a small 'noise' was present. Since the method presented here gives the overpressure distribution as a Fourier series by the aperture data measured at a finite number of points, the overpressure conditions for forming the fracture can be determined for each wavelength. The Fourier coefficient of n = 0 is an important coefficient that gives the average value of the overpressure acting inside the crack. With the exception of n = 0, the Fourier coefficient of n = 1 expresses the longest wavelength component of the irregular overpressure. Thus, because this coefficient including the coefficient of n = 0 gives the longest wavelength component in the irregular overpressure, the component may be an important indicator of the overpressure condition that decides the basic form of the crack. We applied the solution for the inverse analysis to the thickness data of 19 non-feeder dikes exposed in the caldera wall of the Miyake-jima Volcano, Japan. In the analysis, the host-rock Young's modulus and Poisson's ratio were taken as 1 GPa and 0.25. The results show that most of the estimated overpressures increase toward the tips of the dikes and reach about 5 to 15 MPa (average was 8 MPa). In addition, results indicate host-rock fracture toughnesses between 60 MPa m1-2 and 170 MPa m1-2 (average 100 MPa m1-2). For comparison, we also estimated the magma overpressure by the least square method, assuming constant overpressure. This method gives overpressure between 1.5 MPa and 4 MPa (average 2.8 MPa). Similarly, the fracture toughnesses estimated in this way range between 30 MPa m1-2 and 120 MPa m1-2 (average 55 MPa m1-2). These methods and assumptions thus yield somewhat different results, as expected, but indicate the likely ranges of the magma overpressures and host-rock fracture toughnesses both of which are very reasonable and agree with earlier results obtained by different methods.

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

ERIC Educational Resources Information Center

Hanley, Quentin S.

2012-01-01

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

An investigation of density measurement method for yarn-dyed woven fabrics based on dual-side fusion technique

NASA Astrophysics Data System (ADS)

Zhang, Rui; Xin, Binjie

2016-08-01

Yarn density is always considered as the fundamental structural parameter used for the quality evaluation of woven fabrics. The conventional yarn density measurement method is based on one-side analysis. In this paper, a novel density measurement method is developed for yarn-dyed woven fabrics based on a dual-side fusion technique. Firstly, a lab-used dual-side imaging system is established to acquire both face-side and back-side images of woven fabric and the affine transform is used for the alignment and fusion of the dual-side images. Then, the color images of the woven fabrics are transferred from the RGB to the CIE-Lab color space, and the intensity information of the image extracted from the L component is used for texture fusion and analysis. Subsequently, three image fusion methods are developed and utilized to merge the dual-side images: the weighted average method, wavelet transform method and Laplacian pyramid blending method. The fusion efficacy of each method is evaluated by three evaluation indicators and the best of them is selected to do the reconstruction of the complete fabric texture. Finally, the yarn density of the fused image is measured based on the fast Fourier transform, and the yarn alignment image could be reconstructed using the inverse fast Fourier transform. Our experimental results show that the accuracy of density measurement by using the proposed method is close to 99.44% compared with the traditional method and the robustness of this new proposed method is better than that of conventional analysis methods.

Spectroscopic signature of mouse embryonic stem cell-derived hepatocytes using synchrotron Fourier transform infrared microspectroscopy

NASA Astrophysics Data System (ADS)

Thumanu, Kanjana; Tanthanuch, Waraporn; Ye, Danna; Sangmalee, Anawat; Lorthongpanich, Chanchao; Parnpai, Rangsun; Heraud, Philip

2011-05-01

Stem cell-based therapy for liver regeneration has been proposed to overcome the persistent shortage in the supply of suitable donor organs. A requirement for this to succeed is to find a rapid method to detect functional hepatocytes, differentiated from embryonic stem cells. We propose Fourier transform infrared (FTIR) microspectroscopy as a versatile method to identify the early and last stages of the differentiation process leading to the formation of hepatocytes. Using synchrotron-FTIR microspectroscopy, the means of identifying hepatocytes at the single-cell level is possible and explored. Principal component analysis and subsequent partial least-squares (PLS) discriminant analysis is applied to distinguish endoderm induction from hepatic progenitor cells and matured hepatocyte-like cells. The data are well modeled by PLS with endoderm induction, hepatic progenitor cells, and mature hepatocyte-like cells able to be discriminated with very high sensitivity and specificity. This method provides a practical tool to monitor endoderm induction and has the potential to be applied for quality control of cell differentiation leading to hepatocyte formation.

Discrete Fourier Transform-Based Multivariate Image Analysis: Application to Modeling of Aromatase Inhibitory Activity.

PubMed

Barigye, Stephen J; Freitas, Matheus P; Ausina, Priscila; Zancan, Patricia; Sola-Penna, Mauro; Castillo-Garit, Juan A

2018-02-12

We recently generalized the formerly alignment-dependent multivariate image analysis applied to quantitative structure-activity relationships (MIA-QSAR) method through the application of the discrete Fourier transform (DFT), allowing for its application to noncongruent and structurally diverse chemical compound data sets. Here we report the first practical application of this method in the screening of molecular entities of therapeutic interest, with human aromatase inhibitory activity as the case study. We developed an ensemble classification model based on the two-dimensional (2D) DFT MIA-QSAR descriptors, with which we screened the NCI Diversity Set V (1593 compounds) and obtained 34 chemical compounds with possible aromatase inhibitory activity. These compounds were docked into the aromatase active site, and the 10 most promising compounds were selected for in vitro experimental validation. Of these compounds, 7419 (nonsteroidal) and 89 201 (steroidal) demonstrated satisfactory antiproliferative and aromatase inhibitory activities. The obtained results suggest that the 2D-DFT MIA-QSAR method may be useful in ligand-based virtual screening of new molecular entities of therapeutic utility.

Enhancement of Signal-to-noise Ratio in Natural-source Transient Magnetotelluric Data with Wavelet Transform

NASA Astrophysics Data System (ADS)

Zhang, Y.; Paulson, K. V.

For audio-frequency magnetotelluric surveys where the signals are lightning-stroke transients, the conventional Fourier transform method often fails to produce a high quality impedance tensor. An alternative approach is to use the wavelet transform method which is capable of localizing target information simultaneously in both the temporal and frequency domains. Unlike Fourier analysis that yields an average amplitude and phase, the wavelet transform produces an instantaneous estimate of the amplitude and phase of a signal. In this paper a complex well-localized wavelet, the Morlet wavelet, has been used to transform and analyze audio-frequency magnetotelluric data. With the Morlet wavelet, the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. The lightning-stroke transients are easily identified on the dilation-translation plane. Choosing those wavelet transform values where the signals are located, a higher signal-to-noise ratio estimation of the impedance tensor can be obtained. In a test using real data, the wavelet transform showed a significant improvement in the signal-to-noise ratio over the conventional Fourier transform.

Discrimination of healthy and osteoarthritic articular cartilage by Fourier transform infrared imaging and Fisher’s discriminant analysis

PubMed Central

Mao, Zhi-Hua; Yin, Jian-Hua; Zhang, Xue-Xi; Wang, Xiao; Xia, Yang

2016-01-01

Fourier transform infrared spectroscopic imaging (FTIRI) technique can be used to obtain the quantitative information of content and spatial distribution of principal components in cartilage by combining with chemometrics methods. In this study, FTIRI combining with principal component analysis (PCA) and Fisher’s discriminant analysis (FDA) was applied to identify the healthy and osteoarthritic (OA) articular cartilage samples. Ten 10-μm thick sections of canine cartilages were imaged at 6.25μm/pixel in FTIRI. The infrared spectra extracted from the FTIR images were imported into SPSS software for PCA and FDA. Based on the PCA result of 2 principal components, the healthy and OA cartilage samples were effectively discriminated by the FDA with high accuracy of 94% for the initial samples (training set) and cross validation, as well as 86.67% for the prediction group. The study showed that cartilage degeneration became gradually weak with the increase of the depth. FTIRI combined with chemometrics may become an effective method for distinguishing healthy and OA cartilages in future. PMID:26977354

The combined use of order tracking techniques for enhanced Fourier analysis of order components

NASA Astrophysics Data System (ADS)

Wang, K. S.; Heyns, P. S.

2011-04-01

Order tracking is one of the most important vibration analysis techniques for diagnosing faults in rotating machinery. It can be performed in many different ways, each of these with distinct advantages and disadvantages. However, in the end the analyst will often use Fourier analysis to transform the data from a time series to frequency or order spectra. It is therefore surprising that the study of the Fourier analysis of order-tracked systems seems to have been largely ignored in the literature. This paper considers the frequently used Vold-Kalman filter-based order tracking and computed order tracking techniques. The main pros and cons of each technique for Fourier analysis are discussed and the sequential use of Vold-Kalman filtering and computed order tracking is proposed as a novel idea to enhance the results of Fourier analysis for determining the order components. The advantages of the combined use of these order tracking techniques are demonstrated numerically on an SDOF rotor simulation model. Finally, the approach is also demonstrated on experimental data from a real rotating machine.

Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

PubMed

Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

2016-10-01

The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

Error analysis for spectral approximation of the Korteweg-De Vries equation

NASA Technical Reports Server (NTRS)

Maday, Y.; recent years.

1987-01-01

The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.

Analysis of Preconditioning and Relaxation Operators for the Discontinuous Galerkin Method Applied to Diffusion

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Shu, Chi-Wang

2001-01-01

The explicit stability constraint of the discontinuous Galerkin method applied to the diffusion operator decreases dramatically as the order of the method is increased. Block Jacobi and block Gauss-Seidel preconditioner operators are examined for their effectiveness at accelerating convergence. A Fourier analysis for methods of order 2 through 6 reveals that both preconditioner operators bound the eigenvalues of the discrete spatial operator. Additionally, in one dimension, the eigenvalues are grouped into two or three regions that are invariant with order of the method. Local relaxation methods are constructed that rapidly damp high frequencies for arbitrarily large time step.

An evaluation method for nanoscale wrinkle

NASA Astrophysics Data System (ADS)

Liu, Y. P.; Wang, C. G.; Zhang, L. M.; Tan, H. F.

2016-06-01

In this paper, a spectrum-based wrinkling analysis method via two-dimensional Fourier transformation is proposed aiming to solve the difficulty of nanoscale wrinkle evaluation. It evaluates the wrinkle characteristics including wrinkling wavelength and direction simply using a single wrinkling image. Based on this method, the evaluation results of nanoscale wrinkle characteristics show agreement with the open experimental results within an error of 6%. It is also verified to be appropriate for the macro wrinkle evaluation without scale limitations. The spectrum-based wrinkling analysis is an effective method for nanoscale evaluation, which contributes to reveal the mechanism of nanoscale wrinkling.

Structural, vibrational spectroscopic and quantum chemical studies on indole-3-carboxaldehyde

NASA Astrophysics Data System (ADS)

Premkumar, R.; Asath, R. Mohamed; Mathavan, T.; Benial, A. Milton Franklin

2017-05-01

The potential energy surface (PES) scan was performed for indole-3-carboxaldehyde (ICA) and the most stable optimized conformer was predicted using DFT/B3LYP method with 6-31G basis set. The vibrational frequencies of ICA were theoretically calculated by the DFT/B3LYP method with cc-pVTZ basis set using Gaussian 09 program. The vibrational spectra were experimentally recorded by Fourier transform-infrared (FT-IR) and Fourier transform-Raman spectrometer (FT-Raman). The computed vibrational frequencies were scaled by scaling factors to yield a good agreement with observed vibrational frequencies. The theoretically calculated and experimentally observed vibrational frequencies were assigned on the basis of potential energy distribution (PED) calculation using VEDA 4.0 program. The molecular interaction, stability and intramolecular charge transfer of ICA were studied using frontier molecular orbitals (FMOs) analysis and Mulliken atomic charge distribution shows the distribution of the atomic charges. The presence of intramolecular charge transfer was studied using natural bond orbital (NBO) analysis.

Homotopic solutions for unsteady second grade liquid utilizing non-Fourier double diffusion concept

NASA Astrophysics Data System (ADS)

Sohail, A.; Khan, W. A.; Khan, M.; Shah, S. I. A.

Main purpose of the current work is to investigate the features of unsteady Cattaneo-Christov heat and mass flux models on the second grade fluid over a stretching surface. The characteristics of unsteady Cattaneo-Christov heat and mass flux models are incorporated in the energy and concentration equations. The unsteady Cattaneo-Christov heat and mass flux models are the generalization of Fourier's and Fick's laws in which the time space upper-convected derivative are utilized to describe the heat conduction and mass diffusion phenomena. The suitable transformations are used to alter the governing partial differential equations into the ordinary differential equations. The resulting problem under consideration is solved analytically by using the homotopy analysis method (HAM). The effect of non-dimensional pertinent parameters on the temperature and concentration distribution are deliberated by using graphs and tables. Results show that the temperature and concentration profiles diminish for augmented values of the thermal and concentration relaxation parameters. Additionally, it is perceived that the temperature and concentration profiles are higher in case of classical Fourier's and Fick's laws as compared to non-Fourier's and non-Fick's laws.

Application of Fourier transform near-infrared spectroscopy combined with high-performance liquid chromatography in rapid and simultaneous determination of essential components in crude Radix Scrophulariae.

PubMed

Li, Xiaomeng; Fang, Dansi; Cong, Xiaodong; Cao, Gang; Cai, Hao; Cai, Baochang

2012-12-01

A method is described using rapid and sensitive Fourier transform near-infrared spectroscopy combined with high-performance liquid chromatography-diode array detection for the simultaneous identification and determination of four bioactive compounds in crude Radix Scrophulariae samples. Partial least squares regression is selected as the analysis type and multiplicative scatter correction, second derivative, and Savitzky-Golay filter were adopted for the spectral pretreatment. The correlation coefficients (R) of the calibration models were above 0.96 and the root mean square error of predictions were under 0.028. The developed models were applied to unknown samples with satisfactory results. The established method was validated and can be applied to the intrinsic quality control of crude Radix Scrophulariae.

A rheumatoid arthritis study by Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Carvalho, Carolina S.; Silva, Ana Carla A.; Santos, Tatiano J. P. S.; Martin, Airton A.; dos Santos Fernandes, Ana Célia; Andrade, Luís E.; Raniero, Leandro

2012-01-01

Rheumatoid arthritis is a systemic inflammatory disease of unknown causes and a new methods to identify it in early stages are needed. The main purpose of this work is the biochemical differentiation of sera between normal and RA patients, through the establishment of a statistical method that can be appropriately used for serological analysis. The human sera from 39 healthy donors and 39 rheumatics donors were collected and analyzed by Fourier Transform Infrared Spectroscopy. The results show significant spectral variations with p<0.05 in regions corresponding to protein, lipids and immunoglobulins. The technique of latex particles, coated with human IgG and monoclonal anti-CRP by indirect agglutination known as FR and CRP, was performed to confirm possible false-negative results within the groups, facilitating the statistical interpretation and validation of the technique.

Studies of EXAFSSpectra using Copper (II) Schiff Base complexes and Determination of Bond lengths Using Synchrotron Radiation

NASA Astrophysics Data System (ADS)

Mishra, A.; Vibhute, V.; Ninama, S.; Parsai, N.; Jha, S. N.; Sharma, P.

2016-10-01

X-ray absorption fine structure (XAFS) at the K-edge of copper has been studied in some copper (II) complexes with substituted anilines like (2Cl, 4Br, 2NO2, 4NO2 and pure aniline) with o-PDA (orthophenylenediamine) as ligand. The X-ray absorption measurements have been performed at the recently developed BL-8 dispersive EXAFS beam line at 2.5 GeV Indus-2 Synchrotron Source at RRCAT, Indore, India. The data obtained has been processed using EXAFS data analysis program Athena.The graphical method gives the useful information about bond length and also the environment of the absorbing atom. The theoretical bond lengths of the complexes were calculated by using interactive fitting of EXAFS using fast Fourier inverse transformation (IFEFFIT) method. This method is also called as Fourier transform method. The Lytle, Sayers and Stern method and Levy's method have been used for determination of bond lengths experimentally of the studied complexes. The results of both methods have been compared with theoretical IFEFFIT method.

Measurement of subcellular texture by optical Gabor-like filtering with a digital micromirror device

PubMed Central

Pasternack, Robert M.; Qian, Zhen; Zheng, Jing-Yi; Metaxas, Dimitris N.; White, Eileen; Boustany, Nada N.

2010-01-01

We demonstrate an optical Fourier processing method to quantify object texture arising from subcellular feature orientation within unstained living cells. Using a digital micromirror device as a Fourier spatial filter, we measured cellular responses to two-dimensional optical Gabor-like filters optimized to sense orientation of nonspherical particles, such as mitochondria, with a width around 0.45 μm. Our method showed significantly rounder structures within apoptosis-defective cells lacking the proapoptotic mitochondrial effectors Bax and Bak, when compared with Bax/Bak expressing cells functional for apoptosis, consistent with reported differences in mitochondrial shape in these cells. By decoupling spatial frequency resolution from image resolution, this method enables rapid analysis of nonspherical submicrometer scatterers in an under-sampled large field of view and yields spatially localized morphometric parameters that improve the quantitative assessment of biological function. PMID:18830354

Noise-band factor analysis of cancer Fourier transform infrared evanescent-wave fiber optical (FTIR-FEW) spectra

NASA Astrophysics Data System (ADS)

Sukuta, Sydney; Bruch, Reinhard F.

2002-05-01

The goal of this study is to test the feasibility of using noise factor/eigenvector bands as general clinical analytical tools for diagnoses. We developed a new technique, Noise Band Factor Cluster Analysis (NBFCA), to diagnose benign tumors via their Fourier transform IR fiber optic evanescent wave spectral data for the first time. The middle IR region of human normal skin tissue and benign and melanoma tumors, were analyzed using this new diagnostic technique. Our results are not in full-agreement with pathological classifications hence there is a possibility that our approaches could complement or improve these traditional classification schemes. Moreover, the use of NBFCA make it much easier to delineate class boundaries hence this method provides results with much higher certainty.

The spectroscopic (FT-IR, FT-Raman, UV) and first order hyperpolarizability, HOMO and LUMO analysis of 3-aminobenzophenone by density functional method

NASA Astrophysics Data System (ADS)

Karabacak, M.; Kurt, M.; Cinar, M.; Ayyappan, S.; Sudha, S.; Sundaraganesan, N.

In this work, experimental and theoretical study on the molecular structure and the vibrational spectra of 3-aminobenzophenone (3-ABP) is presented. The vibrational frequencies of the title compound were obtained theoretically by DFT/B3LYP calculations employing the standard 6-311++G(d,p) basis set for optimized geometry and were compared with Fourier transform infrared spectrum (FTIR) in the region of 400-4000 cm-1 and with Fourier Transform Raman spectrum in the region of 50-4000 cm-1. Complete vibrational assignments, analysis and correlation of the fundamental modes for the title compound were carried out. The vibrational harmonic frequencies were scaled using scale factor, yielding a good agreement between the experimentally recorded and the theoretically calculated values.

Fourier transform of delayed fluorescence as an indicator of herbicide concentration.

PubMed

Guo, Ya; Tan, Jinglu

2014-12-21

It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems

NASA Astrophysics Data System (ADS)

Leuschner, Matthias; Fritzen, Felix

2017-11-01

Fourier-based homogenization schemes are useful to analyze heterogeneous microstructures represented by 2D or 3D image data. These iterative schemes involve discrete periodic convolutions with global ansatz functions (mostly fundamental solutions). The convolutions are efficiently computed using the fast Fourier transform. FANS operates on nodal variables on regular grids and converges to finite element solutions. Compared to established Fourier-based methods, the number of convolutions is reduced by FANS. Additionally, fast iterations are possible by assembling the stiffness matrix. Due to the related memory requirement, the method is best suited for medium-sized problems. A comparative study involving established Fourier-based homogenization schemes is conducted for a thermal benchmark problem with a closed-form solution. Detailed technical and algorithmic descriptions are given for all methods considered in the comparison. Furthermore, many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.

Photoacoustic detection of blood in dental pulp by using short-time Fourier transform

NASA Astrophysics Data System (ADS)

Yamada, Azusa; Kakino, Satoko; Matsuura, Yuji

2016-03-01

A method based on photoacoustic analysis is proposed to diagnose dental pulp vitality. Photoacoustic analysis enables to get signal from deeper tissues than other optical analyses and therefore, signal detection from root canal of thick dental tissues such as molar teeth is expected. As a light source for excitation of photoacoustic waves, a microchip Q-switched YAG laser with a wavelength of 1064 nm was used and owing to large penetration depth of the near infrared laser, photoacoustic signals from dental root were successfully obtained. It was found that the photoacoustic signals from the teeth containing hemoglobin solution in the pulp cavity provide vibration in high frequency region. It was also shown that the intensities of the high frequency component have correlation with the hemoglobin concentration of solution. We applied short-time Fourier transform for evaluation of photoacoustic signals and this analysis clearly showed photoacoustic signals from dental root.

Application of the Ramanujan Fourier Transform for the analysis of secondary structure content in amino acid sequences.

PubMed

Mainardi, L T; Pattini, L; Cerutti, S

2007-01-01

A novel method is presented for the investigation of protein properties of sequences using Ramanujan Fourier Transform (RFT). The new methodology involves the preprocessing of protein sequence data by numerically encoding it and then applying the RFT. The RFT is based on projecting the obtained numerical series on a set of basis functions constituted by Ramanujan sums (RS). In RS components, periodicities of finite integer length, rather than frequency, (as in classical harmonic analysis) are considered. The potential of the new approach is documented by a few examples in the analysis of hydrophobic profiles of proteins in two classes including abundance of alpha-helices (group A) or beta-strands (group B). Different patterns are provided as evidence. RFT can be used to characterize the structural properties of proteins and integrate complementary information provided by other signal processing transforms.

Comment on {open_quotes}Local frequency analysis and the structure of classical phase space of the LiNC/LiCN molecular system{close_quotes} [J. Chem. Phys. {bold 108}, 63 (1998)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martens, C.C.; Davis, M.J.; Ezra, G.S.

In this Comment, we correct a misunderstanding in the title paper concerning the accuracy of the fast Fourier transform method of local frequency analysis of Martens, Davis, and Ezra. We also discuss the application of the Martens{endash}Davis{endash}Ezra method to a two degree of freedom model of OSC. {copyright} {ital 1998 American Institute of Physics.}

Atmospheric trace gas analysis using matrix isolation-Fourier Transform Infrared Spectroscopy

NASA Astrophysics Data System (ADS)

Griffith, David W. T.; Schuster, Gerhard

1987-03-01

A novel cryogenic sampling method combining the matrix isolation technique with FTIR spectroscopy has been developed for atmospheric trace gas analysis. It is applicable to a wide range of molecules with detection limits typically in the 10-50 ppt range. The method is described along with some measurements of N2O, CFCl3, CF2Cl2, OCS, CS2, SO2 and PAN from samples collected at ground level and from an aircraft between 9 and 14 km.

An efficient solution procedure for the thermoelastic analysis of truss space structures

NASA Technical Reports Server (NTRS)

Givoli, D.; Rand, O.

1992-01-01

A solution procedure is proposed for the thermal and thermoelastic analysis of truss space structures in periodic motion. In this method, the spatial domain is first descretized using a consistent finite element formulation. Then the resulting semi-discrete equations in time are solved analytically by using Fourier decomposition. Geometrical symmetry is taken advantage of completely. An algorithm is presented for the calculation of heat flux distribution. The method is demonstrated via a numerical example of a cylindrically shaped space structure.

Fusion of multiscale wavelet-based fractal analysis on retina image for stroke prediction.

PubMed

Che Azemin, M Z; Kumar, Dinesh K; Wong, T Y; Wang, J J; Kawasaki, R; Mitchell, P; Arjunan, Sridhar P

2010-01-01

In this paper, we present a novel method of analyzing retinal vasculature using Fourier Fractal Dimension to extract the complexity of the retinal vasculature enhanced at different wavelet scales. Logistic regression was used as a fusion method to model the classifier for 5-year stroke prediction. The efficacy of this technique has been tested using standard pattern recognition performance evaluation, Receivers Operating Characteristics (ROC) analysis and medical prediction statistics, odds ratio. Stroke prediction model was developed using the proposed system.

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

NASA Astrophysics Data System (ADS)

Conway, John T.; Cohl, Howard S.

2010-06-01

A new method is presented for Fourier decomposition of the Helmholtz Green function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Green function are split into their half advanced + half retarded and half advanced-half retarded components, and closed form solutions for these components are then obtained in terms of a Horn function and a Kampé de Fériet function respectively. Series solutions for the Fourier coefficients are given in terms of associated Legendre functions, Bessel and Hankel functions and a hypergeometric function. These series are derived either from the closed form 2-dimensional hypergeometric solutions or from an integral representation, or from both. A simple closed form far-field solution for the general Fourier coefficient is derived from the Hankel series. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented. Fourth order ordinary differential equations for the Fourier coefficients are also given and discussed briefly.

A fast iterative convolution weighting approach for gridding-based direct Fourier three-dimensional reconstruction with correction for the contrast transfer function.

PubMed

Abrishami, V; Bilbao-Castro, J R; Vargas, J; Marabini, R; Carazo, J M; Sorzano, C O S

2015-10-01

We describe a fast and accurate method for the reconstruction of macromolecular complexes from a set of projections. Direct Fourier inversion (in which the Fourier Slice Theorem plays a central role) is a solution for dealing with this inverse problem. Unfortunately, the set of projections provides a non-equidistantly sampled version of the macromolecule Fourier transform in the single particle field (and, therefore, a direct Fourier inversion) may not be an optimal solution. In this paper, we introduce a gridding-based direct Fourier method for the three-dimensional reconstruction approach that uses a weighting technique to compute a uniform sampled Fourier transform. Moreover, the contrast transfer function of the microscope, which is a limiting factor in pursuing a high resolution reconstruction, is corrected by the algorithm. Parallelization of this algorithm, both on threads and on multiple CPU's, makes the process of three-dimensional reconstruction even faster. The experimental results show that our proposed gridding-based direct Fourier reconstruction is slightly more accurate than similar existing methods and presents a lower computational complexity both in terms of time and memory, thereby allowing its use on larger volumes. The algorithm is fully implemented in the open-source Xmipp package and is downloadable from http://xmipp.cnb.csic.es. Copyright © 2015 Elsevier B.V. All rights reserved.

Analysis of the physicochemical properties of post-manufacturing waste derived from production of methyl esters from rapeseed oil

NASA Astrophysics Data System (ADS)

Kachel-Jakubowska, Magdalena; Matwijczuk, Arkadiusz; Gagoś, Mariusz

2017-04-01

The technology of transesterification of biodiesel obtained from many agricultural products, which are often referred to as renewable resources, yields substantial amounts of by-products. They exhibit various properties that prompt scientific research into potential application thereof. Various spectroscopic methods, e.g. Fourier transform infrared spectroscopy, are being increasingly used in the research. In this paper, we present the results of Fourier transform infrared spectroscopy spectroscopy analyses of technical glycerine, distilled glycerine, and matter organic non glycerol, i.e. by-products of biodiesel production. To facilitate the spectroscopic analysis, a number of parameters were determined for all the materials, e.g. the calorific value, water content, sulphated ash content, methanol content, acidity, as well as the contents of esters, heavy metals, aldehydes, nitrogen, and phosphorus. The results indicate that the analysed products are characterised by a comparable calorific value in the range from 11.35 to 16.05 MJ kg-1 in the case of matter organic non glycerol and technical glycerine. Observation of changes in the position of selected peaks in the range of 3700-650 cm-1 in the Fourier transform infrared spectroscopy method facilitates determination of the level of degradation of the analysed material. Changes in the wavelength ranges can be used for monitoring the formation of secondary oxidation products containing carbonyl groups.

3D-FFT for Signature Detection in LWIR Images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Medvick, Patricia A.; Lind, Michael A.; Mackey, Patrick S.

Improvements in analysis detection exploitation are possible by applying whitened matched filtering within the Fourier domain to hyperspectral data cubes. We describe an implementation of a Three Dimensional Fast Fourier Transform Whitened Matched Filter (3DFFTMF) approach and, using several example sets of Long Wave Infra Red (LWIR) data cubes, compare the results with those from standard Whitened Matched Filter (WMF) techniques. Since the variability in shape of gaseous plumes precludes the use of spatial conformation in the matched filtering, the 3DFFTMF results were similar to those of two other WMF methods. Including a spatial low-pass filter within the Fourier spacemore » can improve signal to noise ratios and therefore improve detection limit by facilitating the mitigation of high frequency clutter. The improvement only occurs if the low-pass filter diameter is smaller than the plume diameter.« less

Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.

PubMed

Malacarne, Antonio; Park, Yongwoo; Li, Ming; LaRochelle, Sophie; Azaña, José

2015-12-14

We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme.

Computer-assisted techniques to evaluate fringe patterns

NASA Astrophysics Data System (ADS)

Sciammarella, Cesar A.; Bhat, Gopalakrishna K.

1992-01-01

Strain measurement using interferometry requires an efficient way to extract the desired information from interferometric fringes. Availability of digital image processing systems makes it possible to use digital techniques for the analysis of fringes. In the past, there have been several developments in the area of one dimensional and two dimensional fringe analysis techniques, including the carrier fringe method (spatial heterodyning) and the phase stepping (quasi-heterodyning) technique. This paper presents some new developments in the area of two dimensional fringe analysis, including a phase stepping technique supplemented by the carrier fringe method and a two dimensional Fourier transform method to obtain the strain directly from the discontinuous phase contour map.

Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

NASA Astrophysics Data System (ADS)

Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

2018-04-01

The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

Measuring charge nonuniformity in MOS devices

NASA Technical Reports Server (NTRS)

Maserjian, J.; Zamani, N.

1980-01-01

Convenient method of determining inherent lateral charge non-uniformities along silicon dioxide/silicon interface of metal-oxide-semiconductor (MOS) employs rapid measurement of capacitance of interface as function of voltage at liquid nitrogen temperature. Charge distribution is extracted by fast-Fourier-transform analysis of capacitance voltage (C-V) measurement.

Field test method to determine presence and quantity of modifiers in liquid asphalt - follow-up data analysis.

DOT National Transportation Integrated Search

2015-08-01

In an earlier study under the contract grant number BDV25-977-06, two portable Fourier transform infrared spectrometer : (FTIR) were evaluated for their ability to quickly detect and/or quantify the presence of polymer modifiers, including styrene : ...

Applications of FT-IR spectrophotometry in cancer diagnostics.

PubMed

Bunaciu, Andrei A; Hoang, Vu Dang; Aboul-Enein, Hassan Y

2015-01-01

This review provides a brief background to the application of infrared spectroscopy, including Fourier transform-infrared spectroscopy, in biological fluids. It is not meant to be complete or exhaustive but to provide the reader with sufficient background for selected applications in cancer diagnostics. Fourier transform-infrared spectroscopy (FT-IR) is a fast and nondestructive analytical method. The infrared spectrum of a mixture serves as the basis to quantitate its constituents, and a number of common clinical chemistry tests have proven to be feasible using this approach. This review focuses on biomedical FT-IR applications, published in the period 2009-2013, used for early detection of cancer through qualitative and quantitative analysis.

The τq-Fourier transform: Covariance and uniqueness

NASA Astrophysics Data System (ADS)

Kalogeropoulos, Nikolaos

2018-05-01

We propose an alternative definition for a Tsallis entropy composition-inspired Fourier transform, which we call “τq-Fourier transform”. We comment about the underlying “covariance” on the set of algebraic fields that motivates its introduction. We see that the definition of the τq-Fourier transform is automatically invertible in the proper context. Based on recent results in Fourier analysis, it turns that the τq-Fourier transform is essentially unique under the assumption of the exchange of the point-wise product of functions with their convolution.

Cryo-EM image alignment based on nonuniform fast Fourier transform.

PubMed

Yang, Zhengfan; Penczek, Pawel A

2008-08-01

In single particle analysis, two-dimensional (2-D) alignment is a fundamental step intended to put into register various particle projections of biological macromolecules collected at the electron microscope. The efficiency and quality of three-dimensional (3-D) structure reconstruction largely depends on the computational speed and alignment accuracy of this crucial step. In order to improve the performance of alignment, we introduce a new method that takes advantage of the highly accurate interpolation scheme based on the gridding method, a version of the nonuniform fast Fourier transform, and utilizes a multi-dimensional optimization algorithm for the refinement of the orientation parameters. Using simulated data, we demonstrate that by using less than half of the sample points and taking twice the runtime, our new 2-D alignment method achieves dramatically better alignment accuracy than that based on quadratic interpolation. We also apply our method to image to volume registration, the key step in the single particle EM structure refinement protocol. We find that in this case the accuracy of the method not only surpasses the accuracy of the commonly used real-space implementation, but results are achieved in much shorter time, making gridding-based alignment a perfect candidate for efficient structure determination in single particle analysis.

Cryo-EM Image Alignment Based on Nonuniform Fast Fourier Transform

PubMed Central

Yang, Zhengfan; Penczek, Pawel A.

2008-01-01

In single particle analysis, two-dimensional (2-D) alignment is a fundamental step intended to put into register various particle projections of biological macromolecules collected at the electron microscope. The efficiency and quality of three-dimensional (3-D) structure reconstruction largely depends on the computational speed and alignment accuracy of this crucial step. In order to improve the performance of alignment, we introduce a new method that takes advantage of the highly accurate interpolation scheme based on the gridding method, a version of the nonuniform Fast Fourier Transform, and utilizes a multi-dimensional optimization algorithm for the refinement of the orientation parameters. Using simulated data, we demonstrate that by using less than half of the sample points and taking twice the runtime, our new 2-D alignment method achieves dramatically better alignment accuracy than that based on quadratic interpolation. We also apply our method to image to volume registration, the key step in the single particle EM structure refinement protocol. We find that in this case the accuracy of the method not only surpasses the accuracy of the commonly used real-space implementation, but results are achieved in much shorter time, making gridding-based alignment a perfect candidate for efficient structure determination in single particle analysis. PMID:18499351

Electromagnetic Vortex-Based Radar Imaging Using a Single Receiving Antenna: Theory and Experimental Results

PubMed Central

Yuan, Tiezhu; Wang, Hongqiang; Cheng, Yongqiang; Qin, Yuliang

2017-01-01

Radar imaging based on electromagnetic vortex can achieve azimuth resolution without relative motion. The present paper investigates this imaging technique with the use of a single receiving antenna through theoretical analysis and experimental results. Compared with the use of multiple receiving antennas, the echoes from a single receiver cannot be used directly for image reconstruction using Fourier method. The reason is revealed by using the point spread function. An additional phase is compensated for each mode before imaging process based on the array parameters and the elevation of the targets. A proof-of-concept imaging system based on a circular phased array is created, and imaging experiments of corner-reflector targets are performed in an anechoic chamber. The azimuthal image is reconstructed by the use of Fourier transform and spectral estimation methods. The azimuth resolution of the two methods is analyzed and compared through experimental data. The experimental results verify the principle of azimuth resolution and the proposed phase compensation method. PMID:28335487

Generalized Fourier slice theorem for cone-beam image reconstruction.

PubMed

Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

2015-01-01

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

Insights into Fourier Synthesis and Analysis: Part 2--A Simplified Mathematics.

ERIC Educational Resources Information Center

Moore, Guy S. M.

1988-01-01

Introduced is an analysis of a waveform into its Fourier components. Topics included are simplified analysis of a square waveform, a triangular waveform, half-wave rectified alternating current (AC), and impulses. Provides the mathematical expression and simplified analysis diagram of each waveform. (YP)

Fast Fourier Transform Spectral Analysis Program

NASA Technical Reports Server (NTRS)

Daniel, J. A., Jr.; Graves, M. L.; Hovey, N. M.

1969-01-01

Fast Fourier Transform Spectral Analysis Program is used in frequency spectrum analysis of postflight, space vehicle telemetered trajectory data. This computer program with a digital algorithm can calculate power spectrum rms amplitudes and cross spectrum of sampled parameters at even time increments.

Fourier Analysis and Structure Determination: Part I: Fourier Transforms.

ERIC Educational Resources Information Center

Chesick, John P.

1989-01-01

Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Two dimensional Fourier transform methods for fringe pattern analysis

NASA Astrophysics Data System (ADS)

Sciammarella, C. A.; Bhat, G.

An overview of the use of FFTs for fringe pattern analysis is presented, with emphasis on fringe patterns containing displacement information. The techniques are illustrated via analysis of the displacement and strain distributions in the direction perpendicular to the loading, in a disk under diametral compression. The experimental strain distribution is compared to the theoretical, and the agreement is found to be excellent in regions where the elasticity solution models well the actual problem.

[Research on spatially modulated Fourier transform imaging spectrometer data processing method].

PubMed

Huang, Min; Xiangli, Bin; Lü, Qun-Bo; Zhou, Jin-Song; Jing, Juan-Juan; Cui, Yan

2010-03-01

Fourier transform imaging spectrometer is a new technic, and has been developed very rapidly in nearly ten years. The data catched by Fourier transform imaging spectrometer is indirect data, can not be used by user, and need to be processed by various approaches, including data pretreatment, apodization, phase correction, FFT, and spectral radicalization calibration. No paper so far has been found roundly to introduce this method. In the present paper, the author will give an effective method to process the interfering data to spectral data, and with this method we can obtain good result.

KAM Tori Construction Algorithms

NASA Astrophysics Data System (ADS)

Wiesel, W.

In this paper we evaluate and compare two algorithms for the calculation of KAM tori in Hamiltonian systems. The direct fitting of a torus Fourier series to a numerically integrated trajectory is the first method, while an accelerated finite Fourier transform is the second method. The finite Fourier transform, with Hanning window functions, is by far superior in both computational loading and numerical accuracy. Some thoughts on applications of KAM tori are offered.

Analysis of Complex Carbohydrate Composition in Plant Cell Wall Using Fourier Transformed Mid-Infrared Spectroscopy (FT-IR).

PubMed

Badhan, Ajay; Wang, Yuxi; McAllister, Tim A

2017-01-01

Fourier transformed mid-infrared spectroscopy (FTIR) is a powerful tool for compositional analysis of plant cell walls (Acebes et al., Front Plant Sci 5:303, 2014; Badhan et al., Biotechnol Biofuels 7:1-15, 2014; Badhan et al., BioMed Res Int 2015: 562952, 2015; Roach et al., Plant Physiol 156:1351-1363, 2011). The infrared spectrum generates a fingerprint of a sample with absorption peaks corresponding to the frequency of vibrations between the bonds of the atoms making up the material. Here, we describe a method focused on the use of FTIR in combination with principal component analysis (PCA) to characterize the composition of the plant cell wall. This method has been successfully used to study complex enzyme saccharification processes like rumen digestion to identify recalcitrant moieties in low-quality forage which resist rumen digestion (Badhan et al., BioMed Res Int 2015: 562952, 2015), as well as to characterize cell wall mutant lines or transgenic lines expressing exogenous hydrolases (Badhan et al., Biotechnol Biofuels 7:1-15, 2014; Roach et al., Plant Physiol 156:1351-1363, 2011). The FTIR method described here facilitates high-throughput identification of the major compositional differences across a large set of samples in a low cost and nondestructive manner.

Fourier transform infrared spectroscopy combined with chemometrics for discrimination of Curcuma longa, Curcuma xanthorrhiza and Zingiber cassumunar.

PubMed

Rohaeti, Eti; Rafi, Mohamad; Syafitri, Utami Dyah; Heryanto, Rudi

2015-02-25

Turmeric (Curcuma longa), java turmeric (Curcuma xanthorrhiza) and cassumunar ginger (Zingiber cassumunar) are widely used in traditional Indonesian medicines (jamu). They have similar color for their rhizome and possess some similar uses, so it is possible to substitute one for the other. The identification and discrimination of these closely-related plants is a crucial task to ensure the quality of the raw materials. Therefore, an analytical method which is rapid, simple and accurate for discriminating these species using Fourier transform infrared spectroscopy (FTIR) combined with some chemometrics methods was developed. FTIR spectra were acquired in the mid-IR region (4000-400 cm(-1)). Standard normal variate, first and second order derivative spectra were compared for the spectral data. Principal component analysis (PCA) and canonical variate analysis (CVA) were used for the classification of the three species. Samples could be discriminated by visual analysis of the FTIR spectra by using their marker bands. Discrimination of the three species was also possible through the combination of the pre-processed FTIR spectra with PCA and CVA, in which CVA gave clearer discrimination. Subsequently, the developed method could be used for the identification and discrimination of the three closely-related plant species. Copyright © 2014 Elsevier B.V. All rights reserved.

Imaging through ground-level turbulence by Fourier telescopy: Simulations and preliminary experiments

NASA Astrophysics Data System (ADS)

Randunu Pathirannehelage, Nishantha

Fourier telescopy imaging is a recently-developed imaging method that relies on active structured-light illumination of the object. Reflected/scattered light is measured by a large "light bucket" detector; processing of the detected signal yields the magnitude and phase of spatial frequency components of the object reflectance or transmittance function. An inverse Fourier transform results in the image. In 2012 a novel method, known as time-average Fourier telescopy (TAFT), was introduced by William T. Rhodes as a means for diffraction-limited imaging through ground-level atmospheric turbulence. This method, which can be applied to long horizontal-path terrestrial imaging, addresses a need that is not solved by the adaptive optics methods being used in astronomical imaging. Field-experiment verification of the TAFT concept requires instrumentation that is not available at Florida Atlantic University. The objective of this doctoral research program is thus to demonstrate, in the absence of full-scale experimentation, the feasibility of time-average Fourier telescopy through (a) the design, construction, and testing of small-scale laboratory instrumentation capable of exploring basic Fourier telescopy data-gathering operations, and (b) the development of MATLAB-based software capable of demonstrating the effect of kilometer-scale passage of laser beams through ground-level turbulence in a numerical simulation of TAFT.

Application of linear discriminant analysis and Attenuated Total Reflectance Fourier Transform Infrared microspectroscopy for diagnosis of colon cancer.

PubMed

Khanmohammadi, Mohammadreza; Bagheri Garmarudi, Amir; Samani, Simin; Ghasemi, Keyvan; Ashuri, Ahmad

2011-06-01

Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) microspectroscopy was applied for detection of colon cancer according to the spectral features of colon tissues. Supervised classification models can be trained to identify the tissue type based on the spectroscopic fingerprint. A total of 78 colon tissues were used in spectroscopy studies. Major spectral differences were observed in 1,740-900 cm(-1) spectral region. Several chemometric methods such as analysis of variance (ANOVA), cluster analysis (CA) and linear discriminate analysis (LDA) were applied for classification of IR spectra. Utilizing the chemometric techniques, clear and reproducible differences were observed between the spectra of normal and cancer cases, suggesting that infrared microspectroscopy in conjunction with spectral data processing would be useful for diagnostic classification. Using LDA technique, the spectra were classified into cancer and normal tissue classes with an accuracy of 95.8%. The sensitivity and specificity was 100 and 93.1%, respectively.

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wollaber, Allan B., E-mail: wollaber@lanl.go; Larsen, Edward W., E-mail: edlarsen@umich.ed

2011-02-20

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used 'Implicit Monte Carlo' (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or 'Semi-Analog Monte Carlo' (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if {alpha}, the IMC time-discretization parameter, satisfies 0.5 < {alpha} {<=} 1. This is consistent with conventional wisdom. However, wemore » also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.« less

A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

NASA Astrophysics Data System (ADS)

Wollaber, Allan B.; Larsen, Edward W.

2011-02-01

We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used “Implicit Monte Carlo” (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or “Semi-Analog Monte Carlo” (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if α, the IMC time-discretization parameter, satisfies 0.5 < α ⩽ 1. This is consistent with conventional wisdom. However, we also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.

Application of discrete Fourier inter-coefficient difference for assessing genetic sequence similarity.

PubMed

King, Brian R; Aburdene, Maurice; Thompson, Alex; Warres, Zach

2014-01-01

Digital signal processing (DSP) techniques for biological sequence analysis continue to grow in popularity due to the inherent digital nature of these sequences. DSP methods have demonstrated early success for detection of coding regions in a gene. Recently, these methods are being used to establish DNA gene similarity. We present the inter-coefficient difference (ICD) transformation, a novel extension of the discrete Fourier transformation, which can be applied to any DNA sequence. The ICD method is a mathematical, alignment-free DNA comparison method that generates a genetic signature for any DNA sequence that is used to generate relative measures of similarity among DNA sequences. We demonstrate our method on a set of insulin genes obtained from an evolutionarily wide range of species, and on a set of avian influenza viral sequences, which represents a set of highly similar sequences. We compare phylogenetic trees generated using our technique against trees generated using traditional alignment techniques for similarity and demonstrate that the ICD method produces a highly accurate tree without requiring an alignment prior to establishing sequence similarity.

Quantitative analysis of Sudan dye adulteration in paprika powder using FTIR spectroscopy

USDA-ARS?s Scientific Manuscript database

The presence of Sudan dye used illegally for coloring in food stuffs has become a point of food safety concern, especially in paprika- and chili-containing food products. Fourier transform infrared (FTIR) spectroscopy has been extensively used as an analytical method for quality control and safety m...

Simple Analysis of Historical Lime Mortars

ERIC Educational Resources Information Center

Pires, Joa~o

2015-01-01

A laboratory experiment is described in which a simple characterization of a historical lime mortar is made by the determination of its approximate composition by a gravimetric method. Fourier transform infrared (FTIR) spectroscopy and X-ray diffraction (XRD) are also used for the qualitative characterization of the lime mortar components. These…

Fractional-order Fourier analysis for ultrashort pulse characterization.

PubMed

Brunel, Marc; Coetmellec, Sébastien; Lelek, Mickael; Louradour, Frédéric

2007-06-01

We report what we believe to be the first experimental demonstration of ultrashort pulse characterization using fractional-order Fourier analysis. The analysis is applied to the interpretation of spectral interferometry resolved in time (SPIRIT) traces [which are spectral phase interferometry for direct electric field reconstruction (SPIDER)-like interferograms]. First, the fractional-order Fourier transformation is shown to naturally allow the determination of the cubic spectral phase coefficient of pulses to be analyzed. A simultaneous determination of both cubic and quadratic spectral phase coefficients of the pulses using the fractional-order Fourier series expansion is further demonstrated. This latter technique consists of localizing relative maxima in a 2D cartography representing decomposition coefficients. It is further used to reconstruct or filter SPIRIT traces.

Photocatalytic properties of hierarchical ZnO flowers synthesized by a sucrose-assisted hydrothermal method

NASA Astrophysics Data System (ADS)

Lv, Wei; Wei, Bo; Xu, Lingling; Zhao, Yan; Gao, Hong; Liu, Jia

2012-10-01

In this work, hierarchical ZnO flowers were synthesized via a sucrose-assisted urea hydrothermal method. The thermogravimetric analysis/differential thermal analysis (TGA-DTA) and Fourier transform infrared spectra (FTIR) showed that sucrose acted as a complexing agent in the synthesis process and assisted combustion during annealing. Photocatalytic activity was evaluated using the degradation of organic dye methyl orange. The sucrose added ZnO flowers showed improved activity, which was mainly attributed to the better crystallinity as confirmed by X-ray photoelectron spectroscopy (XPS) analysis. The effect of sucrose amount on photocatalytic activity was also studied.

A fast non-Fourier method for Landau-fluid operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimits, A. M., E-mail: dimits1@llnl.gov; Joseph, I.; Umansky, M. V.

An efficient and versatile non-Fourier method for the computation of Landau-fluid (LF) closure operators [Hammett and Perkins, Phys. Rev. Lett. 64, 3019 (1990)] is presented, based on an approximation by a sum of modified-Helmholtz-equation solves (SMHS) in configuration space. This method can yield fast-Fourier-like scaling of the computational time requirements and also provides a very compact data representation of these operators, even for plasmas with large spatial nonuniformity. As a result, the method can give significant savings compared with direct application of “delocalization kernels” [e.g., Schurtz et al., Phys. Plasmas 7, 4238 (2000)], both in terms of computational cost andmore » memory requirements. The method is of interest for the implementation of Landau-fluid models in situations where the spatial nonuniformity, particular geometry, or boundary conditions render a Fourier implementation difficult or impossible. Systematic procedures have been developed to optimize the resulting operators for accuracy and computational cost. The four-moment Landau-fluid model of Hammett and Perkins has been implemented in the BOUT++ code using the SMHS method for LF closure. Excellent agreement has been obtained for the one-dimensional plasma density response function between driven initial-value calculations using this BOUT++ implementation and matrix eigenvalue calculations using both Fourier and SMHS non-Fourier implementations of the LF closures. The SMHS method also forms the basis for the implementation, which has been carried out in the BOUT++ code, of the parallel and toroidal drift-resonance LF closures. The method is a key enabling tool for the extension of gyro-Landau-fluid models [e.g., Beer and Hammett, Phys. Plasmas 3, 4046 (1996)] to codes that treat regions with strong profile variation, such as the tokamak edge and scrapeoff-layer.« less

A fast non-Fourier method for Landau-fluid operatorsa)

NASA Astrophysics Data System (ADS)

Dimits, A. M.; Joseph, I.; Umansky, M. V.

2014-05-01

An efficient and versatile non-Fourier method for the computation of Landau-fluid (LF) closure operators [Hammett and Perkins, Phys. Rev. Lett. 64, 3019 (1990)] is presented, based on an approximation by a sum of modified-Helmholtz-equation solves (SMHS) in configuration space. This method can yield fast-Fourier-like scaling of the computational time requirements and also provides a very compact data representation of these operators, even for plasmas with large spatial nonuniformity. As a result, the method can give significant savings compared with direct application of "delocalization kernels" [e.g., Schurtz et al., Phys. Plasmas 7, 4238 (2000)], both in terms of computational cost and memory requirements. The method is of interest for the implementation of Landau-fluid models in situations where the spatial nonuniformity, particular geometry, or boundary conditions render a Fourier implementation difficult or impossible. Systematic procedures have been developed to optimize the resulting operators for accuracy and computational cost. The four-moment Landau-fluid model of Hammett and Perkins has been implemented in the BOUT++ code using the SMHS method for LF closure. Excellent agreement has been obtained for the one-dimensional plasma density response function between driven initial-value calculations using this BOUT++ implementation and matrix eigenvalue calculations using both Fourier and SMHS non-Fourier implementations of the LF closures. The SMHS method also forms the basis for the implementation, which has been carried out in the BOUT++ code, of the parallel and toroidal drift-resonance LF closures. The method is a key enabling tool for the extension of gyro-Landau-fluid models [e.g., Beer and Hammett, Phys. Plasmas 3, 4046 (1996)] to codes that treat regions with strong profile variation, such as the tokamak edge and scrapeoff-layer.

Modeling open nanophotonic systems using the Fourier modal method: generalization to 3D Cartesian coordinates.

PubMed

Häyrynen, Teppo; Osterkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz; Gregersen, Niels

2017-09-01

Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform k-space discretization was introduced for rotationally symmetric structures, providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)JOAOD61084-752910.1364/JOSAA.33.001298]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates, allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier k space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence, enabling more accurate and efficient modeling of open 3D nanophotonic structures.

Introduction to multigrid methods

NASA Technical Reports Server (NTRS)

Wesseling, P.

1995-01-01

These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered.

[Using 2-DCOS to identify the molecular spectrum peaks for the isomer in the multi-component mixture gases Fourier transform infrared analysis].

PubMed

Zhao, An-Xin; Tang, Xiao-Jun; Zhang, Zhong-Hua; Liu, Jun-Hua

2014-10-01

The generalized two-dimensional correlation spectroscopy and Fourier transform infrared were used to identify hydrocarbon isomers in the mixed gases for absorption spectra resolution enhancement. The Fourier transform infrared spectrum of n-butane and iso-butane and the two-dimensional correlation infrared spectrum of concentration perturbation were used for analysis as an example. The all band and the main absorption peak wavelengths of Fourier transform infrared spectrum for single component gas showed that the spectra are similar, and if they were mixed together, absorption peaks overlap and peak is difficult to identify. The synchronous and asynchronous spectrum of two-dimensional correlation spectrum can clearly identify the iso-butane and normal butane and their respective characteristic absorption peak intensity. Iso-butane has strong absorption characteristics spectrum lines at 2,893, 2,954 and 2,893 cm(-1), and n-butane at 2,895 and 2,965 cm(-1). The analysis result in this paper preliminary verified that the two-dimensional infrared correlation spectroscopy can be used for resolution enhancement in Fourier transform infrared spectrum quantitative analysis.

Synthesis and Characterization of Mesoporous Silica Functionalized with Calix[4]arene Derivatives

PubMed Central

Alahmadi, Sana M.; Mohamad, Sharifah; Maah, Mohd Jamil

2012-01-01

This work reports a new method to covalently attach calix[4]arene derivatives onto MCM-41, using a diisocyanate as a linker. The modified mesoporous silicates were characterized by fourier transform infrared spectroscopy (FTIR), thermal analysis (TGA) and elemental analysis. The FTIR spectra and TGA analysis verified that the calix[4]arene derivates are covalently attached to the mesoporous silica. The preservation of the MCM-41 channel system was checked by X-ray diffraction and nitrogen adsorption analysis. PMID:23202977

SaaS Platform for Time Series Data Handling

NASA Astrophysics Data System (ADS)

Oplachko, Ekaterina; Rykunov, Stanislav; Ustinin, Mikhail

2018-02-01

The paper is devoted to the description of MathBrain, a cloud-based resource, which works as a "Software as a Service" model. It is designed to maximize the efficiency of the current technology and to provide a tool for time series data handling. The resource provides access to the following analysis methods: direct and inverse Fourier transforms, Principal component analysis and Independent component analysis decompositions, quantitative analysis, magnetoencephalography inverse problem solution in a single dipole model based on multichannel spectral data.

Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

NASA Technical Reports Server (NTRS)

Holmes, J. J.; Balanis, C. A.

1974-01-01

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.

Frequency-radial duality based photoacoustic image reconstruction.

PubMed

Akramus Salehin, S M; Abhayapala, Thushara D

2012-07-01

Photoacoustic image reconstruction algorithms are usually slow due to the large sizes of data that are processed. This paper proposes a method for exact photoacoustic reconstruction for the spherical geometry in the limiting case of a continuous aperture and infinite measurement bandwidth that is faster than existing methods namely (1) backprojection method and (2) the Norton-Linzer method [S. J. Norton and M. Linzer, "Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solution for plane, cylindrical and spherical apertures," Biomedical Engineering, IEEE Trans. BME 28, 202-220 (1981)]. The initial pressure distribution is expanded using a spherical Fourier Bessel series. The proposed method estimates the Fourier Bessel coefficients and subsequently recovers the pressure distribution. A concept of frequency-radial duality is introduced that separates the information from the different radial basis functions by using frequencies corresponding to the Bessel zeros. This approach provides a means to analyze the information obtained given a measurement bandwidth. Using order analysis and numerical experiments, the proposed method is shown to be faster than both the backprojection and the Norton-Linzer methods. Further, the reconstructed images using the proposed methodology were of similar quality to the Norton-Linzer method and were better than the approximate backprojection method.

Modeling of earthquake ground motion in the frequency domain

NASA Astrophysics Data System (ADS)

Thrainsson, Hjortur

In recent years, the utilization of time histories of earthquake ground motion has grown considerably in the design and analysis of civil structures. It is very unlikely, however, that recordings of earthquake ground motion will be available for all sites and conditions of interest. Hence, there is a need for efficient methods for the simulation and spatial interpolation of earthquake ground motion. In addition to providing estimates of the ground motion at a site using data from adjacent recording stations, spatially interpolated ground motions can also be used in design and analysis of long-span structures, such as bridges and pipelines, where differential movement is important. The objective of this research is to develop a methodology for rapid generation of horizontal earthquake ground motion at any site for a given region, based on readily available source, path and site characteristics, or (sparse) recordings. The research includes two main topics: (i) the simulation of earthquake ground motion at a given site, and (ii) the spatial interpolation of earthquake ground motion. In topic (i), models are developed to simulate acceleration time histories using the inverse discrete Fourier transform. The Fourier phase differences, defined as the difference in phase angle between adjacent frequency components, are simulated conditional on the Fourier amplitude. Uniformly processed recordings from recent California earthquakes are used to validate the simulation models, as well as to develop prediction formulas for the model parameters. The models developed in this research provide rapid simulation of earthquake ground motion over a wide range of magnitudes and distances, but they are not intended to replace more robust geophysical models. In topic (ii), a model is developed in which Fourier amplitudes and Fourier phase angles are interpolated separately. A simple dispersion relationship is included in the phase angle interpolation. The accuracy of the interpolation model is assessed using data from the SMART-1 array in Taiwan. The interpolation model provides an effective method to estimate ground motion at a site using recordings from stations located up to several kilometers away. Reliable estimates of differential ground motion are restricted to relatively limited ranges of frequencies and inter-station spacings.

Penalized discriminant analysis for the detection of wild-grown and cultivated Ganoderma lucidum using Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Zhu, Ying; Tan, Tuck Lee

2016-04-01

An effective and simple analytical method using Fourier transform infrared (FTIR) spectroscopy to distinguish wild-grown high-quality Ganoderma lucidum (G. lucidum) from cultivated one is of essential importance for its quality assurance and medicinal value estimation. Commonly used chemical and analytical methods using full spectrum are not so effective for the detection and interpretation due to the complex system of the herbal medicine. In this study, two penalized discriminant analysis models, penalized linear discriminant analysis (PLDA) and elastic net (Elnet),using FTIR spectroscopy have been explored for the purpose of discrimination and interpretation. The classification performances of the two penalized models have been compared with two widely used multivariate methods, principal component discriminant analysis (PCDA) and partial least squares discriminant analysis (PLSDA). The Elnet model involving a combination of L1 and L2 norm penalties enabled an automatic selection of a small number of informative spectral absorption bands and gave an excellent classification accuracy of 99% for discrimination between spectra of wild-grown and cultivated G. lucidum. Its classification performance was superior to that of the PLDA model in a pure L1 setting and outperformed the PCDA and PLSDA models using full wavelength. The well-performed selection of informative spectral features leads to substantial reduction in model complexity and improvement of classification accuracy, and it is particularly helpful for the quantitative interpretations of the major chemical constituents of G. lucidum regarding its anti-cancer effects.

Automatic analysis of ciliary beat frequency using optical flow

NASA Astrophysics Data System (ADS)

Figl, Michael; Lechner, Manuel; Werther, Tobias; Horak, Fritz; Hummel, Johann; Birkfellner, Wolfgang

2012-02-01

Ciliary beat frequency (CBF) can be a useful parameter for diagnosis of several diseases, as e.g. primary ciliary dyskinesia. (PCD). CBF computation is usually done using manual evaluation of high speed video sequences, a tedious, observer dependent, and not very accurate procedure. We used the OpenCV's pyramidal implementation of the Lukas-Kanade algorithm for optical flow computation and applied this to certain objects to follow the movements. The objects were chosen by their contrast applying the corner detection by Shi and Tomasi. Discrimination between background/noise and cilia by a frequency histogram allowed to compute the CBF. Frequency analysis was done using the Fourier transform in matlab. The correct number of Fourier summands was found by the slope in an approximation curve. The method showed to be usable to distinguish between healthy and diseased samples. However there remain difficulties in automatically identifying the cilia, and also in finding enough high contrast cilia in the image. Furthermore the some of the higher contrast cilia are lost (and sometimes found) by the method, an easy way to distinguish the correct sub-path of a point's path have yet to be found in the case where the slope methods doesn't work.

Response of Autonomic Nervous System to Body Positions:

NASA Astrophysics Data System (ADS)

Xu, Aiguo; Gonnella, G.; Federici, A.; Stramaglia, S.; Simone, F.; Zenzola, A.; Santostasi, R.

Two mathematical methods, the Fourier and wavelet transforms, were used to study the short term cardiovascular control system. Time series, picked from electrocardiogram and arterial blood pressure lasting 6 minutes, were analyzed in supine position (SUP), during the first (HD1) and the second parts (HD2) of 90° head down tilt, and during recovery (REC). The wavelet transform was performed using the Haar function of period T=2j (j=1,2,...,6) to obtain wavelet coefficients. Power spectra components were analyzed within three bands, VLF (0.003-0.04), LF (0.04-0.15) and HF (0.15-0.4) with the frequency unit cycle/interval. Wavelet transform demonstrated a higher discrimination among all analyzed periods than the Fourier transform. For the Fourier analysis, the LF of R-R intervals and VLF of systolic blood pressure show more evident difference for different body positions. For the wavelet analysis, the systolic blood pressures show much more evident differences than the R-R intervals. This study suggests a difference in the response of the vessels and the heart to different body positions. The partial dissociation between VLF and LF results is a physiologically relevant finding of this work.

Molecular conformational analysis, vibrational spectra and normal coordinate analysis of trans-1,2-bis(3,5-dimethoxy phenyl)-ethene based on density functional theory calculations.

PubMed

Joseph, Lynnette; Sajan, D; Chaitanya, K; Isac, Jayakumary

2014-03-25

The conformational behavior and structural stability of trans-1,2-bis(3,5-dimethoxy phenyl)-ethene (TDBE) were investigated by using density functional theory (DFT) method with the B3LYP/6-311++G(d,p) basis set combination. The vibrational wavenumbers of TDBE were computed at DFT level and complete vibrational assignments were made on the basis of normal coordinate analysis calculations (NCA). The DFT force field transformed to natural internal coordinates was corrected by a well-established set of scale factors that were found to be transferable to the title compound. The infrared and Raman spectra were also predicted from the calculated intensities. The observed Fourier transform infrared (FTIR) and Fourier transform (FT) Raman vibrational wavenumbers were analyzed and compared with the theoretically predicted vibrational spectra. Comparison of the simulated spectra with the experimental spectra provides important information about the ability of the computational method to describe the vibrational modes. Information about the size, shape, charge density distribution and site of chemical reactivity of the molecules has been obtained by mapping electron density isosurface with electrostatic potential surfaces (ESP). Copyright © 2013 Elsevier B.V. All rights reserved.

Hilbert-Huang transform analysis of dynamic and earthquake motion recordings

USGS Publications Warehouse

Zhang, R.R.; Ma, S.; Safak, E.; Hartzell, S.

2003-01-01

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition (EMD) and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function (IMF) components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low- and high-frequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.

Nondestructive surface analysis for material research using fiber optic vibrational spectroscopy

NASA Astrophysics Data System (ADS)

Afanasyeva, Natalia I.

2001-11-01

The advanced methods of fiber optical vibrational spectroscopy (FOVS) has been developed in conjunction with interferometer and low-loss, flexible, and nontoxic optical fibers, sensors, and probes. The combination of optical fibers and sensors with Fourier Transform (FT) spectrometer has been used in the range from 2.5 to 12micrometers . This technique serves as an ideal diagnostic tool for surface analysis of numerous and various diverse materials such as complex structured materials, fluids, coatings, implants, living cells, plants, and tissue. Such surfaces as well as living tissue or plants are very difficult to investigate in vivo by traditional FT infrared or Raman spectroscopy methods. The FOVS technique is nondestructive, noninvasive, fast (15 sec) and capable of operating in remote sampling regime (up to a fiber length of 3m). Fourier transform infrared (FTIR) and Raman fiber optic spectroscopy operating with optical fibers has been suggested as a new powerful tool. These techniques are highly sensitive techniques for structural studies in material research and various applications during process analysis to determine molecular composition, chemical bonds, and molecular conformations. These techniques could be developed as a new tool for quality control of numerous materials as well as noninvasive biopsy.

High-accuracy 3D Fourier forward modeling of gravity field based on the Gauss-FFT technique

NASA Astrophysics Data System (ADS)

Zhao, Guangdong; Chen, Bo; Chen, Longwei; Liu, Jianxin; Ren, Zhengyong

2018-03-01

The 3D Fourier forward modeling of 3D density sources is capable of providing 3D gravity anomalies coincided with the meshed density distribution within the whole source region. This paper firstly derives a set of analytical expressions through employing 3D Fourier transforms for calculating the gravity anomalies of a 3D density source approximated by right rectangular prisms. To reduce the errors due to aliasing and imposed periodicity as well as edge effects in the Fourier domain modeling, we develop the 3D Gauss-FFT technique to the 3D gravity anomalies forward modeling. The capability and adaptability of this scheme are tested by simple synthetic models. The results show that the accuracy of the Fourier forward methods using the Gauss-FFT with 4 Gaussian-nodes (or more) is comparable to that of the spatial modeling. In addition, the "ghost" source effects in the 3D Fourier forward gravity field due to imposed periodicity of the standard FFT algorithm are remarkably depressed by the application of the 3D Gauss-FFT algorithm. More importantly, the execution times of the 4 nodes Gauss-FFT modeling are reduced by two orders of magnitude compared with the spatial forward method. It demonstrates that the improved Fourier method is an efficient and accurate forward modeling tool for the gravity field.

Mapping agroecological zones and time lag in vegetation growth by means of Fourier analysis of time series of NDVI images

NASA Technical Reports Server (NTRS)

Menenti, M.; Azzali, S.; Verhoef, W.; Van Swol, R.

1993-01-01

Examples are presented of applications of a fast Fourier transform algorithm to analyze time series of images of Normalized Difference Vegetation Index values. The results obtained for a case study on Zambia indicated that differences in vegetation development among map units of an existing agroclimatic map were not significant, while reliable differences were observed among the map units obtained using the Fourier analysis.

Application of abstract harmonic analysis to the high-speed recognition of images

NASA Technical Reports Server (NTRS)

Usikov, D. A.

1979-01-01

Methods are constructed for rapidly computing correlation functions using the theory of abstract harmonic analysis. The theory developed includes as a particular case the familiar Fourier transform method for a correlation function which makes it possible to find images which are independent of their translation in the plane. Two examples of the application of the general theory described are the search for images, independent of their rotation and scale, and the search for images which are independent of their translations and rotations in the plane.

Bilinear Time-frequency Analysis for Lamb Wave Signal Detected by Electromagnetic Acoustic Transducer

NASA Astrophysics Data System (ADS)

Sun, Wenxiu; Liu, Guoqiang; Xia, Hui; Xia, Zhengwu

2018-03-01

Accurate acquisition of the detection signal travel time plays a very important role in cross-hole tomography. The experimental platform of aluminum plate under the perpendicular magnetic field is established and the bilinear time-frequency analysis methods, Wigner-Ville Distribution (WVD) and the pseudo-Wigner-Ville distribution (PWVD), are applied to analyse the Lamb wave signals detected by electromagnetic acoustic transducer (EMAT). By extracting the same frequency component of the time-frequency spectrum as the excitation frequency, the travel time information can be obtained. In comparison with traditional linear time-frequency analysis method such as short-time Fourier transform (STFT), the bilinear time-frequency analysis method PWVD is more appropriate in extracting travel time and recognizing patterns of Lamb wave.

Brillouin Scattering Spectrum Analysis Based on Auto-Regressive Spectral Estimation

NASA Astrophysics Data System (ADS)

Huang, Mengyun; Li, Wei; Liu, Zhangyun; Cheng, Linghao; Guan, Bai-Ou

2018-06-01

Auto-regressive (AR) spectral estimation technology is proposed to analyze the Brillouin scattering spectrum in Brillouin optical time-domain refelectometry. It shows that AR based method can reliably estimate the Brillouin frequency shift with an accuracy much better than fast Fourier transform (FFT) based methods provided the data length is not too short. It enables about 3 times improvement over FFT at a moderate spatial resolution.

Vibrational Spectral Studies of Gemfibrozil

NASA Astrophysics Data System (ADS)

Benitta, T. Asenath; Balendiran, G. K.; James, C.

2008-11-01

The Fourier Transform Raman and infrared spectra of the crystallized drug molecule 5-(2,5-Dimethylphenoxy)-2,2-dimethylpentanoic acid (Gemfibrozil) have been recorded and analyzed. Quantum chemical computational methods have been employed using Gaussian 03 software package based on Hartree Fock method for theoretically modeling the grown molecule. The optimized geometry and vibrational frequencies have been predicted. Observed vibrational modes have been assigned with the aid of normal coordinate analysis.

A BASIC program for the removal of noise from reaction traces using Fourier filtering.

PubMed

Brittain, T

1989-04-01

Software for the removal of noise from reaction curves using the principle of Fourier filtering has been written in BASIC to execute on a PC. The program inputs reaction traces which are subjected to a rotation-inversion process, to produce functions suitable for Fourier analysis. Fourier transformation into the frequency domain is followed by multiplication of the transform by a rectangular filter function, to remove the noise frequencies. Inverse transformation then yields a noise-reduced reaction trace suitable for further analysis. The program is interactive at each stage and could easily be modified to remove noise from a range of input data types.

A simplified implementation of edge detection in MATLAB is faster and more sensitive than fast fourier transform for actin fiber alignment quantification.

PubMed

Kemeny, Steven Frank; Clyne, Alisa Morss

2011-04-01

Fiber alignment plays a critical role in the structure and function of cells and tissues. While fiber alignment quantification is important to experimental analysis and several different methods for quantifying fiber alignment exist, many studies focus on qualitative rather than quantitative analysis perhaps due to the complexity of current fiber alignment methods. Speed and sensitivity were compared in edge detection and fast Fourier transform (FFT) for measuring actin fiber alignment in cells exposed to shear stress. While edge detection using matrix multiplication was consistently more sensitive than FFT, image processing time was significantly longer. However, when MATLAB functions were used to implement edge detection, MATLAB's efficient element-by-element calculations and fast filtering techniques reduced computation cost 100 times compared to the matrix multiplication edge detection method. The new computation time was comparable to the FFT method, and MATLAB edge detection produced well-distributed fiber angle distributions that statistically distinguished aligned and unaligned fibers in half as many sample images. When the FFT sensitivity was improved by dividing images into smaller subsections, processing time grew larger than the time required for MATLAB edge detection. Implementation of edge detection in MATLAB is simpler, faster, and more sensitive than FFT for fiber alignment quantification.

Robust alignment of chromatograms by statistically analyzing the shifts matrix generated by moving window fast Fourier transform cross-correlation.

PubMed

Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian

2015-03-01

Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Numerous applications of fiber optic evanescent wave Fourier transform infrared (FEW-FTIR) spectroscopy for subsurface structural analysis

NASA Astrophysics Data System (ADS)

Afanasyeva, Natalia I.; Welser, Leslie; Bruch, Reinhard F.; Kano, Angelique; Makhine, Volodymyr

1999-10-01

A new infrared (IR) interferometric method has been developed in conjunction with low-loss, flexible optical fibers, sensors, and probes. This combination of fiber optical sensors and Fourier Transform (FT) spectrometers can be applied to many fields, including (1) noninvasive medical diagnostics of cancer and other different diseases in vivo, (2) minimally invasive bulk diagnostics of tissue, (3) remote monitoring of tissue, chemical processes, and environment, (4) surface analysis of polymers and other materials, (5) characterization of the quality of food, pharmacological products, cosmetics, paper, and other wood-related products, as well as (6) agricultural, forensic, geological, mining, and archeological field measurements. In particular, our nondestructive, fast, compact, portable, remote and highly sensitive diagnostics tools are very promising for subsurface analysis at the molecular level without sample preparation. For example, this technique is ideal for different types of soft porous foams, rough polymers, and rock surfaces. Such surfaces, as well as living tissue, are very difficult to investigate by traditional FTIR methods. We present here FEW-FTIR spectra of polymers, banana and grapefruit peels, and living tissues detected directly at surfaces. In addition, results on the vibrational spectral analysis of normal and pathological skin tissue in the region of 850 - 4000 cm-1 are discussed.

Exploring functional data analysis and wavelet principal component analysis on ecstasy (MDMA) wastewater data.

PubMed

Salvatore, Stefania; Bramness, Jørgen G; Røislien, Jo

2016-07-12

Wastewater-based epidemiology (WBE) is a novel approach in drug use epidemiology which aims to monitor the extent of use of various drugs in a community. In this study, we investigate functional principal component analysis (FPCA) as a tool for analysing WBE data and compare it to traditional principal component analysis (PCA) and to wavelet principal component analysis (WPCA) which is more flexible temporally. We analysed temporal wastewater data from 42 European cities collected daily over one week in March 2013. The main temporal features of ecstasy (MDMA) were extracted using FPCA using both Fourier and B-spline basis functions with three different smoothing parameters, along with PCA and WPCA with different mother wavelets and shrinkage rules. The stability of FPCA was explored through bootstrapping and analysis of sensitivity to missing data. The first three principal components (PCs), functional principal components (FPCs) and wavelet principal components (WPCs) explained 87.5-99.6 % of the temporal variation between cities, depending on the choice of basis and smoothing. The extracted temporal features from PCA, FPCA and WPCA were consistent. FPCA using Fourier basis and common-optimal smoothing was the most stable and least sensitive to missing data. FPCA is a flexible and analytically tractable method for analysing temporal changes in wastewater data, and is robust to missing data. WPCA did not reveal any rapid temporal changes in the data not captured by FPCA. Overall the results suggest FPCA with Fourier basis functions and common-optimal smoothing parameter as the most accurate approach when analysing WBE data.

Phase-shift detection in a Fourier-transform method for temperature sensing using a tapered fiber microknot resonator.

PubMed

Larocque, Hugo; Lu, Ping; Bao, Xiaoyi

2016-04-01

Phase-shift detection in a fast-Fourier-transform (FFT)-based spectrum analysis technique for temperature sensing using a tapered fiber microknot resonator is proposed and demonstrated. Multiple transmission peaks in the FFT spectrum of the device were identified as optical modes having completed different amounts of round trips within the ring structure. Temperature variation induced phase shifts for each set of peaks were characterized, and experimental results show that different peaks have distinct temperature sensitivities reaching values up to -0.542  rad/°C, which is about 10 times greater than that of a regular adiabatic taper Mach-Zehnder interferometer when using similar phase-tracking schemes.

Vicinal fluorine-fluorine coupling constants: Fourier analysis.

PubMed

San Fabián, J; Westra Hoekzema, A J A

2004-10-01

Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants (3JFF) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (Cn> or =3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason 3JFF do not follow the Karplus equation. (c) 2004 American Institute of Physics

Vicinal fluorine-fluorine coupling constants: Fourier analysis

NASA Astrophysics Data System (ADS)

San Fabián, J.; Westra Hoekzema, A. J. A.

2004-10-01

Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants (3JFF) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (Cn⩾3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason 3JFF do not follow the Karplus equation.

Apparatus for direct-to-digital spatially-heterodyned holography

DOEpatents

Thomas, Clarence E.; Hanson, Gregory R.

2006-12-12

An apparatus operable to record a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis includes: a laser; a beamsplitter optically coupled to the laser; an object optically coupled to the beamsplitter; a focusing lens optically coupled to both the beamsplitter and the object; a digital recorder optically coupled to the focusing lens; and a computer that performs a Fourier transform, applies a digital filter, and performs an inverse Fourier transform. A reference beam and an object beam are focused by the focusing lens at a focal plane of the digital recorder to form a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis which is recorded by the digital recorder, and the computer transforms the recorded spatially low-frequency heterodyne hologram including spatially heterodyne fringes and shifts axes in Fourier space to sit on top of a heterodyne carrier frequency defined by an angle between the reference beam and the object beam and cuts off signals around an original origin before performing the inverse Fourier transform.

On the matrix Fourier filtering problem for a class of models of nonlinear optical systems with a feedback

NASA Astrophysics Data System (ADS)

Razgulin, A. V.; Sazonova, S. V.

2017-09-01

A novel statement of the Fourier filtering problem based on the use of matrix Fourier filters instead of conventional multiplier filters is considered. The basic properties of the matrix Fourier filtering for the filters in the Hilbert-Schmidt class are established. It is proved that the solutions with a finite energy to the periodic initial boundary value problem for the quasi-linear functional differential diffusion equation with the matrix Fourier filtering Lipschitz continuously depend on the filter. The problem of optimal matrix Fourier filtering is formulated, and its solvability for various classes of matrix Fourier filters is proved. It is proved that the objective functional is differentiable with respect to the matrix Fourier filter, and the convergence of a version of the gradient projection method is also proved.

Mountain Wave Analysis Using Fourier Methods

DTIC Science & Technology

2007-10-01

model for altitudes up to 18 km for the same location using the Hilo , Hawaii 1200 UTC rawinsonde for the background velocity and temperature profile... Hawaii terrain and atmosphere 46 for 12 Dec 2002 vii Tables 1...20 3. Three-Layer Model Specifications for Hawaii 12 December 2002 06 UTC 22 4. Three-Layer Model

[Fast determination of induction period of motor gasoline using Fourier transform attenuated total reflection infrared spectroscopy].

PubMed

Liu, Ya-Fei; Yuan, Hong-Fu; Song, Chun-Feng; Xie, Jin-Chun; Li, Xiao-Yu; Yan, De-Lin

2014-11-01

A new method is proposed for the fast determination of the induction period of gasoline using Fourier transform attenuated total reflection infrared spectroscopy (ATR-FTIR). A dedicated analysis system with the function of spectral measurement, data processing, display and storage was designed and integrated using a Fourier transform infrared spectrometer module and chemometric software. The sample presentation accessory designed which has advantages of constant optical path, convenient sample injection and cleaning is composed of a nine times reflection attenuated total reflectance (ATR) crystal of zinc selenide (ZnSe) coated with a diamond film and a stainless steel lid with sealing device. The influence of spectral scanning number and repeated sample loading times on the spectral signal-to-noise ratio was studied. The optimum spectral scanning number is 15 times and the optimum sample loading number is 4 times. Sixty four different gasoline samples were collected from the Beijing-Tianjin area and the induction period values were determined as reference data by standard method GB/T 8018-87. The infrared spectra of these samples were collected in the operating condition mentioned above using the dedicated fast analysis system. Spectra were pretreated using mean centering and 1st derivative to reduce the influence of spectral noise and baseline shift A PLS calibration model for the induction period was established by correlating the known induction period values of the samples with their spectra. The correlation coefficient (R2), standard error of calibration (SEC) and standard error of prediction (SEP) of the model are 0.897, 68.3 and 91.9 minutes, respectively. The relative deviation of the model for gasoline induction period prediction is less than 5%, which meets the requirements of repeatability tolerance in GB method. The new method is simple and fast. It takes no more than 3 minutes to detect one sample. Therefore, the method is feasible for implementing fast determination of gasoline induction period, and of a positive meaning in the evaluation of fuel quality.

Fourier-domain angle-resolved low coherence interferometry for clinical detection of dysplasia

NASA Astrophysics Data System (ADS)

Terry, Neil G.; Zhu, Yizheng; Wax, Adam

2010-02-01

Improved methods for detecting dysplasia, or pre-cancerous growth are a current clinical need, particularly in the esophagus. The currently accepted method of random biopsy and histological analysis provides only a limited examination of tissue in question while being coupled with a long time delay for diagnosis. Light scattering spectroscopy, in contrast, allows for inspection of the cellular structure and organization of tissue in vivo. Fourier-domain angle-resolved low-coherence interferometry (a/LCI) is a novel light scattering spectroscopy technique that provides quantitative depth-resolved morphological measurements of the size and optical density of the examined cell nuclei, which are characteristic biomarkers of dysplasia. Previously, clinical viability of the a/LCI system was demonstrated through analysis of ex vivo human esophageal tissue in Barrett's esophagus patients using a portable a/LCI, as was the development of a clinical a/LCI system. Data indicating the feasibility of the technique in other organ sites (colon, oral cavity) will be presented. We present an adaptation of the a/LCI system that will be used to investigate the presence of dysplasia in vivo in Barrett's esophagus patients.

A new method to cluster genomes based on cumulative Fourier power spectrum.

PubMed

Dong, Rui; Zhu, Ziyue; Yin, Changchuan; He, Rong L; Yau, Stephen S-T

2018-06-20

Analyzing phylogenetic relationships using mathematical methods has always been of importance in bioinformatics. Quantitative research may interpret the raw biological data in a precise way. Multiple Sequence Alignment (MSA) is used frequently to analyze biological evolutions, but is very time-consuming. When the scale of data is large, alignment methods cannot finish calculation in reasonable time. Therefore, we present a new method using moments of cumulative Fourier power spectrum in clustering the DNA sequences. Each sequence is translated into a vector in Euclidean space. Distances between the vectors can reflect the relationships between sequences. The mapping between the spectra and moment vector is one-to-one, which means that no information is lost in the power spectra during the calculation. We cluster and classify several datasets including Influenza A, primates, and human rhinovirus (HRV) datasets to build up the phylogenetic trees. Results show that the new proposed cumulative Fourier power spectrum is much faster and more accurately than MSA and another alignment-free method known as k-mer. The research provides us new insights in the study of phylogeny, evolution, and efficient DNA comparison algorithms for large genomes. The computer programs of the cumulative Fourier power spectrum are available at GitHub (https://github.com/YaulabTsinghua/cumulative-Fourier-power-spectrum). Copyright © 2018. Published by Elsevier B.V.

Step-scan T cell-based differential Fourier transform infrared photoacoustic spectroscopy (DFTIR-PAS) for detection of ambient air contaminants

NASA Astrophysics Data System (ADS)

Liu, Lixian; Mandelis, Andreas; Huan, Huiting; Melnikov, Alexander

2016-10-01

A step-scan differential Fourier transform infrared photoacoustic spectroscopy (DFTIR-PAS) using a commercial FTIR spectrometer was developed theoretically and experimentally for air contaminant monitoring. The configuration comprises two identical, small-size and low-resonance-frequency T cells satisfying the conflicting requirements of low chopping frequency and limited space in the sample compartment. Carbon dioxide (CO2) IR absorption spectra were used to demonstrate the capability of the DFTIR-PAS method to detect ambient pollutants. A linear amplitude response to CO2 concentrations from 100 to 10,000 ppmv was observed, leading to a theoretical detection limit of 2 ppmv. The differential mode was able to suppress the coherent noise, thereby imparting the DFTIR-PAS method with a better signal-to-noise ratio and lower theoretical detection limit than the single mode. The results indicate that it is possible to use step-scan DFTIR-PAS with T cells as a quantitative method for high sensitivity analysis of ambient contaminants.

Wavefront-aberration measurement and systematic-error analysis of a high numerical-aperture objective

NASA Astrophysics Data System (ADS)

Liu, Zhixiang; Xing, Tingwen; Jiang, Yadong; Lv, Baobin

2018-02-01

A two-dimensional (2-D) shearing interferometer based on an amplitude chessboard grating was designed to measure the wavefront aberration of a high numerical-aperture (NA) objective. Chessboard gratings offer better diffraction efficiencies and fewer disturbing diffraction orders than traditional cross gratings. The wavefront aberration of the tested objective was retrieved from the shearing interferogram using the Fourier transform and differential Zernike polynomial-fitting methods. Grating manufacturing errors, including the duty-cycle and pattern-deviation errors, were analyzed with the Fourier transform method. Then, according to the relation between the spherical pupil and planar detector coordinates, the influence of the distortion of the pupil coordinates was simulated. Finally, the systematic error attributable to grating alignment errors was deduced through the geometrical ray-tracing method. Experimental results indicate that the measuring repeatability (3σ) of the wavefront aberration of an objective with NA 0.4 was 3.4 mλ. The systematic-error results were consistent with previous analyses. Thus, the correct wavefront aberration can be obtained after calibration.

Evaluation of algorithms for geological thermal-inertia mapping

NASA Technical Reports Server (NTRS)

Miller, S. H.; Watson, K.

1977-01-01

The errors incurred in producing a thermal inertia map are of three general types: measurement, analysis, and model simplification. To emphasize the geophysical relevance of these errors, they were expressed in terms of uncertainty in thermal inertia and compared with the thermal inertia values of geologic materials. Thus the applications and practical limitations of the technique were illustrated. All errors were calculated using the parameter values appropriate to a site at the Raft River, Id. Although these error values serve to illustrate the magnitudes that can be expected from the three general types of errors, extrapolation to other sites should be done using parameter values particular to the area. Three surface temperature algorithms were evaluated: linear Fourier series, finite difference, and Laplace transform. In terms of resulting errors in thermal inertia, the Laplace transform method is the most accurate (260 TIU), the forward finite difference method is intermediate (300 TIU), and the linear Fourier series method the least accurate (460 TIU).

A fast Fourier transform on multipoles (FFTM) algorithm for solving Helmholtz equation in acoustics analysis.

PubMed

Ong, Eng Teo; Lee, Heow Pueh; Lim, Kian Meng

2004-09-01

This article presents a fast algorithm for the efficient solution of the Helmholtz equation. The method is based on the translation theory of the multipole expansions. Here, the speedup comes from the convolution nature of the translation operators, which can be evaluated rapidly using fast Fourier transform algorithms. Also, the computations of the translation operators are accelerated by using the recursive formulas developed recently by Gumerov and Duraiswami [SIAM J. Sci. Comput. 25, 1344-1381(2003)]. It is demonstrated that the algorithm can produce good accuracy with a relatively low order of expansion. Efficiency analyses of the algorithm reveal that it has computational complexities of O(Na), where a ranges from 1.05 to 1.24. However, this method requires substantially more memory to store the translation operators as compared to the fast multipole method. Hence, despite its simplicity in implementation, this memory requirement issue may limit the application of this algorithm to solving very large-scale problems.

Fourier holographic display for augmented reality using holographic optical element

NASA Astrophysics Data System (ADS)

Li, Gang; Lee, Dukho; Jeong, Youngmo; Lee, Byoungho

2016-03-01

A method for realizing a three-dimensional see-through augmented reality in Fourier holographic display is proposed. A holographic optical element (HOE) with the function of Fourier lens is adopted in the system. The Fourier hologram configuration causes the real scene located behind the lens to be distorted. In the proposed method, since the HOE is transparent and it functions as the lens just for Bragg matched condition, there is not any distortion when people observe the real scene through the lens HOE (LHOE). Furthermore, two optical characteristics of the recording material are measured for confirming the feasibility of using LHOE in the proposed see-through augmented reality holographic display. The results are verified experimentally.

Rapid differentiation of Listeria monocytogenes epidemic clones III and IV and their intact compared with heat-killed populations using Fourier transform infrared spectroscopy and chemometrics.

PubMed

Nyarko, Esmond B; Puzey, Kenneth A; Donnelly, Catherine W

2014-06-01

The objectives of this study were to determine if Fourier transform infrared (FT-IR) spectroscopy and multivariate statistical analysis (chemometrics) could be used to rapidly differentiate epidemic clones (ECs) of Listeria monocytogenes, as well as their intact compared with heat-killed populations. FT-IR spectra were collected from dried thin smears on infrared slides prepared from aliquots of 10 μL of each L. monocytogenes ECs (ECIII: J1-101 and R2-499; ECIV: J1-129 and J1-220), and also from intact and heat-killed cell populations of each EC strain using 250 scans at a resolution of 4 cm(-1) in the mid-infrared region in a reflectance mode. Chemometric analysis of spectra involved the application of the multivariate discriminant method for canonical variate analysis (CVA) and linear discriminant analysis (LDA). CVA of the spectra in the wavelength region 4000 to 600 cm(-1) separated the EC strains while LDA resulted in a 100% accurate classification of all spectra in the data set. Further, CVA separated intact and heat-killed cells of each EC strain and there was 100% accuracy in the classification of all spectra when LDA was applied. FT-IR spectral wavenumbers 1650 to 1390 cm(-1) were used to separate heat-killed and intact populations of L. monocytogenes. The FT-IR spectroscopy method allowed discrimination between strains that belong to the same EC. FT-IR is a highly discriminatory and reproducible method that can be used for the rapid subtyping of L. monocytogenes, as well as for the detection of live compared with dead populations of the organism. Fourier transform infrared (FT-IR) spectroscopy and multivariate statistical analysis can be used for L. monocytogenes source tracking and for clinical case isolate comparison during epidemiological investigations since the method is capable of differentiating epidemic clones and it uses a library of well-characterized strains. The FT-IR method is potentially less expensive and more rapid compared to genetic subtyping methods, and can be used for L. monocytogenes strain typing by food industries and public health agencies to enable faster response and intervention to listeriosis outbreaks. FT-IR can also be applied for routine monitoring of the pathogen in food processing plants and for investigating postprocessing contamination because it is capable of differentiating heat-killed and viable L. monocytogenes populations. © 2014 Institute of Food Technologists®

Improved Plane-Wave Ultrasound Beamforming by Incorporating Angular Weighting and Coherent Compounding in Fourier Domain.

PubMed

Chen, Chuan; Hendriks, Gijs A G M; van Sloun, Ruud J G; Hansen, Hendrik H G; de Korte, Chris L

2018-05-01

In this paper, a novel processing framework is introduced for Fourier-domain beamforming of plane-wave ultrasound data, which incorporates coherent compounding and angular weighting in the Fourier domain. Angular weighting implies spectral weighting by a 2-D steering-angle-dependent filtering template. The design of this filter is also optimized as part of this paper. Two widely used Fourier-domain plane-wave ultrasound beamforming methods, i.e., Lu's f-k and Stolt's f-k methods, were integrated in the framework. To enable coherent compounding in Fourier domain for the Stolt's f-k method, the original Stolt's f-k method was modified to achieve alignment of the spectra for different steering angles in k-space. The performance of the framework was compared for both methods with and without angular weighting using experimentally obtained data sets (phantom and in vivo), and data sets (phantom) provided by the IEEE IUS 2016 plane-wave beamforming challenge. The addition of angular weighting enhanced the image contrast while preserving image resolution. This resulted in images of equal quality as those obtained by conventionally used delay-and-sum (DAS) beamforming with apodization and coherent compounding. Given the lower computational load of the proposed framework compared to DAS, to our knowledge it can, therefore, be concluded that it outperforms commonly used beamforming methods such as Stolt's f-k, Lu's f-k, and DAS.

Assessing resolution in live cell structured illumination microscopy

NASA Astrophysics Data System (ADS)

Pospíšil, Jakub; Fliegel, Karel; Klíma, Miloš

2017-12-01

Structured Illumination Microscopy (SIM) is a powerful super-resolution technique, which is able to enhance the resolution of optical microscope beyond the Abbe diffraction limit. In the last decade, numerous SIM methods that achieve the resolution of 100 nm in the lateral dimension have been developed. The SIM setups with new high-speed cameras and illumination pattern generators allow rapid acquisition of the live specimen. Therefore, SIM is widely used for investigation of the live structures in molecular and live cell biology. Quantitative evaluation of resolution enhancement in a real sample is essential to describe the efficiency of super-resolution microscopy technique. However, measuring the resolution of a live cell sample is a challenging task. Based on our experimental findings, the widely used Fourier ring correlation (FRC) method does not seem to be well suited for measuring the resolution of SIM live cell video sequences. Therefore, the resolution assessing methods based on Fourier spectrum analysis are often used. We introduce a measure based on circular average power spectral density (PSDca) estimated from a single SIM image (one video frame). PSDca describes the distribution of the power of a signal with respect to its spatial frequency. Spatial resolution corresponds to the cut-off frequency in Fourier space. In order to estimate the cut-off frequency from a noisy signal, we use a spectral subtraction method for noise suppression. In the future, this resolution assessment approach might prove useful also for single-molecule localization microscopy (SMLM) live cell imaging.

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces.

PubMed

Hornikx, Maarten; Dragna, Didier

2015-07-01

The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

The New Physical Optics Notebook: Tutorials in Fourier Optics.

ERIC Educational Resources Information Center

Reynolds, George O.; And Others

This is a textbook of Fourier optics for the classroom or self-study. Major topics included in the 38 chapters are: Huygens' principle and Fourier transforms; image formation; optical coherence theory; coherent imaging; image analysis; coherent noise; interferometry; holography; communication theory techniques; analog optical computing; phase…

Discrimination between Bacillus and Alicyclobacillus isolates in apple juice by Fourier transform infrared spectroscopy and multivariate analysis.

PubMed

Al-Holy, Murad A; Lin, Mengshi; Alhaj, Omar A; Abu-Goush, Mahmoud H

2015-02-01

Alicyclobacillus is a causative agent of spoilage in pasteurized and heat-treated apple juice products. Differentiating between this genus and the closely related Bacillus is crucially important. In this study, Fourier transform infrared spectroscopy (FT-IR) was used to identify and discriminate between 4 Alicyclobacillus strains and 4 Bacillus isolates inoculated individually into apple juice. Loading plots over the range of 1350 and 1700 cm(-1) reflected the most distinctive biochemical features of Bacillus and Alicyclobacillus. Multivariate statistical methods (for example, principal component analysis and soft independent modeling of class analogy) were used to analyze the spectral data. Distinctive separation of spectral samples was observed. This study demonstrates that FT-IR spectroscopy in combination with multivariate analysis could serve as a rapid and effective tool for fruit juice industry to differentiate between Bacillus and Alicyclobacillus and to distinguish between species belonging to these 2 genera. © 2015 Institute of Food Technologists®

Big Data in Reciprocal Space: Sliding Fast Fourier Transforms for Determining Periodicity

DOE PAGES

Vasudevan, Rama K.; Belianinov, Alex; Gianfrancesco, Anthony G.; ...

2015-03-03

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La5/8Ca3/8MnO3 films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) of themore » Sliding FFT dataset reveal the distinct changes in crystallography, step edges and boundaries between the multiple sub-lattices. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.« less

Big Data in Reciprocal Space: Sliding Fast Fourier Transforms for Determining Periodicity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasudevan, Rama K.; Belianinov, Alex; Gianfrancesco, Anthony G.

Significant advances in atomically resolved imaging of crystals and surfaces have occurred in the last decade allowing unprecedented insight into local crystal structures and periodicity. Yet, the analysis of the long-range periodicity from the local imaging data, critical to correlation of functional properties and chemistry to the local crystallography, remains a challenge. Here, we introduce a Sliding Fast Fourier Transform (FFT) filter to analyze atomically resolved images of in-situ grown La5/8Ca3/8MnO3 films. We demonstrate the ability of sliding FFT algorithm to differentiate two sub-lattices, resulting from a mixed-terminated surface. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) of themore » Sliding FFT dataset reveal the distinct changes in crystallography, step edges and boundaries between the multiple sub-lattices. The method is universal for images with any periodicity, and is especially amenable to atomically resolved probe and electron-microscopy data for rapid identification of the sub-lattices present.« less

Fully-automated identification of fish species based on otolith contour: using short-time Fourier transform and discriminant analysis (STFT-DA).

PubMed

Salimi, Nima; Loh, Kar Hoe; Kaur Dhillon, Sarinder; Chong, Ving Ching

2016-01-01

Background. Fish species may be identified based on their unique otolith shape or contour. Several pattern recognition methods have been proposed to classify fish species through morphological features of the otolith contours. However, there has been no fully-automated species identification model with the accuracy higher than 80%. The purpose of the current study is to develop a fully-automated model, based on the otolith contours, to identify the fish species with the high classification accuracy. Methods. Images of the right sagittal otoliths of 14 fish species from three families namely Sciaenidae, Ariidae, and Engraulidae were used to develop the proposed identification model. Short-time Fourier transform (STFT) was used, for the first time in the area of otolith shape analysis, to extract important features of the otolith contours. Discriminant Analysis (DA), as a classification technique, was used to train and test the model based on the extracted features. Results. Performance of the model was demonstrated using species from three families separately, as well as all species combined. Overall classification accuracy of the model was greater than 90% for all cases. In addition, effects of STFT variables on the performance of the identification model were explored in this study. Conclusions. Short-time Fourier transform could determine important features of the otolith outlines. The fully-automated model proposed in this study (STFT-DA) could predict species of an unknown specimen with acceptable identification accuracy. The model codes can be accessed at http://mybiodiversityontologies.um.edu.my/Otolith/ and https://peerj.com/preprints/1517/. The current model has flexibility to be used for more species and families in future studies.

[The investigation and simulation of a novel spatially modulated micro-Fourier transform spectrometer].

PubMed

Kong, Yan-mei; Liang, Jing-qiu; Wang, Bo; Liang, Zhong-zhu; Xu, Da-wei; Zhang, Jun

2009-04-01

Fourier transform spectrometer (FTS) is widely used in science and industry for the measurement of electromagnetic spectra, and it's trend of minimization is particularly pronounced in many applications. A novel model of a micro FTS with no moving parts is proposed and analyzed. During the analysis, the gradients which mainly introduce the phase error are accounted for in details. Based on these assumptions and the improved Mertz phase correcting method, the spectrum of the signal is simulated, given the real extended light source. The resolution can reach 3.43 nm@800 nm, with high SNR limiting resolving ability 6.8 dB. The novel micro FTS could be made by MOEMS technology, which has some advantages over the conventional micro dispersive spectrometers based on the traditional technology, and this method can also afford some new concepts on the design of spectrometers. The research work is underway to demonstrate the theory.

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fouriermore » transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.« less

Capillary waves' dynamics at the nanoscale

NASA Astrophysics Data System (ADS)

Delgado-Buscalioni, Rafael; Chacón, Enrique; Tarazona, Pedro

2008-12-01

We study the dynamics of thermally excited capillary waves (CW) at molecular scales, using molecular dynamics simulations of simple liquid slabs. The analysis is based on the Fourier modes of the liquid surface, constructed via the intrinsic sampling method (Chacón and Tarazona 2003 Phys. Rev. Lett. 91 166103). We obtain the time autocorrelation of the Fourier modes to get the frequency and damping rate Γd(q) of each mode, with wavenumber q. Continuum hydrodynamics predicts \\Gamma (q) \\propto q\\gamma (q) and thus provides a dynamic measure of the q-dependent surface tension, γd(q). The dynamical estimation is much more robust than the structural prediction based on the amplitude of the Fourier mode, γs(q). Using the optimal estimation of the intrinsic surface, we obtain quantitative agreement between the structural and dynamic pictures. Quite surprisingly, the hydrodynamic prediction for CW remains valid up to wavelengths of about four molecular diameters. Surface tension hydrodynamics break down at shorter scales, whereby a transition to a molecular diffusion regime is observed.

Near-common-path interferometer for imaging Fourier-transform spectroscopy in wide-field microscopy

PubMed Central

Wadduwage, Dushan N.; Singh, Vijay Raj; Choi, Heejin; Yaqoob, Zahid; Heemskerk, Hans; Matsudaira, Paul; So, Peter T. C.

2017-01-01

Imaging Fourier-transform spectroscopy (IFTS) is a powerful method for biological hyperspectral analysis based on various imaging modalities, such as fluorescence or Raman. Since the measurements are taken in the Fourier space of the spectrum, it can also take advantage of compressed sensing strategies. IFTS has been readily implemented in high-throughput, high-content microscope systems based on wide-field imaging modalities. However, there are limitations in existing wide-field IFTS designs. Non-common-path approaches are less phase-stable. Alternatively, designs based on the common-path Sagnac interferometer are stable, but incompatible with high-throughput imaging. They require exhaustive sequential scanning over large interferometric path delays, making compressive strategic data acquisition impossible. In this paper, we present a novel phase-stable, near-common-path interferometer enabling high-throughput hyperspectral imaging based on strategic data acquisition. Our results suggest that this approach can improve throughput over those of many other wide-field spectral techniques by more than an order of magnitude without compromising phase stability. PMID:29392168

Use of Fourier transforms for asynoptic mapping: Applications to the Upper Atmosphere Research Satellite microwave limb sounder

NASA Technical Reports Server (NTRS)

Elson, Lee S.; Froidevaux, Lucien

1993-01-01

Fourier analysis has been applied to data obtained from limb viewing instruments on the Upper Atmosphere Research Satellite. A coordinate system rotation facilitates the efficient computation of Fourier transforms in the temporal and longitudinal domains. Fields such as ozone (O3), chlorine monoxide (ClO), temperature, and water vapor have been transformed by this process. The transforms have been inverted to provide maps of these quantities at selected times, providing a method of accurate time interpolation. Maps obtained by this process show evidence of both horizontal and vertical transport of important trace species such as O3 and ClO. An examination of the polar regions indicates that large-scale planetary variations are likely to play a significant role in transporting midstratospheric O3 into the polar regions. There is also evidence that downward transport occurs, providing a means of moving O3 into the polar vortex at lower altitudes. The transforms themselves show the structure and propagation characteristics of wave variations.

Fourier Transform Ultrasound Spectroscopy for the determination of wave propagation parameters.

PubMed

Pal, Barnana

2017-01-01

The reported results for ultrasonic wave attenuation constant (α) in pure water show noticeable inconsistency in magnitude. A "Propagating-Wave" model analysis of the most popular pulse-echo technique indicates that this is a consequence of the inherent wave propagation characteristics in a bounded medium. In the present work Fourier Transform Ultrasound Spectroscopy (FTUS) is adopted to determine ultrasonic wave propagation parameters, the wave number (k) and attenuation constant (α) at 1MHz frequency in tri-distilled water at room temperature (25°C). Pulse-echo signals obtained under same experimental conditions regarding the exciting input signal and reflecting boundary wall of the water container for various lengths of water columns are captured. The Fast Fourier Transform (FFT) components of the echo signals are taken to compute k, α and r, the reflection constant at the boundary, using Oak Ridge and Oxford method. The results are compared with existing literature values. Copyright © 2016 Elsevier B.V. All rights reserved.

A Heuristic Fast Method to Solve the Nonlinear Schroedinger Equation in Fiber Bragg Gratings with Arbitrary Shape Input Pulse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emami, F.; Hatami, M.; Keshavarz, A. R.

2009-08-13

Using a combination of Runge-Kutta and Jacobi iterative method, we could solve the nonlinear Schroedinger equation describing the pulse propagation in FBGs. By decomposing the electric field to forward and backward components in fiber Bragg grating and utilizing the Fourier series analysis technique, the boundary value problem of a set of coupled equations governing the pulse propagation in FBG changes to an initial condition coupled equations which can be solved by simple Runge-Kutta method.

Power maps and wavefront for progressive addition lenses in eyeglass frames.

PubMed

Mejía, Yobani; Mora, David A; Díaz, Daniel E

2014-10-01

To evaluate a method for measuring the cylinder, sphere, and wavefront of progressive addition lenses (PALs) in eyeglass frames. We examine the contour maps of cylinder, sphere, and wavefront of a PAL assembled in an eyeglass frame using an optical system based on a Hartmann test. To reduce the data noise, particularly in the border of the eyeglass frame, we implement a method based on the Fourier analysis to extrapolate spots outside the eyeglass frame. The spots are extrapolated up to a circular pupil that circumscribes the eyeglass frame and compared with data obtained from a circular uncut PAL. By using the Fourier analysis to extrapolate spots outside the eyeglass frame, we can remove the edge artifacts of the PAL within its frame and implement the modal method to fit wavefront data with Zernike polynomials within a circular aperture that circumscribes the frame. The extrapolated modal maps from framed PALs accurately reflect maps obtained from uncut PALs and provide smoothed maps for the cylinder and sphere inside the eyeglass frame. The proposed method for extrapolating spots outside the eyeglass frame removes edge artifacts of the contour maps (wavefront, cylinder, and sphere), which may be useful to facilitate measurements such as the length and width of the progressive corridor for a PAL in its frame. The method can be applied to any shape of eyeglass frame.

Real-Time Stability Margin Measurements for X-38 Robustness Analysis

NASA Technical Reports Server (NTRS)

Bosworth, John T.; Stachowiak, Susan J.

2005-01-01

A method has been developed for real-time stability margin measurement calculations. The method relies on a tailored-forced excitation targeted to a specific frequency range. Computation of the frequency response is matched to the specific frequencies contained in the excitation. A recursive Fourier transformation is used to make the method compatible with real-time calculation. The method was incorporated into the X-38 nonlinear simulation and applied to an X-38 robustness test. X-38 stability margins were calculated for different variations in aerodynamic and mass properties over the vehicle flight trajectory. The new method showed results comparable to more traditional stability analysis techniques, and at the same time, this new method provided coverage that is more complete and increased efficiency.

A Quantitative Approach to Scar Analysis

PubMed Central

Khorasani, Hooman; Zheng, Zhong; Nguyen, Calvin; Zara, Janette; Zhang, Xinli; Wang, Joyce; Ting, Kang; Soo, Chia

2011-01-01

Analysis of collagen architecture is essential to wound healing research. However, to date no consistent methodologies exist for quantitatively assessing dermal collagen architecture in scars. In this study, we developed a standardized approach for quantitative analysis of scar collagen morphology by confocal microscopy using fractal dimension and lacunarity analysis. Full-thickness wounds were created on adult mice, closed by primary intention, and harvested at 14 days after wounding for morphometrics and standard Fourier transform-based scar analysis as well as fractal dimension and lacunarity analysis. In addition, transmission electron microscopy was used to evaluate collagen ultrastructure. We demonstrated that fractal dimension and lacunarity analysis were superior to Fourier transform analysis in discriminating scar versus unwounded tissue in a wild-type mouse model. To fully test the robustness of this scar analysis approach, a fibromodulin-null mouse model that heals with increased scar was also used. Fractal dimension and lacunarity analysis effectively discriminated unwounded fibromodulin-null versus wild-type skin as well as healing fibromodulin-null versus wild-type wounds, whereas Fourier transform analysis failed to do so. Furthermore, fractal dimension and lacunarity data also correlated well with transmission electron microscopy collagen ultrastructure analysis, adding to their validity. These results demonstrate that fractal dimension and lacunarity are more sensitive than Fourier transform analysis for quantification of scar morphology. PMID:21281794

Glaucoma diagnosis by mapping macula with Fourier domain optical coherence tomography

NASA Astrophysics Data System (ADS)

Tan, Ou; Lu, Ake; Chopra, Vik; Varma, Rohit; Hiroshi, Ishikawa; Schuman, Joel; Huang, David

2008-03-01

A new image segmentation method was developed to detect macular retinal sub-layers boundary on newly-developed Fourier-Domain Optical Coherence Tomography (FD-OCT) with macular grid scan pattern. The segmentation results were used to create thickness map of macular ganglion cell complex (GCC), which contains the ganglion cell dendrites, cell bodies and axons. Overall average and several pattern analysis parameters were defined on the GCC thickness map and compared for the diagnosis of glaucoma. Intraclass correlation (ICC) is used to compare the reproducibility of the parameters. Area under receiving operative characteristic curve (AROC) was calculated to compare the diagnostic power. The result is also compared to the output of clinical time-domain OCT (TD-OCT). We found that GCC based parameters had good repeatability and comparable diagnostic power with circumpapillary nerve fiber layer (cpNFL) thickness. Parameters based on pattern analysis can increase the diagnostic power of GCC macular mapping.

Spectral analysis based on fast Fourier transformation (FFT) of surveillance data: the case of scarlet fever in China.

PubMed

Zhang, T; Yang, M; Xiao, X; Feng, Z; Li, C; Zhou, Z; Ren, Q; Li, X

2014-03-01

Many infectious diseases exhibit repetitive or regular behaviour over time. Time-domain approaches, such as the seasonal autoregressive integrated moving average model, are often utilized to examine the cyclical behaviour of such diseases. The limitations for time-domain approaches include over-differencing and over-fitting; furthermore, the use of these approaches is inappropriate when the assumption of linearity may not hold. In this study, we implemented a simple and efficient procedure based on the fast Fourier transformation (FFT) approach to evaluate the epidemic dynamic of scarlet fever incidence (2004-2010) in China. This method demonstrated good internal and external validities and overcame some shortcomings of time-domain approaches. The procedure also elucidated the cycling behaviour in terms of environmental factors. We concluded that, under appropriate circumstances of data structure, spectral analysis based on the FFT approach may be applicable for the study of oscillating diseases.

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Discrimination among populations of sockeye salmon fry with Fourier analysis of otolith banding patterns formed during incubation

USGS Publications Warehouse

Finn, James E.; Burger, Carl V.; Holland-Bartels, Leslie E.

1997-01-01

We used otolith banding patterns formed during incubation to discriminate among hatchery- and wild-incubated fry of sockeye salmon Oncorhynchus nerka from Tustumena Lake, Alaska. Fourier analysis of otolith luminance profiles was used to describe banding patterns: the amplitudes of individual Fourier harmonics were discriminant variables. Correct classification of otoliths to either hatchery or wild origin was 83.1% (cross-validation) and 72.7% (test data) with the use of quadratic discriminant function analysts on 10 Fourier amplitudes. Overall classification rates among the six test groups (one hatchery and five wild groups) were 46.5% (cross-validation) and 39.3% (test data) with the use of linear discriminant function analysis on 16 Fourier amplitudes. Although classification rates for wild-incubated fry from any one site never exceeded 67% (cross-validation) or 60% (test data), location-specific information was evident for all groups because the probability of classifying an individual to its true incubation location was significantly greater than chance. Results indicate phenotypic differences in otolith microstructure among incubation sites separated by less than 10 km. Analysis of otolith luminance profiles is a potentially useful technique for discriminating among and between various populations of hatchery and wild fish.

Harmonic Fourier beads method for studying rare events on rugged energy surfaces.

PubMed

Khavrutskii, Ilja V; Arora, Karunesh; Brooks, Charles L

2006-11-07

We present a robust, distributable method for computing minimum free energy paths of large molecular systems with rugged energy landscapes. The method, which we call harmonic Fourier beads (HFB), exploits the Fourier representation of a path in an appropriate coordinate space and proceeds iteratively by evolving a discrete set of harmonically restrained path points-beads-to generate positions for the next path. The HFB method does not require explicit knowledge of the free energy to locate the path. To compute the free energy profile along the final path we employ an umbrella sampling method in two generalized dimensions. The proposed HFB method is anticipated to aid the study of rare events in biomolecular systems. Its utility is demonstrated with an application to conformational isomerization of the alanine dipeptide in gas phase.

Sparsity guided empirical wavelet transform for fault diagnosis of rolling element bearings

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yi, Cai; Tsui, Kwok-Leung; Lin, Jianhui

2018-02-01

Rolling element bearings are widely used in various industrial machines, such as electric motors, generators, pumps, gearboxes, railway axles, turbines, and helicopter transmissions. Fault diagnosis of rolling element bearings is beneficial to preventing any unexpected accident and reducing economic loss. In the past years, many bearing fault detection methods have been developed. Recently, a new adaptive signal processing method called empirical wavelet transform attracts much attention from readers and engineers and its applications to bearing fault diagnosis have been reported. The main problem of empirical wavelet transform is that Fourier segments required in empirical wavelet transform are strongly dependent on the local maxima of the amplitudes of the Fourier spectrum of a signal, which connotes that Fourier segments are not always reliable and effective if the Fourier spectrum of the signal is complicated and overwhelmed by heavy noises and other strong vibration components. In this paper, sparsity guided empirical wavelet transform is proposed to automatically establish Fourier segments required in empirical wavelet transform for fault diagnosis of rolling element bearings. Industrial bearing fault signals caused by single and multiple railway axle bearing defects are used to verify the effectiveness of the proposed sparsity guided empirical wavelet transform. Results show that the proposed method can automatically discover Fourier segments required in empirical wavelet transform and reveal single and multiple railway axle bearing defects. Besides, some comparisons with three popular signal processing methods including ensemble empirical mode decomposition, the fast kurtogram and the fast spectral correlation are conducted to highlight the superiority of the proposed method.

An Investigation into the Use of Spatially-Filtered Fourier Transforms to Classify Mammary Lesions.

DTIC Science & Technology

difference in Fourier space between lesioned breast tissue which would enable accurate computer classification of benign and malignant lesions. Low...separate benign and malignant breast tissue. However, no success was achieved when using two-dimensional Fourier transform and power spectrum analysis. (Author)

An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.

ERIC Educational Resources Information Center

Eastman, M. P.; And Others

1986-01-01

Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.

Supervision of Ethylene Propylene Diene M-Class (EPDM) Rubber Vulcanization and Recovery Processes Using Attenuated Total Reflection Fourier Transform Infrared (ATR FT-IR) Spectroscopy and Multivariate Analysis.

PubMed

Riba Ruiz, Jordi-Roger; Canals, Trini; Cantero, Rosa

2017-01-01

Ethylene propylene diene monomer (EPDM) rubber is widely used in a diverse type of applications, such as the automotive, industrial and construction sectors among others. Due to its appealing features, the consumption of vulcanized EPDM rubber is growing significantly. However, environmental issues are forcing the application of devulcanization processes to facilitate recovery, which has led rubber manufacturers to implement strict quality controls. Consequently, it is important to develop methods for supervising the vulcanizing and recovery processes of such products. This paper deals with the supervision process of EPDM compounds by means of Fourier transform mid-infrared (FT-IR) spectroscopy and suitable multivariate statistical methods. An expedited and nondestructive classification approach was applied to a sufficient number of EPDM samples with different applied processes, that is, with and without application of vulcanizing agents, vulcanized samples, and microwave treated samples. First the FT-IR spectra of the samples is acquired and next it is processed by applying suitable feature extraction methods, i.e., principal component analysis and canonical variate analysis to obtain the latent variables to be used for classifying test EPDM samples. Finally, the k nearest neighbor algorithm was used in the classification stage. Experimental results prove the accuracy of the proposed method and the potential of FT-IR spectroscopy in this area, since the classification accuracy can be as high as 100%.

Fast focus estimation using frequency analysis in digital holography.

PubMed

Oh, Seungtaik; Hwang, Chi-Young; Jeong, Il Kwon; Lee, Sung-Keun; Park, Jae-Hyeung

2014-11-17

A novel fast frequency-based method to estimate the focus distance of digital hologram for a single object is proposed. The focus distance is computed by analyzing the distribution of intersections of smoothed-rays. The smoothed-rays are determined by the directions of energy flow which are computed from local spatial frequency spectrum based on the windowed Fourier transform. So our method uses only the intrinsic frequency information of the optical field on the hologram and therefore does not require any sequential numerical reconstructions and focus detection techniques of conventional photography, both of which are the essential parts in previous methods. To show the effectiveness of our method, numerical results and analysis are presented as well.

Analysis of calibration-free wavelength-scanned wavelength modulation spectroscopy for practical gas sensing using tunable diode lasers

NASA Astrophysics Data System (ADS)

Sun, K.; Chao, X.; Sur, R.; Goldenstein, C. S.; Jeffries, J. B.; Hanson, R. K.

2013-12-01

A novel strategy has been developed for analysis of wavelength-scanned, wavelength modulation spectroscopy (WMS) with tunable diode lasers (TDLs). The method simulates WMS signals to compare with measurements to determine gas properties (e.g., temperature, pressure and concentration of the absorbing species). Injection-current-tuned TDLs have simultaneous wavelength and intensity variation, which severely complicates the Fourier expansion of the simulated WMS signal into harmonics of the modulation frequency (fm). The new method differs from previous WMS analysis strategies in two significant ways: (1) the measured laser intensity is used to simulate the transmitted laser intensity and (2) digital lock-in and low-pass filter software is used to expand both simulated and measured transmitted laser intensities into harmonics of the modulation frequency, WMS-nfm (n = 1, 2, 3,…), avoiding the need for an analytic model of intensity modulation or Fourier expansion of the simulated WMS harmonics. This analysis scheme is valid at any optical depth, modulation index, and at all values of scanned-laser wavelength. The method is demonstrated and validated with WMS of H2O dilute in air (1 atm, 296 K, near 1392 nm). WMS-nfm harmonics for n = 1 to 6 are extracted and the simulation and measurements are found in good agreement for the entire WMS lineshape. The use of 1f-normalization strategies to realize calibration-free wavelength-scanned WMS is also discussed.

Tomography: Three Dimensional Image Construction. Applications of Analysis to Medical Radiology. [and] Genetic Counseling. Applications of Probability to Medicine. [and] The Design of Honeycombs. Applications of Differential Equations to Biology. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 318, 456, 502.

ERIC Educational Resources Information Center

Solomon, Frederick; And Others.

This document consists of three modules. The first looks at applications of analysis to medical radiology. The goals are to provide: 1) acquaintance with a significant applied mathematics problem utilizing Fourier Transforms; 2) generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) introduction to…

A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger-Poisson equations with discontinuous potentials

NASA Astrophysics Data System (ADS)

Lu, Tiao; Cai, Wei

2008-10-01

In this paper, we propose a high order Fourier spectral-discontinuous Galerkin method for time-dependent Schrödinger-Poisson equations in 3-D spaces. The Fourier spectral Galerkin method is used for the two periodic transverse directions and a high order discontinuous Galerkin method for the longitudinal propagation direction. Such a combination results in a diagonal form for the differential operators along the transverse directions and a flexible method to handle the discontinuous potentials present in quantum heterojunction and supperlattice structures. As the derivative matrices are required for various time integration schemes such as the exponential time differencing and Crank Nicholson methods, explicit derivative matrices of the discontinuous Galerkin method of various orders are derived. Numerical results, using the proposed method with various time integration schemes, are provided to validate the method.

A simplified analysis of the multigrid V-cycle as a fast elliptic solver

NASA Technical Reports Server (NTRS)

Decker, Naomi H.; Taasan, Shlomo

1988-01-01

For special model problems, Fourier analysis gives exact convergence rates for the two-grid multigrid cycle and, for more general problems, provides estimates of the two-grid convergence rates via local mode analysis. A method is presented for obtaining mutigrid convergence rate estimates for cycles involving more than two grids (using essentially the same analysis as for the two-grid cycle). For the simple cast of the V-cycle used as a fast Laplace solver on the unit square, the k-grid convergence rate bounds obtained by this method are sharper than the bounds predicted by the variational theory. Both theoretical justification and experimental evidence are presented.

Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method.

PubMed

Guizal, Brahim; Barchiesi, Dominique; Felbacq, Didier

2003-12-01

We have developed a new formulation of the coupled-wave method (CWM) to handle aperiodic lamellar structures, and it will be referred to as the aperiodic coupled-wave method (ACWM). The space is still divided into three regions, but the fields are written by use of their Fourier integrals instead of the Fourier series. In the modulated region the relative permittivity is represented by its Fourier transform, and then a set of integro-differential equations is derived. Discretizing the last system leads to a set of ordinary differential equations that is reduced to an eigenvalue problem, as is usually done in the CWM. To assess the method, we compare our results with three independent formalisms: the Rayleigh perturbation method for small samples, the volume integral method, and the finite-element method.

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Brody, Dorje C.

2018-04-01

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

Construction of high frame rate images with Fourier transform

NASA Astrophysics Data System (ADS)

Peng, Hu; Lu, Jian-Yu

2002-05-01

Traditionally, images are constructed with a delay-and-sum method that adjusts the phases of received signals (echoes) scattered from the same point in space so that they are summed in phase. Recently, the relationship between the delay-and-sum method and the Fourier transform is investigated [Jian-yu Lu, Anjun Liu, and Hu Peng, ``High frame rate and delay-and-sum imaging methods,'' IEEE Trans. Ultrason. Ferroelectr. Freq. Control (submitted)]. In this study, a generic Fourier transform method is developed. Two-dimensional (2-D) or three-dimensional (3-D) high frame rate images can be constructed using the Fourier transform with a single transmission of an ultrasound pulse from an array as long as the transmission field of the array is known. To verify our theory, computer simulations have been performed with a linear array, a 2-D array, a convex curved array, and a spherical 2-D array. The simulation results are consistent with our theory. [Work supported in part by Grant 5RO1 HL60301 from NIH.

Determination of trans Fat in Selected Fast Food Products and Hydrogenated Fats of India Using Attenuated Total Reflection Fourier Transform Infrared (ATR-FTIR) Spectroscopy.

PubMed

Khan, Mohd Umar; Hassan, Mohammad Fahimul; Rauf, Abdul

2017-01-01

This paper reports the application of a simple and rapid method for the determination of trans fatty acid (TFA) content in some of the selected Indian fast food products and hydrogenated fats using Fourier transform infrared (FTIR) spectroscopy in conjunction with second derivative procedure. FTIR spectroscopy has been successfully applied to trans measurement using the absorbance bands at or near 966 cm -1 in the FTIR spectra. It was found from the analysis that TFA content of fast food product was ranging from 1.57% to 3.83% of the total fat while for hydrogenated fats, comparatively large quantity of TFA was detected in the range of 3.31% to 4.73%. Since GC-FID is most widely used method for the determination of fatty acid (FA) composition, this method was used for the sake of comparison. Value of regression coefficient was found very close to one (0.99503) with standard deviation of 0.10247 showing a good agreement between GC-FID and proposed ATR-FTIR method.

Determination of vibration-rotation lines intensities from absorption Fourier spectra

NASA Technical Reports Server (NTRS)

Mandin, J. Y.

1979-01-01

The method presented allows the line intensities to be calculated from either their equivalent widths, heights, or quantities deduced from spectra obtained by Fourier spectrometry. This method has proven its effectiveness in measuring intensities of 60 lines of the molecule H2O with a precision of 10%. However, this method cannot be applied to isolated lines.

A Fourier-based compressed sensing technique for accelerated CT image reconstruction using first-order methods.

PubMed

Choi, Kihwan; Li, Ruijiang; Nam, Haewon; Xing, Lei

2014-06-21

As a solution to iterative CT image reconstruction, first-order methods are prominent for the large-scale capability and the fast convergence rate [Formula: see text]. In practice, the CT system matrix with a large condition number may lead to slow convergence speed despite the theoretically promising upper bound. The aim of this study is to develop a Fourier-based scaling technique to enhance the convergence speed of first-order methods applied to CT image reconstruction. Instead of working in the projection domain, we transform the projection data and construct a data fidelity model in Fourier space. Inspired by the filtered backprojection formalism, the data are appropriately weighted in Fourier space. We formulate an optimization problem based on weighted least-squares in the Fourier space and total-variation (TV) regularization in image space for parallel-beam, fan-beam and cone-beam CT geometry. To achieve the maximum computational speed, the optimization problem is solved using a fast iterative shrinkage-thresholding algorithm with backtracking line search and GPU implementation of projection/backprojection. The performance of the proposed algorithm is demonstrated through a series of digital simulation and experimental phantom studies. The results are compared with the existing TV regularized techniques based on statistics-based weighted least-squares as well as basic algebraic reconstruction technique. The proposed Fourier-based compressed sensing (CS) method significantly improves both the image quality and the convergence rate compared to the existing CS techniques.

Performance of the Wavelet Decomposition on Massively Parallel Architectures

NASA Technical Reports Server (NTRS)

El-Ghazawi, Tarek A.; LeMoigne, Jacqueline; Zukor, Dorothy (Technical Monitor)

2001-01-01

Traditionally, Fourier Transforms have been utilized for performing signal analysis and representation. But although it is straightforward to reconstruct a signal from its Fourier transform, no local description of the signal is included in its Fourier representation. To alleviate this problem, Windowed Fourier transforms and then wavelet transforms have been introduced, and it has been proven that wavelets give a better localization than traditional Fourier transforms, as well as a better division of the time- or space-frequency plane than Windowed Fourier transforms. Because of these properties and after the development of several fast algorithms for computing the wavelet representation of any signal, in particular the Multi-Resolution Analysis (MRA) developed by Mallat, wavelet transforms have increasingly been applied to signal analysis problems, especially real-life problems, in which speed is critical. In this paper we present and compare efficient wavelet decomposition algorithms on different parallel architectures. We report and analyze experimental measurements, using NASA remotely sensed images. Results show that our algorithms achieve significant performance gains on current high performance parallel systems, and meet scientific applications and multimedia requirements. The extensive performance measurements collected over a number of high-performance computer systems have revealed important architectural characteristics of these systems, in relation to the processing demands of the wavelet decomposition of digital images.

Generalized Fourier analyses of the advection-diffusion equation - Part I: one-dimensional domains

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Martinez, Mario J.; Voth, Thomas E.

2004-07-01

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

Fourier series expansion for nonlinear Hamiltonian oscillators.

PubMed

Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac

2010-06-01

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.

Vibrations Detection in Industrial Pumps Based on Spectral Analysis to Increase Their Efficiency

NASA Astrophysics Data System (ADS)

Rachid, Belhadef; Hafaifa, Ahmed; Boumehraz, Mohamed

2016-03-01

Spectral analysis is the key tool for the study of vibration signals in rotating machinery. In this work, the vibration analysis applied for conditional preventive maintenance of such machines is proposed, as part of resolved problems related to vibration detection on the organs of these machines. The vibration signal of a centrifugal pump was treated to mount the benefits of the approach proposed. The obtained results present the signal estimation of a pump vibration using Fourier transform technique compared by the spectral analysis methods based on Prony approach.

Is the algorithm used to process heart rate variability data clinically relevant? Analysis in male adolescents.

PubMed

Soares, Antonio Henrique Germano; Farah, Breno Quintella; Cucato, Gabriel Grizzo; Bastos-Filho, Carmelo José Albanez; Christofaro, Diego Giulliano Destro; Vanderlei, Luiz Carlos Marques; Lima, Aluísio Henrique Rodrigues de Andrade; Ritti-Dias, Raphael Mendes

2016-01-01

To analyze whether the algorithm used for the heart rate variability assessment (fast Fourier transform versus autoregressive methods) influenced its association with cardiovascular risk factors in male adolescents. This cross-sectional study included 1,152 male adolescents (aged 14 to 19 years). The low frequency, high frequency components (absolute numbers and normalized units), low frequency/high frequency ratio, and total power of heart rate variability parameters were obtained using the fast Fourier transform and autoregressive methods, while the adolescents were resting in a supine position. All heart rate variability parameters calculated from both methods were different (p<0.05). However, a low effect size (<0.1) was found for all parameters. The intra-class correlation between methods ranged from 0.96 to 0.99, whereas the variation coefficient ranged from 7.4 to 14.8%. Furthermore, waist circumference was negatively associated with high frequency, and positively associated with low frequency and sympatovagal balance (p<0.001 for both fast Fourier transform and autoregressive methods in all associations). Systolic blood pressure was negatively associated with total power and high frequency, whereas it was positively associated with low frequency and sympatovagal balance (p<0.001 for both fast Fourier transform and autoregressive methods in all associations). Body mass index was negatively associated with high frequency, while it was positively associated with low frequency and sympatovagal balance (p values ranged from <0.001 to 0.007). There are significant differences in heart rate variability parameters obtained with the fast Fourier transform and autoregressive methods in male adolescent; however, these differences are not clinically significant. Analisar se o algoritmo usado para avaliação da variabilidade da frequência cardíaca (transformada rápida de Fourier versus autoregressivo) influencia em sua associação com fatores de risco cardiovascular adolescentes do gênero masculino. Estudo transversal, que incluiu 1.152 adolescentes do gênero masculino (14 a 19 anos). Componentes de baixa e alta frequência (absolutos e unidades normalizadas), razão componente de baixa frequência/componente de alta frequência e poder total da variabilidade da frequência cardíaca foram obtidos em repouso, na posição supina, usando os métodos transformada rápida de Fourier e autorregressivo. Todos os parâmetros da variabilidade da frequência cardíaca para ambos os métodos foram diferentes (p<0,05). Entretanto, um pequeno tamanho do efeito (<0,1) foi observado para todos os parâmetros. Os coeficientes de correlação intraclasse entre os métodos variaram de 0,96 a 0,99, enquanto os coeficientes de variação foram de 7,4 a 14,8%. A circunferência abdominal foi negativamente associada com o componente de alta frequência, e positivamente associada com o componente de baixa frequência e o balanço simpatovagal (p<0,001 para a transformada rápida de Fourier e o autorregressivo em todas as associações). A pressão arterial sistólica foi negativamente associada com o poder total e o componente de alta frequência, enquanto foi positivamente associada com o componente de baixa frequência e o balanço simpatovagal (p<0,001 para a transformada rápida de Fourier e o autorregressivo em todas as associações). O índice de massa corporal foi negativamente associado com o componente de alta frequência, enquanto foi positivamente associado com o componente de baixa frequência e o balanço simpatovagal (valores de p variando de <0,001 a 0,007). Houve diferenças significantes nos parâmetros da variabilidade da frequência cardíaca obtidos com os métodos transformada rápida de Fourier e autorregressivo em adolescentes masculinos, mas essas diferenças não foram clinicamente significativas.

Microscale Solubility Measurements of Matrix-Assisted Laser Desorption-Ionization (MALDI) Matrices Using Attenuated Total Reflection (ATR) Fourier Transform Infrared Spectroscopy (FT-IR) Coupled with Partial Least Squares (PLS) Analysis.

PubMed

Gorre, Elsa; Owens, Kevin G

2016-11-01

In this work an attenuated total reflection Fourier transform infrared (FT-IR) absorption based method is used to measure the solubility of two matrix-assisted laser desorption-ionization (MALDI) matrices in a few pure solvents and mixtures of acetonitrile and water using low microliter amounts of solution. Results from a method that averages the values obtained from multiple calibration curves created by manual peak picking are compared to those predicted using a partial least squares (PLS) chemometrics approach. The PLS method provided solubility values that were in good agreement with the manual method with significantly greater ease of analysis. As a test, the solubility of adipic acid in acetone was measured using the two methods of analysis, and the values are in good agreement with solubility values reported in literature. The solubilities of the MALDI matrices α-cyano-4-hydroxy cinnamic acid (CHCA) and sinapinic acid (SA) were measured in a series of mixtures made from acetonitrile (ACN) and water; surprisingly, the results show a highly nonlinear trend. While both CHCA and SA show solubility values of less than 10 mg/mL in the pure solvents, the solubility value for SA increases to 56.3 mg/mL in a 75:25 v/v ACN:water mixture. This can have a significant effect on the matrix-to-analyte ratios in the MALDI experiment when sample protocols call for preparation of a saturated solution of the matrix in the chosen solvent system. © The Author(s) 2016.

A projection operator method for the analysis of magnetic neutron form factors

NASA Astrophysics Data System (ADS)

Kaprzyk, S.; Van Laar, B.; Maniawski, F.

1981-03-01

A set of projection operators in matrix form has been derived on the basis of decomposition of the spin density into a series of fully symmetrized cubic harmonics. This set of projection operators allows a formulation of the Fourier analysis of magnetic form factors in a convenient way. The presented method is capable of checking the validity of various theoretical models used for spin density analysis up to now. The general formalism is worked out in explicit form for the fcc and bcc structures and deals with that part of spin density which is contained within the sphere inscribed in the Wigner-Seitz cell. This projection operator method has been tested on the magnetic form factors of nickel and iron.

Penalized discriminant analysis for the detection of wild-grown and cultivated Ganoderma lucidum using Fourier transform infrared spectroscopy.

PubMed

Zhu, Ying; Tan, Tuck Lee

2016-04-15

An effective and simple analytical method using Fourier transform infrared (FTIR) spectroscopy to distinguish wild-grown high-quality Ganoderma lucidum (G. lucidum) from cultivated one is of essential importance for its quality assurance and medicinal value estimation. Commonly used chemical and analytical methods using full spectrum are not so effective for the detection and interpretation due to the complex system of the herbal medicine. In this study, two penalized discriminant analysis models, penalized linear discriminant analysis (PLDA) and elastic net (Elnet),using FTIR spectroscopy have been explored for the purpose of discrimination and interpretation. The classification performances of the two penalized models have been compared with two widely used multivariate methods, principal component discriminant analysis (PCDA) and partial least squares discriminant analysis (PLSDA). The Elnet model involving a combination of L1 and L2 norm penalties enabled an automatic selection of a small number of informative spectral absorption bands and gave an excellent classification accuracy of 99% for discrimination between spectra of wild-grown and cultivated G. lucidum. Its classification performance was superior to that of the PLDA model in a pure L1 setting and outperformed the PCDA and PLSDA models using full wavelength. The well-performed selection of informative spectral features leads to substantial reduction in model complexity and improvement of classification accuracy, and it is particularly helpful for the quantitative interpretations of the major chemical constituents of G. lucidum regarding its anti-cancer effects. Copyright © 2016 Elsevier B.V. All rights reserved.

Application of wavelet and Fuorier transforms as powerful alternatives for derivative spectrophotometry in analysis of binary mixtures: A comparative study

NASA Astrophysics Data System (ADS)

Hassan, Said A.; Abdel-Gawad, Sherif A.

2018-02-01

Two signal processing methods, namely, Continuous Wavelet Transform (CWT) and the second was Discrete Fourier Transform (DFT) were introduced as alternatives to the classical Derivative Spectrophotometry (DS) in analysis of binary mixtures. To show the advantages of these methods, a comparative study was performed on a binary mixture of Naltrexone (NTX) and Bupropion (BUP). The methods were compared by analyzing laboratory prepared mixtures of the two drugs. By comparing performance of the three methods, it was proved that CWT and DFT methods are more efficient and advantageous in analysis of mixtures with overlapped spectra than DS. The three signal processing methods were adopted for the quantification of NTX and BUP in pure and tablet forms. The adopted methods were validated according to the ICH guideline where accuracy, precision and specificity were found to be within appropriate limits.

Optical image encryption by random shifting in fractional Fourier domains

NASA Astrophysics Data System (ADS)

Hennelly, B.; Sheridan, J. T.

2003-02-01

A number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require random phase screen keys for decrypting the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. A new technique based on a random shifting, or jigsaw, algorithm is proposed. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in fractional Fourier domains. The new method has been compared with existing methods and shows comparable or superior robustness to blind decryption. Optical implementation is discussed, and the sensitivity of the various encryption keys to blind decryption is examined.

A new method to estimate local pitch angles in spiral galaxies: Application to spiral arms and feathers in M81 and M51

DOE Office of Scientific and Technical Information (OSTI.GOV)

Puerari, Ivânio; Elmegreen, Bruce G.; Block, David L., E-mail: puerari@inaoep.mx

2014-12-01

We examine 8 μm IRAC images of the grand design two-arm spiral galaxies M81 and M51 using a new method whereby pitch angles are locally determined as a function of scale and position, in contrast to traditional Fourier transform spectral analyses which fit to average pitch angles for whole galaxies. The new analysis is based on a correlation between pieces of a galaxy in circular windows of (lnR,θ) space and logarithmic spirals with various pitch angles. The diameter of the windows is varied to study different scales. The result is a best-fit pitch angle to the spiral structure as amore » function of position and scale, or a distribution function of pitch angles as a function of scale for a given galactic region or area. We apply the method to determine the distribution of pitch angles in the arm and interarm regions of these two galaxies. In the arms, the method reproduces the known pitch angles for the main spirals on a large scale, but also shows higher pitch angles on smaller scales resulting from dust feathers. For the interarms, there is a broad distribution of pitch angles representing the continuation and evolution of the spiral arm feathers as the flow moves into the interarm regions. Our method shows a multiplicity of spiral structures on different scales, as expected from gas flow processes in a gravitating, turbulent and shearing interstellar medium. We also present results for M81 using classical 1D and 2D Fourier transforms, together with a new correlation method, which shows good agreement with conventional 2D Fourier transforms.« less

Zero-crossing sampling of Fourier-transform interferograms and spectrum reconstruction using the real-zero interpolation method.

PubMed

Minami, K; Kawata, S; Minami, S

1992-10-10

The real-zero interpolation method is applied to a Fourier-transformed infrared (FT-IR) interferogram. With this method an interferogram is reconstructed from its zero-crossing information only, without the use of a long-word analog-to-digital converter. We installed a phase-locked loop circuit into an FT-IR spectrometer for oversampling the interferogram. Infrared absorption spectra of polystyrene and Mylar films were measured as binary interferograms by the FT-IR spectrometer, which was equipped with the developed circuits, and their Fourier spectra were successfully reconstructed. The relationship of the oversampling ratio to the dynamic range of the reconstructed interferogram was evaluated through computer simulations. We also discuss the problems of this method for practical applications.

Fourier-transform and global contrast interferometer alignment methods

DOEpatents

Goldberg, Kenneth A.

2001-01-01

Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.

Cryo-EM Structure Determination Using Segmented Helical Image Reconstruction.

PubMed

Fromm, S A; Sachse, C

2016-01-01

Treating helices as single-particle-like segments followed by helical image reconstruction has become the method of choice for high-resolution structure determination of well-ordered helical viruses as well as flexible filaments. In this review, we will illustrate how the combination of latest hardware developments with optimized image processing routines have led to a series of near-atomic resolution structures of helical assemblies. Originally, the treatment of helices as a sequence of segments followed by Fourier-Bessel reconstruction revealed the potential to determine near-atomic resolution structures from helical specimens. In the meantime, real-space image processing of helices in a stack of single particles was developed and enabled the structure determination of specimens that resisted classical Fourier helical reconstruction and also facilitated high-resolution structure determination. Despite the progress in real-space analysis, the combination of Fourier and real-space processing is still commonly used to better estimate the symmetry parameters as the imposition of the correct helical symmetry is essential for high-resolution structure determination. Recent hardware advancement by the introduction of direct electron detectors has significantly enhanced the image quality and together with improved image processing procedures has made segmented helical reconstruction a very productive cryo-EM structure determination method. © 2016 Elsevier Inc. All rights reserved.

Predicting the thermal/structural performance of the atmospheric trace molecules spectroscopy /ATMOS/ Fourier transform spectrometer

NASA Technical Reports Server (NTRS)

Miller, J. M.

1980-01-01

ATMOS is a Fourier transform spectrometer to measure atmospheric trace molecules over a spectral range of 2-16 microns. Assessment of the system performance of ATMOS includes evaluations of optical system errors induced by thermal and structural effects. In order to assess the optical system errors induced from thermal and structural effects, error budgets are assembled during system engineering tasks and line of sight and wavefront deformations predictions (using operational thermal and vibration environments and computer models) are subsequently compared to the error budgets. This paper discusses the thermal/structural error budgets, modelling and analysis methods used to predict thermal/structural induced errors and the comparisons that show that predictions are within the error budgets.

Studies of higher-order flow harmonics in PbPb collisions at 2.76 TeV with CMS

NASA Astrophysics Data System (ADS)

Tuo, Shengquan

2013-05-01

High-order Fourier harmonics (vn, n>2) in the azimuthal distributions of charged particles produced in PbPb collisions at a nucleon-nucleon center-of-mass energy s=2.76TeV are presented. The vn coefficients are studied using the event-plane method and a Fourier decomposition analysis of the two particle correlations in various collision centrality, pT and η ranges. A unique measurement of vn in the ultra-central collisions (UCC) is performed using the long-range component of the two particle correlations. These data provide strong constraints on the theoretical models of the initial condition in heavy ion collisions and the transport properties of the produced medium.

Authenticity identification and classification of Rhodiola species in traditional Tibetan medicine based on Fourier transform near-infrared spectroscopy and chemometrics analysis.

PubMed

Li, Tao; Su, Chen

2018-06-02

Rhodiola is an increasingly widely used traditional Tibetan medicine and traditional Chinese medicine in China. The composition profiles of bioactive compounds are somewhat jagged according to different species, which makes it crucial to identify authentic Rhodiola species accurately so as to ensure clinical application of Rhodiola. In this paper, a nondestructive, rapid, and efficient method in classification of Rhodiola was developed by Fourier transform near-infrared (FT-NIR) spectroscopy combined with chemometrics analysis. A total of 160 batches of raw spectra were obtained from four different species of Rhodiola by FT-NIR, such as Rhodiola crenulata, Rhodiola fastigiata, Rhodiola kirilowii, and Rhodiola brevipetiolata. After excluding the outliers, different performances of 3 sample dividing methods, 12 spectral preprocessing methods, 2 wavelength selection methods, and 2 modeling evaluation methods were compared. The results indicated that this combination was superior than others in the authenticity identification analysis, which was FT-NIR combined with sample set partitioning based on joint x-y distances (SPXY), standard normal variate transformation (SNV) + Norris-Williams (NW) + 2nd derivative, competitive adaptive reweighted sampling (CARS), and kernel extreme learning machine (KELM). The accuracy (ACCU), sensitivity (SENS), and specificity (SPEC) of the optimal model were all 1, which showed that this combination of FT-NIR and chemometrics methods had the optimal authenticity identification performance. The classification performance of the partial least squares discriminant analysis (PLS-DA) model was slightly lower than KELM model, and PLS-DA model results were ACCU = 0.97, SENS = 0.93, and SPEC = 0.98, respectively. It can be concluded that FT-NIR combined with chemometrics analysis has great potential in authenticity identification and classification of Rhodiola, which can provide a valuable reference for the safety and effectiveness of clinical application of Rhodiola. Copyright © 2018 Elsevier B.V. All rights reserved.

Short-time fractional Fourier methods for the time-frequency representation of chirp signals.

PubMed

Capus, Chris; Brown, Keith

2003-06-01

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.

A non-Fourier approach towards the analysis of heat transfer enhancement with water based nanofluids through a channel

NASA Astrophysics Data System (ADS)

Dil, Taimoor; Khan, M. Sabeel

2018-05-01

In this article, a non-Fourier approach to model the heat transfer phenomenon in nanofluids having application to automotive industry is studied. In this respect, a recently proposed hyperbolic heat flux equation is embedded into the heat energy equation and thereby incorporating the effect of thermal relaxation time. Nanofluids are formed by considering copper oxide (CuO), Titanium dioxide (TiO2) and Aluminum oxide (Al2O3) nano-solid particles in the base fluid. The flow governing system of PDEs along with boundary conditions is transformed into its respective coupled system of nonlinear ODEs using suitable similarity functions. Runge-Kutta-Fehlberg (RK-5) numerical scheme embedded with shooting method is implemented and used to solve the obtained boundary value problem. Numerical simulations are performed and tabulated to analyze the influence of solid volume fraction on local coefficient of skin-friction and Nusselt number. A comparison is made between the results by Fourier and present heat flux model. We conclude that the presented new approach is more general and thus allows predicting the influence of thermal relaxation time on the heat transfer characteristics. Moreover, consideration of present model over the Fourier model helps to predict the actual temporal behavior of solution.

Analytical Method Used to Calculate Pile Foundations with the Widening Up on a Horizontal Static Impact

NASA Astrophysics Data System (ADS)

Kupchikova, N. V.; Kurbatskiy, E. N.

2017-11-01

This paper presents a methodology for the analytical research solutions for the work pile foundations with surface broadening and inclined side faces in the ground array, based on the properties of Fourier transform of finite functions. The comparative analysis of the calculation results using the suggested method for prismatic piles, piles with surface broadening prismatic with precast piles and end walls with precast wedges on the surface is described.

Automated acid and base number determination of mineral-based lubricants by fourier transform infrared spectroscopy: commercial laboratory evaluation.

PubMed

Winterfield, Craig; van de Voort, F R

2014-12-01

The Fluid Life Corporation assessed and implemented Fourier transform infrared spectroscopy (FTIR)-based methods using American Society for Testing and Materials (ASTM)-like stoichiometric reactions for determination of acid and base number for in-service mineral-based oils. The basic protocols, quality control procedures, calibration, validation, and performance of these new quantitative methods are assessed. ASTM correspondence is attained using a mixed-mode calibration, using primary reference standards to anchor the calibration, supplemented by representative sample lubricants analyzed by ASTM procedures. A partial least squares calibration is devised by combining primary acid/base reference standards and representative samples, focusing on the main spectral stoichiometric response with chemometrics assisting in accounting for matrix variability. FTIR(AN/BN) methodology is precise, accurate, and free of most interference that affects ASTM D664 and D4739 results. Extensive side-by-side operational runs produced normally distributed differences with mean differences close to zero and standard deviations of 0.18 and 0.26 mg KOH/g, respectively. Statistically, the FTIR methods are a direct match to the ASTM methods, with superior performance in terms of analytical throughput, preparation time, and solvent use. FTIR(AN/BN) analysis is a viable, significant advance for in-service lubricant analysis, providing an economic means of trending samples instead of tedious and expensive conventional ASTM(AN/BN) procedures. © 2014 Society for Laboratory Automation and Screening.

Comparative evaluation of bioactivity of crystalline trypsin for drying by Fourier-transformed infrared spectroscopy.

PubMed

Otsuka, Makoto; Fukui, Yuya; Ozaki, Yukihiro

2009-03-01

The purpose of this study was to evaluate the enzymatic stability of colloidal trypsin powder during heating in a solid-state by using Fourier transform infrared (FT-IR) spectra with chemoinformatics and generalized two-dimensional (2D) correlation spectroscopy. Colloidal crystalline trypsin powders were heated using differential scanning calorimetry. The enzymatic activity of trypsin was assayed by the kinetic degradation method. Spectra of 10 calibration sample sets were recorded three times with a FT-IR spectrometer. The maximum intensity at 1634cm(-1) of FT-IR spectra and enzymatic activity of trypsin decreased as the temperature increased. The FT-IR spectra of trypsin samples were analyzed by a principal component regression analysis (PCR). A plot of the calibration data obtained was made between the actual and predicted trypsin activity based on a two-component model with gamma(2)=0.962. On the other hand, a 2D method was applied to FT-IR spectra of heat-treated trypsin. The result was consistent with that of the chemoinformetrical method. The results for deactivation of colloidal trypsin powder by heat-treatment indicated that nano-structure of crystalline trypsin changed by heating reflecting that the beta-sheet was mainly transformed, since the peak at 1634cm(-1) decreased with dehydration. The FT-IR chemoinformetrical method allows for a solid-state quantitative analysis of the bioactivity of the bulk powder of trypsin during drying.

MR Image Reconstruction Using Block Matching and Adaptive Kernel Methods.

PubMed

Schmidt, Johannes F M; Santelli, Claudio; Kozerke, Sebastian

2016-01-01

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ1-regularized parallel imaging methods.

Fourier analysis of finite element preconditioned collocation schemes

NASA Technical Reports Server (NTRS)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Molecular Characterization of Thiols in Fossil Fuels by Michael Addition Reaction Derivatization and Electrospray Ionization Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

PubMed

Wang, Meng; Zhao, Suoqi; Liu, Xuxia; Shi, Quan

2016-10-04

Thiols widely occur in sediments and fossil fuels. However, the molecular composition of these compounds is unclear due to the lack of appropriate analytical methods. In this work, a characterization method for thiols in fossil fuels was developed on the basis of Michael addition reaction derivatization followed by electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS). Model thiol compound studies showed that thiols were selectively reacted with phenylvinylsulfone and transformed to sulfones with greater than 98% conversions. This method was applied to a coker naphtha, light and heavy gas oils, and crude oils from various geological sources. The results showed that long alkyl chain thiols are readily present in petroleum, which have up to 30 carbon atoms. Large DBE dispersity of thiols indicates that naphthenic and aromatic thiols are also present in the petroleum. This method is capable of detecting thiol compounds in the part per million range by weight. This method allows characterization of thiols in a complex hydrocarbon matrix, which is complementary to the comprehensive analysis of sulfur compounds in fossil fuels.

Fourier Analysis and the Rhythm of Conversation.

ERIC Educational Resources Information Center

Dabbs, James M., Jr.

Fourier analysis, a common technique in engineering, breaks down a complex wave form into its simple sine wave components. Communication researchers have recently suggested that this technique may provide an index of the rhythm of conversation, since vocalizing and pausing produce a complex wave form pattern of alternation between two speakers. To…

Introduction to Flight Test Engineering (Introduction aux techniques des essais en vol)

DTIC Science & Technology

2005-07-01

or aircraft parameters • Calculations in the frequency domain ( Fast Fourier Transform) • Data analysis with dedicated software for: • Signal...density Fast Fourier Transform Transfer function analysis Frequency response analysis Etc. PRESENTATION Color/black & white Display screen...envelope by operating the airplane at increasing ranges - representing increasing risk - of engine operation, airspeeds both fast and slow, altitude

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

PubMed

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms.

PubMed

Volkov, V V; Han, M G; Zhu, Y

2013-11-01

We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. Published by Elsevier B.V.

[Research of dual-photoelastic-modulator-based beat frequency modulation and Fourier-Bessel transform imaging spectrometer].

PubMed

Wang, Zhi-Bin; Zhang, Rui; Wang, Yao-Li; Huang, Yan-Fei; Chen, You-Hua; Wang, Li-Fu; Yang, Qiang

2014-02-01

As the existing photoelastic-modulator(PEM) modulating frequency in the tens of kHz to hundreds of kHz between, leading to frequency of modulated interference signal is higher, so ordinary array detector cannot effectively caprure interference signal..A new beat frequency modulation method based on dual-photoelastic-modulator (Dual-PEM) and Fourier-Bessel transform is proposed as an key component of dual-photoelastic-modulator-based imaging spectrometer (Dual-PEM-IS) combined with charge coupled device (CCD). The dual-PEM are operated as an electro-optic circular retardance modulator, Operating the PEMs at slightly different resonant frequencies w1 and w2 respectively, generates a differential signal at a much lower heterodyne frequency that modulates the incident light. This method not only retains the advantages of the existing PEM, but also the frequency of modulated photocurrent decreased by 2-3 orders of magnitude (10-500 Hz) and can be detected by common array detector, and the incident light spectra can be obtained by Fourier-Bessel transform of low frequency component in the modulated signal. The method makes the PEM has the dual capability of imaging and spectral measurement. The basic principle is introduced, the basic equations is derived, and the feasibility is verified through the corresponding numerical simulation and experiment. This method has' potential applications in imaging spectrometer technology, and analysis of the effect of deviation of the optical path difference. This work provides the necessary theoretical basis for remote sensing of new Dual-PEM-IS and for engineering implementation of spectra inversion.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fahimian, Benjamin P.; Zhao Yunzhe; Huang Zhifeng

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). Inmore » each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. Conclusions: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.« less

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

PubMed Central

Fahimian, Benjamin P.; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J.; Osher, Stanley J.; McNitt-Gray, Michael F.; Miao, Jianwei

2013-01-01

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. Conclusions: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method. PMID:23464329

Do's and don'ts in Fourier analysis of steady-state potentials.

PubMed

Bach, M; Meigen, T

1999-01-01

Fourier analysis is a powerful tool in signal analysis that can be very fruitfully applied to steady-state evoked potentials (flicker ERG, pattern ERG, VEP, etc.). However, there are some inherent assumptions in the underlying discrete Fourier transform (DFT) that are not necessarily fulfilled in typical electrophysiological recording and analysis conditions. Furthermore, engineering software-packages may be ill-suited and/or may not fully exploit the information of steady-state recordings. Specifically: * In the case of steady-state stimulation we know more about the stimulus than in standard textbook situations (exact frequency, phase stability), so 'windowing' and calculation of the 'periodogram' are not necessary. * It is mandatory to choose an integer relationship between sampling rate and frame rate when employing a raster-based CRT stimulator. * The analysis interval must comprise an exact integer number (e.g., 10) of stimulus periods. * The choice of the number of stimulus periods per analysis interval needs a wise compromise: A high number increases the frequency resolution, but makes artifact removal difficult; a low number 'spills' noise into the response frequency. * There is no need to feel tied to a power-of-two number of data points as required by standard FFT, 'resampling' is an easy and efficient alternative. * Proper estimates of noise-corrected Fourier magnitude and statistical significance can be calculated that take into account the non-linear superposition of signal and noise. These aspects are developed in an intuitive approach with examples using both simulations and recordings. Proper use of Fourier analysis of our electrophysiological records will reduce recording time and/or increase the reliability of physiologic or pathologic interpretations.

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

The morphing of geographical features by Fourier transformation.

PubMed

Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

A novel power harmonic analysis method based on Nuttall-Kaiser combination window double spectrum interpolated FFT algorithm

NASA Astrophysics Data System (ADS)

Jin, Tao; Chen, Yiyang; Flesch, Rodolfo C. C.

2017-11-01

Harmonics pose a great threat to safe and economical operation of power grids. Therefore, it is critical to detect harmonic parameters accurately to design harmonic compensation equipment. The fast Fourier transform (FFT) is widely used for electrical popular power harmonics analysis. However, the barrier effect produced by the algorithm itself and spectrum leakage caused by asynchronous sampling often affects the harmonic analysis accuracy. This paper examines a new approach for harmonic analysis based on deducing the modifier formulas of frequency, phase angle, and amplitude, utilizing the Nuttall-Kaiser window double spectrum line interpolation method, which overcomes the shortcomings in traditional FFT harmonic calculations. The proposed approach is verified numerically and experimentally to be accurate and reliable.

Probing multi-scale self-similarity of tissue structures using light scattering spectroscopy: prospects in pre-cancer detection

NASA Astrophysics Data System (ADS)

Chatterjee, Subhasri; Das, Nandan K.; Kumar, Satish; Mohapatra, Sonali; Pradhan, Asima; Panigrahi, Prasanta K.; Ghosh, Nirmalya

2013-02-01

Multi-resolution analysis on the spatial refractive index inhomogeneities in the connective tissue regions of human cervix reveals clear signature of multifractality. We have thus developed an inverse analysis strategy for extraction and quantification of the multifractality of spatial refractive index fluctuations from the recorded light scattering signal. The method is based on Fourier domain pre-processing of light scattering data using Born approximation, and its subsequent analysis through Multifractal Detrended Fluctuation Analysis model. The method has been validated on several mono- and multi-fractal scattering objects whose self-similar properties are user controlled and known a-priori. Following successful validation, this approach has initially been explored for differentiating between different grades of precancerous human cervical tissues.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

NASA Astrophysics Data System (ADS)

Zhao, Jin; Han-Ming, Zhang; Bin, Yan; Lei, Li; Lin-Yuan, Wang; Ai-Long, Cai

2016-03-01

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively. Projected supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603) and the National Natural Science Foundation of China (Grant No. 61372172).

Frequency-Domain Identification Of Aeroelastic Modes

NASA Technical Reports Server (NTRS)

Acree, C. W., Jr.; Tischler, Mark B.

1991-01-01

Report describes flight measurements and frequency-domain analyses of aeroelastic vibrational modes of wings of XV-15 tilt-rotor aircraft. Begins with description of flight-test methods. Followed by brief discussion of methods of analysis, which include Fourier-transform computations using chirp z transformers, use of coherence and other spectral functions, and methods and computer programs to obtain frequencies and damping coefficients from measurements. Includes brief description of results of flight tests and comparisions among various experimental and theoretical results. Ends with section on conclusions and recommended improvements in techniques.

Automatic Fringe Detection for Oil Film Interferometry Measurement of Skin Friction

NASA Technical Reports Server (NTRS)

Naughton, Jonathan W.; Decker, Robert K.; Jafari, Farhad

2001-01-01

This report summarizes two years of work on investigating algorithms for automatically detecting fringe patterns in images acquired using oil-drop interferometry for the determination of skin friction. Several different analysis methods were tested, and a combination of a windowed Fourier transform followed by a correlation was found to be most effective. The implementation of this method is discussed and details of the process are described. The results indicate that this method shows promise for automating the fringe detection process, but further testing is required.

Detailed description of oil shale organic and mineralogical heterogeneity via fourier transform infrared mircoscopy

USGS Publications Warehouse

Washburn, Kathryn E.; Birdwell, Justin E.; Foster, Michael; Gutierrez, Fernando

2015-01-01

Mineralogical and geochemical information on reservoir and source rocks is necessary to assess and produce from petroleum systems. The standard methods in the petroleum industry for obtaining these properties are bulk measurements on homogenized, generally crushed, and pulverized rock samples and can take from hours to days to perform. New methods using Fourier transform infrared (FTIR) spectroscopy have been developed to more rapidly obtain information on mineralogy and geochemistry. However, these methods are also typically performed on bulk, homogenized samples. We present a new approach to rock sample characterization incorporating multivariate analysis and FTIR microscopy to provide non-destructive, spatially resolved mineralogy and geochemistry on whole rock samples. We are able to predict bulk mineralogy and organic carbon content within the same margin of error as standard characterization techniques, including X-ray diffraction (XRD) and total organic carbon (TOC) analysis. Validation of the method was performed using two oil shale samples from the Green River Formation in the Piceance Basin with differing sedimentary structures. One sample represents laminated Green River oil shales, and the other is representative of oil shale breccia. The FTIR microscopy results on the oil shales agree with XRD and LECO TOC data from the homogenized samples but also give additional detail regarding sample heterogeneity by providing information on the distribution of mineral phases and organic content. While measurements for this study were performed on oil shales, the method could also be applied to other geological samples, such as other mudrocks, complex carbonates, and soils.

Interferogram conditioning for improved Fourier analysis and application to X-ray phase imaging by grating interferometry.

PubMed

Montaux-Lambert, Antoine; Mercère, Pascal; Primot, Jérôme

2015-11-02

An interferogram conditioning procedure, for subsequent phase retrieval by Fourier demodulation, is presented here as a fast iterative approach aiming at fulfilling the classical boundary conditions imposed by Fourier transform techniques. Interference fringe patterns with typical edge discontinuities were simulated in order to reveal the edge artifacts that classically appear in traditional Fourier analysis, and were consecutively used to demonstrate the correction efficiency of the proposed conditioning technique. Optimization of the algorithm parameters is also presented and discussed. Finally, the procedure was applied to grating-based interferometric measurements performed in the hard X-ray regime. The proposed algorithm enables nearly edge-artifact-free retrieval of the phase derivatives. A similar enhancement of the retrieved absorption and fringe visibility images is also achieved.

The Fourier analysis applied to the relationship between (7)Be activity in the Serbian atmosphere and meteorological parameters.

PubMed

Rajačić, M M; Todorović, D J; Krneta Nikolić, J D; Janković, M M; Djurdjević, V S

2016-09-01

Air sample monitoring in Serbia, Belgrade started in the 1960s, while (7)Be activity in air and total (dry and wet) deposition has been monitored for the last 22 years by the Environment and Radiation Protection Department of the Institute for Nuclear Sciences, Vinca. Using this data collection, the changes of the (7)Be activity in the air and the total (wet and dry) deposition samples, as well as their correlation with meteorological parameters (temperature, pressure, cloudiness, sunshine duration, precipitation and humidity) that affect (7)Be concentration in the atmosphere, were mathematically described using the Fourier analysis. Fourier analysis confirmed the expected; the frequency with the largest intensity in the harmonic spectra of the (7)Be activity corresponds to a period of 1 year, the same as the largest intensity frequency in Fourier series of meteorological parameters. To analyze the quality of the results produced by the Fourier analysis, we compared the measured values of the parameters with the values calculated according to the Fourier series. Absolute deviations between measured and predicted mean monthly values are in range from 0.02 mBq/m(3) to 0.7 mBq/m(3) for (7)Be activity in air, and 0.01 Bq/m(2) and 0.6 Bq/m(2) for (7)Be activity in deposition samples. Relatively good agreement of measured and predicted results offers the possibility of prediction of the (7)Be activity. Copyright © 2016 Elsevier Ltd. All rights reserved.

Determination of acoustical transfer functions using an impulse method

NASA Astrophysics Data System (ADS)

MacPherson, J.

1985-02-01

The Transfer Function of a system may be defined as the relationship of the output response to the input of a system. Whilst recent advances in digital processing systems have enabled Impulse Transfer Functions to be determined by computation of the Fast Fourier Transform, there has been little work done in applying these techniques to room acoustics. Acoustical Transfer Functions have been determined for auditoria, using an impulse method. The technique is based on the computation of the Fast Fourier Transform (FFT) of a non-ideal impulsive source, both at the source and at the receiver point. The Impulse Transfer Function (ITF) is obtained by dividing the FFT at the receiver position by the FFT of the source. This quantity is presented both as linear frequency scale plots and also as synthesized one-third octave band data. The technique enables a considerable quantity of data to be obtained from a small number of impulsive signals recorded in the field, thereby minimizing the time and effort required on site. As the characteristics of the source are taken into account in the calculation, the choice of impulsive source is non-critical. The digital analysis equipment required for the analysis is readily available commercially.

Theoretical investigations on molecular structure, vibrational spectra, HOMO, LUMO, NBO analysis and hyperpolarizability calculations of thiophene-2-carbohydrazide.

PubMed

Balachandran, V; Janaki, A; Nataraj, A

2014-01-24

The Fourier-Transform infrared and Fourier-Transform Raman spectra of thiophene-2-carbohydrazide (TCH) was recorded in the region 4000-400 cm(-1) and 3500-100 cm(-1). Quantum chemical calculations of energies, geometrical structure and vibrational wavenumbers of TCH were carried out by DFT (B3LYP) method with 6-311++G(d,p) as basis set. The difference between the observed and scaled wavenumber values of most of the fundamentals is very small. Stability of the molecule arising from hyper conjugative interaction and charge delocalization has been analyzed using natural bond orbital (NBO) analysis. UV spectrum was measured in different solvent. The energy and oscillator strength are calculated by Time Dependant Density Functional Theory (TD-DFT) results. The calculated HOMO and LUMO energies also confirm that charge transfer occurs within the molecule. The complete assignments were performed on the basis of the potential energy distribution (PED) of vibrational modes, calculated with scaled quantum mechanics (SQM) method. Finally the theoretical FT-IR, FT-Raman, and UV spectra of the title molecule have also been constructed. Copyright © 2013 Elsevier B.V. All rights reserved.

Rapid quantification of casein in skim milk using Fourier transform infrared spectroscopy, enzymatic perturbation, and multiway partial least squares regression: Monitoring chymosin at work.

PubMed

Baum, A; Hansen, P W; Nørgaard, L; Sørensen, John; Mikkelsen, J D

2016-08-01

In this study, we introduce enzymatic perturbation combined with Fourier transform infrared (FTIR) spectroscopy as a concept for quantifying casein in subcritical heated skim milk using chemometric multiway analysis. Chymosin is a protease that cleaves specifically caseins. As a result of hydrolysis, all casein proteins clot to form a creamy precipitate, and whey proteins remain in the supernatant. We monitored the cheese-clotting reaction in real time using FTIR and analyzed the resulting evolution profiles to establish calibration models using parallel factor analysis and multiway partial least squares regression. Because we observed casein-specific kinetic changes, the retrieved models were independent of the chemical background matrix and were therefore robust against possible covariance effects. We tested the robustness of the models by spiking the milk solutions with whey, calcium, and cream. This method can be used at different stages in the dairy production chain to ensure the quality of the delivered milk. In particular, the cheese-making industry can benefit from such methods to optimize production control. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Time-frequency analysis of acoustic signals in the audio-frequency range generated during Hadfield's steel friction

NASA Astrophysics Data System (ADS)

Dobrynin, S. A.; Kolubaev, E. A.; Smolin, A. Yu.; Dmitriev, A. I.; Psakhie, S. G.

2010-07-01

Time-frequency analysis of sound waves detected by a microphone during the friction of Hadfield’s steel has been performed using wavelet transform and window Fourier transform methods. This approach reveals a relationship between the appearance of quasi-periodic intensity outbursts in the acoustic response signals and the processes responsible for the formation of wear products. It is shown that the time-frequency analysis of acoustic emission in a tribosystem can be applied, along with traditional approaches, to studying features in the wear and friction process.

Comparisons between real and complex Gauss wavelet transform methods of three-dimensional shape reconstruction

NASA Astrophysics Data System (ADS)

Xu, Luopeng; Dan, Youquan; Wang, Qingyuan

2015-10-01

The continuous wavelet transform (CWT) introduces an expandable spatial and frequency window which can overcome the inferiority of localization characteristic in Fourier transform and windowed Fourier transform. The CWT method is widely applied in the non-stationary signal analysis field including optical 3D shape reconstruction with remarkable performance. In optical 3D surface measurement, the performance of CWT for optical fringe pattern phase reconstruction usually depends on the choice of wavelet function. A large kind of wavelet functions of CWT, such as Mexican Hat wavelet, Morlet wavelet, DOG wavelet, Gabor wavelet and so on, can be generated from Gauss wavelet function. However, so far, application of the Gauss wavelet transform (GWT) method (i.e. CWT with Gauss wavelet function) in optical profilometry is few reported. In this paper, the method using GWT for optical fringe pattern phase reconstruction is presented first and the comparisons between real and complex GWT methods are discussed in detail. The examples of numerical simulations are also given and analyzed. The results show that both the real GWT method along with a Hilbert transform and the complex GWT method can realize three-dimensional surface reconstruction; and the performance of reconstruction generally depends on the frequency domain appearance of Gauss wavelet functions. For the case of optical fringe pattern of large phase variation with position, the performance of real GWT is better than that of complex one due to complex Gauss series wavelets existing frequency sidelobes. Finally, the experiments are carried out and the experimental results agree well with our theoretical analysis.

Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

PubMed

Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

2009-06-01

Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

Teaching Fourier optics through ray matrices

NASA Astrophysics Data System (ADS)

Moreno, I.; Sánchez-López, M. M.; Ferreira, C.; Davis, J. A.; Mateos, F.

2005-03-01

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics.

Solving the multi-frequency electromagnetic inverse source problem by the Fourier method

NASA Astrophysics Data System (ADS)

Wang, Guan; Ma, Fuming; Guo, Yukun; Li, Jingzhi

2018-07-01

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and the polarization vector decomposition, we propose a novel method for determining the source function in the full vector Maxwell's system. Rigorous mathematical justifications of the method are given and numerical examples are provided to demonstrate the feasibility and effectiveness of the method.

Areal and Temporal Analysis of Precipitation Patterns In Slovakia Using Spectral Analysis

NASA Astrophysics Data System (ADS)

Pishvaei, M. R.

Harmonic analysis as an objective method of precipitation seasonality studying is ap- plied to the 1901-2000 monthly precipitation averages at five stations in the low-land part of Slovakia with elevation less than 800 m a.s.l. The significant harmonics of long-term precipitation series have been separately computed for eight 30-year peri- ods, which cover the 20th century and some properties and the variations are com- pared to 100-year monthly precipitation averages. The selected results show that the first and the second harmonics pre-dominantly influence on the annual distribution and climatic seasonal regimes of pre-cipitation that contribute to the precipitation am- plitude/pattern with about 20% and 10%, respectively. These indicate annual and half year variations. The rest harmon-ics often have each less than 5% contribution on the Fourier interpolation course. Maximum in yearly precipitation course, which oc- curs approximately at the begin-ning of July, because of phase changing shifts then to the middle of June. Some probable reasons regarding to Fourier components are discussed. In addition, a tem-poral analysis over precipitation time series belonging to the Hurbanovo Observa-tory as the longest observational series on the territory of Slovakia (with 130-year precipitation records) has been individually performed and possible meteorological factors responsible for the observed patterns are suggested. A comparison of annual precipitation course obtained from daily precipitation totals analysis and polynomial trends with Fourier interpolation has been done too. Daily precipitation data in the latest period are compared for some stations in Slovakia as well. Only selected results are pre-sented in the poster.

Scaled nonuniform Fourier transform for image reconstruction in swept source optical coherence tomography

NASA Astrophysics Data System (ADS)

Mezgebo, Biniyam; Nagib, Karim; Fernando, Namal; Kordi, Behzad; Sherif, Sherif

2018-02-01

Swept Source optical coherence tomography (SS-OCT) is an important imaging modality for both medical and industrial diagnostic applications. A cross-sectional SS-OCT image is obtained by applying an inverse discrete Fourier transform (DFT) to axial interferograms measured in the frequency domain (k-space). This inverse DFT is typically implemented as a fast Fourier transform (FFT) that requires the data samples to be equidistant in k-space. As the frequency of light produced by a typical wavelength-swept laser is nonlinear in time, the recorded interferogram samples will not be uniformly spaced in k-space. Many image reconstruction methods have been proposed to overcome this problem. Most such methods rely on oversampling the measured interferogram then use either hardware, e.g., Mach-Zhender interferometer as a frequency clock module, or software, e.g., interpolation in k-space, to obtain equally spaced samples that are suitable for the FFT. To overcome the problem of nonuniform sampling in k-space without any need for interferogram oversampling, an earlier method demonstrated the use of the nonuniform discrete Fourier transform (NDFT) for image reconstruction in SS-OCT. In this paper, we present a more accurate method for SS-OCT image reconstruction from nonuniform samples in k-space using a scaled nonuniform Fourier transform. The result is demonstrated using SS-OCT images of Axolotl salamander eggs.

Synthesis, Analysis, and Processing of Fractal Signals

DTIC Science & Technology

1991-10-01

coordinator in hockey, squash, volleyball, and softball, but also for reminding me periodically that 1/f noise can exist outside a computer. More...similar signals as Fourier-based representations are for stationary and periodic signals. Furthermore, because wave- let transformations can be...and periodic signals. Furthermore, just as the discovery of fast Fourier transform (FFT) algorithms dramatically increased the viability the Fourier

Fourier spatial frequency analysis for image classification: training the training set

NASA Astrophysics Data System (ADS)

Johnson, Timothy H.; Lhamo, Yigah; Shi, Lingyan; Alfano, Robert R.; Russell, Stewart

2016-04-01

The Directional Fourier Spatial Frequencies (DFSF) of a 2D image can identify similarity in spatial patterns within groups of related images. A Support Vector Machine (SVM) can then be used to classify images if the inter-image variance of the FSF in the training set is bounded. However, if variation in FSF increases with training set size, accuracy may decrease as the size of the training set increases. This calls for a method to identify a set of training images from among the originals that can form a vector basis for the entire class. Applying the Cauchy product method we extract the DFSF spectrum from radiographs of osteoporotic bone, and use it as a matched filter set to eliminate noise and image specific frequencies, and demonstrate that selection of a subset of superclassifiers from within a set of training images improves SVM accuracy. Central to this challenge is that the size of the search space can become computationally prohibitive for all but the smallest training sets. We are investigating methods to reduce the search space to identify an optimal subset of basis training images.

Visual and Quantitative Analysis Methods of Respiratory Patterns for Respiratory Gated PET/CT.

PubMed

Son, Hye Joo; Jeong, Young Jin; Yoon, Hyun Jin; Park, Jong-Hwan; Kang, Do-Young

2016-01-01

We integrated visual and quantitative methods for analyzing the stability of respiration using four methods: phase space diagrams, Fourier spectra, Poincaré maps, and Lyapunov exponents. Respiratory patterns of 139 patients were grouped based on the combination of the regularity of amplitude, period, and baseline positions. Visual grading was done by inspecting the shape of diagram and classified into two states: regular and irregular. Quantitation was done by measuring standard deviation of x and v coordinates of Poincaré map (SD x , SD v ) or the height of the fundamental peak ( A 1 ) in Fourier spectrum or calculating the difference between maximal upward and downward drift. Each group showed characteristic pattern on visual analysis. There was difference of quantitative parameters (SD x , SD v , A 1 , and MUD-MDD) among four groups (one way ANOVA, p = 0.0001 for MUD-MDD, SD x , and SD v , p = 0.0002 for A 1 ). In ROC analysis, the cutoff values were 0.11 for SD x (AUC: 0.982, p < 0.0001), 0.062 for SD v (AUC: 0.847, p < 0.0001), 0.117 for A 1 (AUC: 0.876, p < 0.0001), and 0.349 for MUD-MDD (AUC: 0.948, p < 0.0001). This is the first study to analyze multiple aspects of respiration using various mathematical constructs and provides quantitative indices of respiratory stability and determining quantitative cutoff value for differentiating regular and irregular respiration.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction.

PubMed

Fahimian, Benjamin P; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J; Osher, Stanley J; McNitt-Gray, Michael F; Miao, Jianwei

2013-03-01

A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.

Hypercomplex Fourier transforms of color images.

PubMed

Ell, Todd A; Sangwine, Stephen J

2007-01-01

Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed.

Modified slanted-edge method for camera modulation transfer function measurement using nonuniform fast Fourier transform technique

NASA Astrophysics Data System (ADS)

Duan, Yaxuan; Xu, Songbo; Yuan, Suochao; Chen, Yongquan; Li, Hongguang; Da, Zhengshang; Gao, Limin

2018-01-01

ISO 12233 slanted-edge method experiences errors using fast Fourier transform (FFT) in the camera modulation transfer function (MTF) measurement due to tilt angle errors in the knife-edge resulting in nonuniform sampling of the edge spread function (ESF). In order to resolve this problem, a modified slanted-edge method using nonuniform fast Fourier transform (NUFFT) for camera MTF measurement is proposed. Theoretical simulations for images with noise at a different nonuniform sampling rate of ESF are performed using the proposed modified slanted-edge method. It is shown that the proposed method successfully eliminates the error due to the nonuniform sampling of the ESF. An experimental setup for camera MTF measurement is established to verify the accuracy of the proposed method. The experiment results show that under different nonuniform sampling rates of ESF, the proposed modified slanted-edge method has improved accuracy for the camera MTF measurement compared to the ISO 12233 slanted-edge method.

Size and shape measurement in contemporary cephalometrics.

PubMed

McIntyre, Grant T; Mossey, Peter A

2003-06-01

The traditional method of analysing cephalograms--conventional cephalometric analysis (CCA)--involves the calculation of linear distance measurements, angular measurements, area measurements, and ratios. Because shape information cannot be determined from these 'size-based' measurements, an increasing number of studies employ geometric morphometric tools in the cephalometric analysis of craniofacial morphology. Most of the discussions surrounding the appropriateness of CCA, Procrustes superimposition, Euclidean distance matrix analysis (EDMA), thin-plate spline analysis (TPS), finite element morphometry (FEM), elliptical Fourier functions (EFF), and medial axis analysis (MAA) have centred upon mathematical and statistical arguments. Surprisingly, little information is available to assist the orthodontist in the clinical relevance of each technique. This article evaluates the advantages and limitations of the above methods currently used to analyse the craniofacial morphology on cephalograms and investigates their clinical relevance and possible applications.

A novel recursive Fourier transform for nonuniform sampled signals: application to heart rate variability spectrum estimation.

PubMed

Holland, Alexander; Aboy, Mateo

2009-07-01

We present a novel method to iteratively calculate discrete Fourier transforms for discrete time signals with sample time intervals that may be widely nonuniform. The proposed recursive Fourier transform (RFT) does not require interpolation of the samples to uniform time intervals, and each iterative transform update of N frequencies has computational order N. Because of the inherent non-uniformity in the time between successive heart beats, an application particularly well suited for this transform is power spectral density (PSD) estimation for heart rate variability. We compare RFT based spectrum estimation with Lomb-Scargle Transform (LST) based estimation. PSD estimation based on the LST also does not require uniform time samples, but the LST has a computational order greater than Nlog(N). We conducted an assessment study involving the analysis of quasi-stationary signals with various levels of randomly missing heart beats. Our results indicate that the RFT leads to comparable estimation performance to the LST with significantly less computational overhead and complexity for applications requiring iterative spectrum estimations.

Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

NASA Astrophysics Data System (ADS)

Ren, Maodong; Liang, Jin; Wei, Bin

2016-12-01

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

Full information acquisition in scanning probe microscopy and spectroscopy

DOEpatents

Jesse, Stephen; Belianinov, Alex; Kalinin, Sergei V.; Somnath, Suhas

2017-04-04

Apparatus and methods are described for scanning probe microscopy and spectroscopy based on acquisition of full probe response. The full probe response contains valuable information about the probe-sample interaction that is lost in traditional scanning probe microscopy and spectroscopy methods. The full probe response is analyzed post data acquisition using fast Fourier transform and adaptive filtering, as well as multivariate analysis. The full response data is further compressed to retain only statistically significant components before being permanently stored.

On several aspects and applications of the multigrid method for solving partial differential equations

NASA Technical Reports Server (NTRS)

Dinar, N.

1978-01-01

Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.

Numerical analysis of soliton solutions of the modified Korteweg-de Vries-sine-Gordon equation

NASA Astrophysics Data System (ADS)

Popov, S. P.

2015-03-01

Multisoliton solutions of the modified Korteweg-de Vries-sine-Gordon equation (mKdV-SG) are found numerically by applying the quasi-spectral Fourier method and the fourth-order Runge-Kutta method. The accuracy and features of the approach are determined as applied to problems with initial data in the form of various combinations of perturbed soliton distributions. Three-soliton solutions are obtained, and the generation of kinks, breathers, wobblers, perturbed kinks, and nonlinear oscillatory waves is studied.

Study on time-frequency analysis method of very fast transient overvoltage

NASA Astrophysics Data System (ADS)

Li, Shuai; Liu, Shiming; Huang, Qiyan; Fu, Chuanshun

2018-04-01

The operation of the disconnector in the gas insulated substation (GIS) may produce very fast transient overvoltage (VFTO), which has the characteristics of short rise time, short duration, high amplitude and rich frequency components. VFTO can cause damage to GIS and secondary equipment, and the frequency components contained in the VFTO can cause resonance overvoltage inside the transformer, so it is necessary to study the spectral characteristics of the VFTO. From the perspective of signal processing, VFTO is a kind of non-stationary signal, the traditional Fourier transform is difficult to describe its frequency which changes with time, so it is necessary to use time-frequency analysis to analyze VFTO spectral characteristics. In this paper, we analyze the performance of short time Fourier transform (STFT), Wigner-Ville distribution (WVD), pseudo Wigner-Ville distribution (PWVD) and smooth pseudo Wigner-Ville distribution (SPWVD). The results show that SPWVD transform is the best. The time-frequency aggregation of SPWVD is higher than STFT, and it does not have cross-interference terms, which can meet the requirements of VFTO spectrum analysis.

Top-Down Analysis of Highly Post-Translationally Modified Peptides by Fourier Transform Ion Cyclotron Resonance Mass Spectrometry

NASA Astrophysics Data System (ADS)

Guerrero, Andres; Lerno, Larry; Barile, Daniela; Lebrilla, Carlito B.

2015-03-01

Bovine κ-caseinoglycomacropeptide (GMP) is a highly modified peptide from κ-casein produced during the cheese making process. The chemical nature of GMP makes analysis by traditional proteomic approaches difficult, as the peptide bears a strong net negative charge and a variety of post-translational modifications. In this work, we describe the use of electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS) for the top-down analysis of GMP. The method allows the simultaneous detection of different GMP forms that result from the combination of amino acid genetic variations and post-translational modifications, specifically phosphorylation and O-glycosylation. The different GMP forms were identified by high resolution mass spectrometry in both negative and positive mode and confirmation was achieved by tandem MS. The results showed the predominance of two genetic variants of GMP that occur as either mono- or bi-phosphorylated species. Additionally, these four forms can be modified with up to two O-glycans generally sialylated. The results demonstrate the presence of glycosylated, bi-phosphorylated forms of GMP never described before.

Fiber-optic evanescent-wave spectroscopy for fast multicomponent analysis of human blood

NASA Astrophysics Data System (ADS)

Simhi, Ronit; Gotshal, Yaron; Bunimovich, David; Katzir, Abraham; Sela, Ben-Ami

1996-07-01

A spectral analysis of human blood serum was undertaken by fiber-optic evanescent-wave spectroscopy (FEWS) by the use of a Fourier-transform infrared spectrometer. A special cell for the FEWS measurements was designed and built that incorporates an IR-transmitting silver halide fiber and a means for introducing the blood-serum sample. Further improvements in analysis were obtained by the adoption of multivariate calibration techniques that are already used in clinical chemistry. The partial least-squares algorithm was used to calculate the concentrations of cholesterol, total protein, urea, and uric acid in human blood serum. The estimated prediction errors obtained (in percent from the average value) were 6% for total protein, 15% for cholesterol, 30% for urea, and 30% for uric acid. These results were compared with another independent prediction method that used a neural-network model. This model yielded estimated prediction errors of 8.8% for total protein, 25% for cholesterol, and 21% for uric acid. spectroscopy, fiber-optic evanescent-wave spectroscopy, Fourier-transform infrared spectrometer, blood, multivariate calibration, neural networks.

Asymptotic formula for the Riesz means of the spectral functions of Laplace-Beltrami operator on unit sphere

NASA Astrophysics Data System (ADS)

Fadly Nurullah Rasedee, Ahmad; Ahmedov, Anvarjon; Sathar, Mohammad Hasan Abdul

2017-09-01

The mathematical models of the heat and mass transfer processes on the ball type solids can be solved using the theory of convergence of Fourier-Laplace series on unit sphere. Many interesting models have divergent Fourier-Laplace series, which can be made convergent by introducing Riesz and Cesaro means of the series. Partial sums of the Fourier-Laplace series summed by Riesz method are integral operators with the kernel known as Riesz means of the spectral function. In order to obtain the convergence results for the partial sums by Riesz means we need to know an asymptotic behavior of the latter kernel. In this work the estimations for Riesz means of spectral function of Laplace-Beltrami operator which guarantees the convergence of the Fourier-Laplace series by Riesz method are obtained.

Application of Fourier analysis to multispectral/spatial recognition

NASA Technical Reports Server (NTRS)

Hornung, R. J.; Smith, J. A.

1973-01-01

One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.

Fourier transform-wavefront reconstruction for the pyramid wavefront sensor

NASA Astrophysics Data System (ADS)

Quirós-Pacheco, Fernando; Correia, Carlos; Esposito, Simone

The application of Fourier-transform reconstruction techniques to the pyramid wavefront sensor has been investigated. A preliminary study based on end-to-end simulations of an adaptive optics system with ≈40x40 subapertures and actuators shows that the performance of the Fourier-transform reconstructor (FTR) is of the same order of magnitude than the one obtained with a conventional matrix-vector multiply (MVM) method.

Fast Implicit Methods For Elliptic Moving Interface Problems

DTIC Science & Technology

2015-12-11

analyzed, and tested for the Fourier transform of piecewise polynomials given on d-dimensional simplices in D-dimensional Euclidean space. These transforms...evaluation, and one to three orders of magnitude slower than the classical uniform Fast Fourier Transform. Second, bilinear quadratures ---which...a fast algorithm was derived, analyzed, and tested for the Fourier transform of pi ecewise polynomials given on d-dimensional simplices in D

Comparison of fMRI analysis methods for heterogeneous BOLD responses in block design studies.

PubMed

Liu, Jia; Duffy, Ben A; Bernal-Casas, David; Fang, Zhongnan; Lee, Jin Hyung

2017-02-15

A large number of fMRI studies have shown that the temporal dynamics of evoked BOLD responses can be highly heterogeneous. Failing to model heterogeneous responses in statistical analysis can lead to significant errors in signal detection and characterization and alter the neurobiological interpretation. However, to date it is not clear that, out of a large number of options, which methods are robust against variability in the temporal dynamics of BOLD responses in block-design studies. Here, we used rodent optogenetic fMRI data with heterogeneous BOLD responses and simulations guided by experimental data as a means to investigate different analysis methods' performance against heterogeneous BOLD responses. Evaluations are carried out within the general linear model (GLM) framework and consist of standard basis sets as well as independent component analysis (ICA). Analyses show that, in the presence of heterogeneous BOLD responses, conventionally used GLM with a canonical basis set leads to considerable errors in the detection and characterization of BOLD responses. Our results suggest that the 3rd and 4th order gamma basis sets, the 7th to 9th order finite impulse response (FIR) basis sets, the 5th to 9th order B-spline basis sets, and the 2nd to 5th order Fourier basis sets are optimal for good balance between detection and characterization, while the 1st order Fourier basis set (coherence analysis) used in our earlier studies show good detection capability. ICA has mostly good detection and characterization capabilities, but detects a large volume of spurious activation with the control fMRI data. Copyright © 2016 Elsevier Inc. All rights reserved.

Stress and reliability analyses of multilayered composite cylinder under thermal and mechanical loads

NASA Astrophysics Data System (ADS)

Wang, Xiaohua

The coupling resulting from the mutual influence of material thermal and mechanical parameters is examined in the thermal stress analysis of a multilayered isotropic composite cylinder subjected to sudden axisymmetric external and internal temperature. The method of complex frequency response functions together with the Fourier transform technique is utilized. Because the coupling parameters for some composite materials, such as carbon-carbon, are very small, the effect of coupling is neglected in the orthotropic thermal stress analysis. The stress distributions in multilayered orthotropic cylinders subjected to sudden axisymmetric temperature loading combined with dynamic pressure as well as asymmetric temperature loading are also obtained. The method of Fourier series together with the Laplace transform is utilized in solving the heat conduction equation and thermal stress analysis. For brittle materials, like carbon-carbon composites, the strength variability is represented by two or three parameter Weibull distributions. The 'weakest link' principle which takes into account both the carbon-carbon composite cylinders. The complex frequency response analysis is performed on a multilayered orthotropic cylinder under asymmetrical thermal load. Both deterministic and random thermal stress and reliability analyses can be based on the results of this frequency response analysis. The stress and displacement distributions and reliability of rocket motors under static or dynamic line loads are analyzed by an elasticity approach. Rocket motors are modeled as long hollow multilayered cylinders with an air core, a thick isotropic propellant inner layer and a thin orthotropic kevlar-epoxy case. The case is treated as a single orthotropic layer or a ten layered orthotropic structure. Five material properties and the load are treated as random variable with normal distributions when the reliability of the rocket motor is analyzed by the first-order, second-moment method (FOSM).

Projection multiplex recording of computer-synthesised one-dimensional Fourier holograms for holographic memory systems: mathematical and experimental modelling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Betin, A Yu; Bobrinev, V I; Verenikina, N M

A multiplex method of recording computer-synthesised one-dimensional Fourier holograms intended for holographic memory devices is proposed. The method potentially allows increasing the recording density in the previously proposed holographic memory system based on the computer synthesis and projection recording of data page holograms. (holographic memory)

Application of Fourier transforms for microwave radiometric inversions

NASA Technical Reports Server (NTRS)

Holmes, J. J.; Balanis, C. A.; Truman, W. M.

1975-01-01

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

The morphing of geographical features by Fourier transformation

PubMed Central

Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features’ continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable. PMID:29351344

[Continuum based fast Fourier transform processing of infrared spectrum].

PubMed

Liu, Qing-Jie; Lin, Qi-Zhong; Wang, Qin-Jun; Li, Hui; Li, Shuai

2009-12-01

To recognize ground objects with infrared spectrum, high frequency noise removing is one of the most important phases in spectrum feature analysis and extraction. A new method for infrared spectrum preprocessing was given combining spectrum continuum processing and Fast Fourier Transform (CFFT). Continuum was firstly removed from the noise polluted infrared spectrum to standardize hyper-spectra. Then the spectrum was transformed into frequency domain (FD) with fast Fourier transform (FFT), separating noise information from target information After noise eliminating from useful information with a low-pass filter, the filtered FD spectrum was transformed into time domain (TD) with fast Fourier inverse transform. Finally the continuum was recovered to the spectrum, and the filtered infrared spectrum was achieved. Experiment was performed for chlorite spectrum in USGS polluted with two kinds of simulated white noise to validate the filtering ability of CFFT by contrast with cubic function of five point (CFFP) in time domain and traditional FFT in frequency domain. A circle of CFFP has limited filtering effect, so it should work much with more circles and consume more time to achieve better filtering result. As for conventional FFT, Gibbs phenomenon has great effect on preprocessing result at edge bands because of special character of rock or mineral spectra, while works well at middle bands. Mean squared error of CFFT is 0. 000 012 336 with cut-off frequency of 150, while that of FFT and CFFP is 0. 000 061 074 with cut-off frequency of 150 and 0.000 022 963 with 150 working circles respectively. Besides the filtering result of CFFT can be improved by adjusting the filter cut-off frequency, and has little effect on working time. The CFFT method overcomes the Gibbs problem of FFT in spectrum filtering, and can be more convenient, dependable, and effective than traditional TD filter methods.

Kinetics of lisinopril intramolecular cyclization in solid phase monitored by Fourier transform infrared microscopy.

PubMed

Widjaja, Effendi; Tan, Wei Jian

2008-08-01

The solid-state intramolecular cyclization of lisinopril to diketopiperazine was investigated by in situ Fourier transform infrared (FT-IR) microscopy. Using a controllable heating cell, the isothermal transformation was monitored in situ at 147.5, 150, 152.5, 155, and 157.5 degrees C. The collected time-dependent FT-IR spectra at each isothermal temperature were preprocessed and analyzed using a multivariate chemometric approach. The pure component spectra of the observable component (lisinopril and diketopiperazine) were resolved and their time-dependent relative contributions were also determined. Model-free and various model fitting methods were implemented in the kinetic analysis to estimate the activation energy of the intramolecular cyclization reaction. Arrhenius plots indicate that the activation energy is circa 327 kJ/mol.

Contrast computation methods for interferometric measurement of sensor modulation transfer function

NASA Astrophysics Data System (ADS)

Battula, Tharun; Georgiev, Todor; Gille, Jennifer; Goma, Sergio

2018-01-01

Accurate measurement of image-sensor frequency response over a wide range of spatial frequencies is very important for analyzing pixel array characteristics, such as modulation transfer function (MTF), crosstalk, and active pixel shape. Such analysis is especially significant in computational photography for the purposes of deconvolution, multi-image superresolution, and improved light-field capture. We use a lensless interferometric setup that produces high-quality fringes for measuring MTF over a wide range of frequencies (here, 37 to 434 line pairs per mm). We discuss the theoretical framework, involving Michelson and Fourier contrast measurement of the MTF, addressing phase alignment problems using a moiré pattern. We solidify the definition of Fourier contrast mathematically and compare it to Michelson contrast. Our interferometric measurement method shows high detail in the MTF, especially at high frequencies (above Nyquist frequency). We are able to estimate active pixel size and pixel pitch from measurements. We compare both simulation and experimental MTF results to a lens-free slanted-edge implementation using commercial software.

Dissipative structure and global existence in critical space for Timoshenko system of memory type

NASA Astrophysics Data System (ADS)

Mori, Naofumi

2018-08-01

In this paper, we consider the initial value problem for the Timoshenko system with a memory term in one dimensional whole space. In the first place, we consider the linearized system: applying the energy method in the Fourier space, we derive the pointwise estimate of the solution in the Fourier space, which first gives the optimal decay estimate of the solution. Next, we give a characterization of the dissipative structure of the system by using the spectral analysis, which confirms our pointwise estimate is optimal. In the second place, we consider the nonlinear system: we show that the global-in-time existence and uniqueness result could be proved in the minimal regularity assumption in the critical Sobolev space H2. In the proof we don't need any time-weighted norm as recent works; we use just an energy method, which is improved to overcome the difficulties caused by regularity-loss property of Timoshenko system.

Development of Michelson interferometer based spatial phase-shift digital shearography

NASA Astrophysics Data System (ADS)

Xie, Xin

Digital shearography is a non-contact, full field, optical measurement method, which has the capability of directly measuring the gradient of deformation. For high measurement sensitivity, phase evaluation method has to be introduced into digital shearography by phase-shift technique. Catalog by phase-shift method, digital phase-shift shearography can be divided into Temporal Phase-Shift Digital Shearography (TPS-DS) and Spatial Phase-Shift Digital Shearography (SPS-DS). TPS-DS is the most widely used phase-shift shearography system, due to its simple algorithm, easy operation and good phase-map quality. However, the application of TPS-DS is only limited in static/step-by-step loading measurement situation, due to its multi-step shifting process. In order to measure the strain under dynamic/continuous loading situation, a SPS-DS system has to be developed. This dissertation aims to develop a series of Michelson Interferometer based SPS-DS measurement methods to achieve the strain measurement by using only a single pair of speckle pattern images. The Michelson Interferometer based SPS-DS systems utilize special designed optical setup to introduce extra carrier frequency into the laser wavefront. The phase information corresponds to the strain field can be separated on the Fourier domain using a Fourier Transform and can further be evaluated with a Windowed Inverse Fourier Transform. With different optical setups and carrier frequency arrangements, the Michelson Interferometer based SPS-DS method is capable to achieve a variety of measurement tasks using only single pair of speckle pattern images. Catalog by the aimed measurand, these capable measurement tasks can be divided into five categories: 1) measurement of out-of-plane strain field with small shearing amount; 2) measurement of relative out-of-plane deformation field with big shearing amount; 3) simultaneous measurement of relative out-of-plane deformation field and deformation gradient field by using multiple carrier frequencies; 4) simultaneous measurement of two directional strain field using dual measurement channels 5) measurement of pure in-plane strain and pure out-of-plane strain with multiple carrier frequencies. The basic theory, optical path analysis, preliminary studies, results analysis and research plan are shown in detail in this dissertation.

Anterior Chamber Angle Measurements Using Schwalbe's Line with High Resolution Fourier-Domain Optical Coherence Tomography

PubMed Central

Qin, Bing; Francis, Brian A.; Li, Yan; Tang, Maolong; Zhang, Xinbo; Jiang, Chunhui; Cleary, Catherine; Huang, David

2012-01-01

Purpose To use Fourier-domain optical coherence tomography (OCT) to measure the angle opening distance at Schwalbe's line (AOD-SL) and determine its value in anterior chamber angle assessment. Methods Horizontal scans of the nasal and temporal anterior chamber angles in glaucoma subjects were performed by 830 nm wavelength Fourier-domain OCT. Images were graded by two ophthalmologists who assessed the visibility of Schwalbe’s line (SL), anterior limbus (AL), scleral spur (SS), and angle recess (AR). AOD-SL was measured with computer calipers. SL was manually identified by the termination of the corneal endothelium. Gonioscopy was used to classify anterior chamber angles according to a modified Shaffer system. Spearman's rho analysis was performed to assess correlation between AOD-SL and modified Shaffer grade. A cut-off value of AOD-SL for diagnosing occludable angles (modified Shaffer grade ≤1) was determined by receiver operating characteristic (ROC) analyses. Results Thirty-five glaucoma subjects (65 eyes) were enrolled. SL, AL, AR, and SS were visible by OCT in 97.7%, 99.2%, 87.3%, and 80.8% of eyes, respectively. Nasal and temporal AOD-SLs were 322.6 ± 200.2 µm and 341.4 ± 197.4 µm, respectively. Correlation coefficients between AOD-SL and modified Shaffer grade were 0.80 (nasal) and 0.81 (temporal). The diagnostic cut-off value of AOD-SL for occludable angles was 290 µm. The areas under the ROC curve, sensitivity, specificity values were 0.90, 0.80, 0.87 (nasal) and 0.90, 0.85, 0.77 (temporal). Conclusions The measurement of AOD-SL by Fourier-domain OCT is highly correlated with gonioscopy and may be a useful noncontact method of assessing angle closure risk. PMID:22827999

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

NASA Astrophysics Data System (ADS)

Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua

2016-07-01

On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.

Dynamic characterization of a damaged beam using empirical mode decomposition and Hilbert spectrum method

NASA Astrophysics Data System (ADS)

Chang, Chih-Chen; Poon, Chun-Wing

2004-07-01

Recently, the empirical mode decomposition (EMD) in combination with the Hilbert spectrum method has been proposed to identify the dynamic characteristics of linear structures. In this study, this EMD and Hilbert spectrum method is used to analyze the dynamic characteristics of a damaged reinforced concrete (RC) beam in the laboratory. The RC beam is 4m long with a cross section of 200mm X 250mm. The beam is sequentially subjected to a concentrated load of different magnitudes at the mid-span to produce different degrees of damage. An impact load is applied around the mid-span to excite the beam. Responses of the beam are recorded by four accelerometers. Results indicate that the EMD and Hilbert spectrum method can reveal the variation of the dynamic characteristics in the time domain. These results are also compared with those obtained using the Fourier analysis. In general, it is found that the two sets of results correlate quite well in terms of mode counts and frequency values. Some differences, however, can be seen in the damping values, which perhaps can be attributed to the linear assumption of the Fourier transform.

Application of multibounce attenuated total reflectance fourier transform infrared spectroscopy and chemometrics for determination of aspartame in soft drinks.

PubMed

Khurana, Harpreet Kaur; Cho, Il Kyu; Shim, Jae Yong; Li, Qing X; Jun, Soojin

2008-02-13

Aspartame is a low-calorie sweetener commonly used in soft drinks; however, the maximum usage dose is limited by the U.S. Food and Drug Administration. Fourier transform infrared (FTIR) spectroscopy with attenuated total reflectance sampling accessory and partial least-squares regression (PLS) was used for rapid determination of aspartame in soft drinks. On the basis of spectral characterization, the highest R2 value, and lowest PRESS value, the spectral region between 1600 and 1900 cm(-1) was selected for quantitative estimation of aspartame. The potential of FTIR spectroscopy for aspartame quantification was examined and validated by the conventional HPLC method. Using the FTIR method, aspartame contents in four selected carbonated diet soft drinks were found to average from 0.43 to 0.50 mg/mL with prediction errors ranging from 2.4 to 5.7% when compared with HPLC measurements. The developed method also showed a high degree of accuracy because real samples were used for calibration, thus minimizing potential interference errors. The FTIR method developed can be suitably used for routine quality control analysis of aspartame in the beverage-manufacturing sector.

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

NASA Technical Reports Server (NTRS)

Noah, S. T.; Kim, Y. B.

1991-01-01

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

In-situ chemical analyses of trans-polyisoprene by histochemical staining and Fourier transform infrared microspectroscopy in a rubber-producing plant, Eucommia ulmoides Oliver.

PubMed

Bamba, Takeshi; Fukusaki, Ei-Ichiro; Nakazawa, Yoshihisa; Kobayashi, Akio

2002-10-01

The localization of polyisoprene in young stem tissues of Eucommia ulmoides Oliver was investigated by histochemical staining and Fourier transform infrared (FT-IR) microspectroscopy. The fibrous structures were stained with Oil Red O. FT-IR microspectroscopic analysis proved that the fibrous structures were trans-polyisoprene. Granular structures stained with the dye, and characteristic absorptions at 2,960 cm(-1) and 1,430 cm(-1) in FT-IR suggested that trans-polyisoprene accumulated in the vicinity of the cambium layer. We have thus successfully shown for the first time the localization of trans-polyisoprene in plant tissues, and our histological investigation allowed us to presume the main sites of biosynthesis and accumulation of trans-rubber. Furthermore, a new technical approach, the preparation of sections using an electronic freezing unit and the in situ analysis of polyisoprene using FT-IR microspectroscopy, is demonstrated to be a promising method for determining the accumulation of polyisoprene as well as other metabolites.

Identification of aerodynamic models for maneuvering aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Hu, C. C.

1992-01-01

The method based on Fourier functional analysis and indicial formulation for aerodynamic modeling as proposed by Chin and Lan is extensively examined and improved for the purpose of general applications to realistic airplane configurations. Improvement is made to automate the calculation of model coefficients, and to evaluate more accurately the indicial integral. Test data of large angle-of-attack ranges for two different models, a 70 deg. delta wing and an F-18 model, are used to further verify the applicability of Fourier functional analysis and validate the indicial formulation. The results show that the general expression for harmonic motions throughout a range of k is capable of accurately modeling the nonlinear responses with large phase lag except in the region where an inconsistent hysteresis behavior from one frequency to the other occurs. The results by the indicial formulation indicate that more accurate results can be obtained when the motion starts from a low angle of attack where hysteresis effect is not important.

Isogyres - Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference

NASA Astrophysics Data System (ADS)

Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.

2016-09-01

Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.

Isogyres - Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference.

PubMed

Samlan, C T; Naik, Dinesh N; Viswanathan, Nirmal K

2016-09-14

Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.

Fluorescence lifetime imaging and Fourier transform infrared spectroscopy of Michelangelo's David.

PubMed

Comelli, Daniela; Valentini, Gianluca; Cubeddu, Rinaldo; Toniolo, Lucia

2005-09-01

We developed a combined procedure for the analysis of works of art based on a portable system for fluorescence imaging integrated with analytical measurements on microsamples. The method allows us to localize and identify organic and inorganic compounds present on the surface of artworks. The fluorescence apparatus measures the temporal and spectral features of the fluorescence emission, excited by ultraviolet (UV) laser pulses. The kinetic of the emission is studied through a fluorescence lifetime imaging system, while an optical multichannel analyzer measures the fluorescence spectra of selected points. The chemical characterization of the compounds present on the artistic surfaces is then performed by means of analytical measurements on microsamples collected with the assistance of the fluorescence maps. The previous concepts have been successfully applied to study the contaminants on the surface of Michelangelo's David. The fluorescence analysis combined with Fourier transform infrared (FT-IR) measurements revealed the presence of beeswax, which permeates most of the statue surface, and calcium oxalate deposits mainly arranged in vertical patterns and related to rain washing.

Comparison study on biosynthesis of silver nanoparticles using fresh and hot air oven dried IMPERATA CYLINDRICA leaf

NASA Astrophysics Data System (ADS)

Najmi Bonnia, Noor; Fairuzi, Afiza Ahmad; Akhir, Rabiatuladawiyah Md.; Yahya, Sabrina M.; Rani, Mohd Azri Ab; Ratim, Suzana; Rahman, Norafifah A.; Akil, Hazizan Md

2018-01-01

The perennial rhizomatous grass; Imperata cylindrica (I. cylindrica) has been reported rich in various phytochemicals. In present study, silver nanoparticles were synthesized from aqueous leaf extract of I. cylindrica at two different leaf conditions; fresh leaves and hot-air oven dried leaves. Biosynthesized silver nanoparticles were characterized by UV-visible spectroscopy, field emission scanning electron microscopy (FESEM) and Fourier transform infrared spectroscopy (FTIR). Maximum absorption was recorded between 400 nm to 500 nm. FESEM analysis revealed that the silver nanoparticles predominantly form spherical shapes. The particles sizes were ranging from 22-37 nm. The elemental composition of the synthesized silver nanoparticles was confirmed by using energy dispersive X-ray spectroscopy (EDX) analysis. Fourier transform infrared spectroscopy (FTIR) confirmed the reducing and stabilizing actions came from biomolecules associated with I. cylindrica leaf extract. Thus in this investigation, an environmentally safe method to synthesized silver nanoparticles using local plant extract was successfully established.

Independent component analysis for onset detection in piano trills

NASA Astrophysics Data System (ADS)

Brown, Judith C.; Todd, Jeremy G.; Smaragdis, Paris

2002-05-01

The detection of onsets in piano music is difficult due to the presence of many notes simultaneously and their long decay times from pedaling. This is even more difficult for trills where the rapid note changes make it difficult to observe a decrease in amplitude for individual notes in either the temporal wave form or the time dependent Fourier components. Occasionally one note of the trill has a much lower amplitude than the other making an unambiguous determination of its onset virtually impossible. We have analyzed a number of trills from CD's of performances by Horowitz, Ashkenazy, and Goode, choosing the same trill and different performances where possible. The Fourier transform was calculated as a function of time, and the magnitude coefficients served as input for a calculation using the method of independent component analysis. In most cases this gave a more definitive determination of the onset times, as can be demonstrated graphically. For comparison identical calculations have been carried out on recordings of midi generated performances on a Yamaha Disclavier piano.

Analysis of grain boundary phase devitrification of Y2O3- and Al2O3-doped Si3N4

NASA Technical Reports Server (NTRS)

Hench, L. L.; Vaidyanathan, P. N.

1983-01-01

The present study has the objective to show that a Fourier Transform IR (FTIR) spectrometer in a single-beam reflection mode can be used for direct comparison of fractured vs nonfractured Si3N4 surfaces. This can be done because the FTIR method permits a digital summation of nearly 1000 scans of the fracture surface. Commercial-grade Si3N4, Y2O3, and Al2O3 were used in the study. The samples were heat treated in a vacuum induction heating furnace at either 1000 C for 10 h or 1200 C for 10 h each. Use of Fourier transform IR reflection spectroscopic analysis and X-ray diffraction shows that 10 h at 1200 C is sufficient to devitrify the amorphous grain boundary phase of Si3N4 containing 15 percent Y2O3 + 2 percent Al2O3 densification aids.

Phase unwrapping with a virtual Hartmann-Shack wavefront sensor.

PubMed

Akondi, Vyas; Falldorf, Claas; Marcos, Susana; Vohnsen, Brian

2015-10-05

The use of a spatial light modulator for implementing a digital phase-shifting (PS) point diffraction interferometer (PDI) allows tunability in fringe spacing and in achieving PS without the need for mechanically moving parts. However, a small amount of detector or scatter noise could affect the accuracy of wavefront sensing. Here, a novel method of wavefront reconstruction incorporating a virtual Hartmann-Shack (HS) wavefront sensor is proposed that allows easy tuning of several wavefront sensor parameters. The proposed method was tested and compared with a Fourier unwrapping method implemented on a digital PS PDI. The rewrapping of the Fourier reconstructed wavefronts resulted in phase maps that matched well the original wrapped phase and the performance was found to be more stable and accurate than conventional methods. Through simulation studies, the superiority of the proposed virtual HS phase unwrapping method is shown in comparison with the Fourier unwrapping method in the presence of noise. Further, combining the two methods could improve accuracy when the signal-to-noise ratio is sufficiently high.

Thermal image analysis using the serpentine method

NASA Astrophysics Data System (ADS)

Koprowski, Robert; Wilczyński, Sławomir

2018-03-01

Thermal imaging is an increasingly widespread alternative to other imaging methods. As a supplementary method in diagnostics, it can be used both statically and with dynamic temperature changes. The paper proposes a new image analysis method that allows for the acquisition of new diagnostic information as well as object segmentation. The proposed serpentine analysis uses known and new methods of image analysis and processing proposed by the authors. Affine transformations of an image and subsequent Fourier analysis provide a new diagnostic quality. The method is fully repeatable and automatic and independent of inter-individual variability in patients. The segmentation results are by 10% better than those obtained from the watershed method and the hybrid segmentation method based on the Canny detector. The first and second harmonics of serpentine analysis enable to determine the type of temperature changes in the region of interest (gradient, number of heat sources etc.). The presented serpentine method provides new quantitative information on thermal imaging and more. Since it allows for image segmentation and designation of contact points of two and more heat sources (local minimum), it can be used to support medical diagnostics in many areas of medicine.

On the action of Heisenberg's uncertainty principle in discrete linear methods for calculating the components of the deflection of the vertical

NASA Astrophysics Data System (ADS)

Mazurova, Elena; Lapshin, Aleksey

2013-04-01

The method of discrete linear transformations that can be implemented through the algorithms of the Standard Fourier Transform (SFT), Short-Time Fourier Transform (STFT) or Wavelet transform (WT) is effective for calculating the components of the deflection of the vertical from discrete values of gravity anomaly. The SFT due to the action of Heisenberg's uncertainty principle indicates weak spatial localization that manifests in the following: firstly, it is necessary to know the initial digital signal on the complete number line (in case of one-dimensional transform) or in the whole two-dimensional space (if a two-dimensional transform is performed) in order to find the SFT. Secondly, the localization and values of the "peaks" of the initial function cannot be derived from its Fourier transform as the coefficients of the Fourier transform are formed by taking into account all the values of the initial function. Thus, the SFT gives the global information on all frequencies available in the digital signal throughout the whole time period. To overcome this peculiarity it is necessary to localize the signal in time and apply the Fourier transform only to a small portion of the signal; the STFT that differs from the SFT only by the presence of an additional factor (window) is used for this purpose. A narrow enough window is chosen to localize the signal in time and, according to Heisenberg's uncertainty principle, it results in have significant enough uncertainty in frequency. If one chooses a wide enough window it, according to the same principle, will increase time uncertainty. Thus, if the signal is narrowly localized in time its spectrum, on the contrary, is spread on the complete axis of frequencies, and vice versa. The STFT makes it possible to improve spatial localization, that is, it allows one to define the presence of any frequency in the signal and the interval of its presence. However, owing to Heisenberg's uncertainty principle, it is impossible to tell precisely, what frequency is present in the signal at the current moment of time: it is possible to speak only about the range of frequencies. Besides, it is impossible to specify precisely the time moment of the presence of this or that frequency: it is possible to speak only about the time frame. It is this feature that imposes major constrains on the applicability of the STFT. In spite of the fact that the problems of resolution in time and frequency result from a physical phenomenon (Heisenberg's uncertainty principle) and exist independent of the transform applied, there is a possibility to analyze any signal, using the alternative approach - the multiresolutional analysis (MRA). The wavelet-transform is one of the methods for making a MRA-type analysis. Thanks to it, low frequencies can be shown in a more detailed form with respect to time, and high ones - with respect to frequency. The paper presents the results of calculating of the components of the deflection of the vertical, done by the SFT, STFT and WT. The results are presented in the form of 3-d models that visually show the action of Heisenberg's uncertainty principle in the specified algorithms. The research conducted allows us to recommend the application of wavelet-transform to calculate of the components of the deflection of the vertical in the near-field zone. Keywords: Standard Fourier Transform, Short-Time Fourier Transform, Wavelet Transform, Heisenberg's uncertainty principle.

LORAKS Makes Better SENSE: Phase-Constrained Partial Fourier SENSE Reconstruction without Phase Calibration

PubMed Central

Kim, Tae Hyung; Setsompop, Kawin; Haldar, Justin P.

2016-01-01

Purpose Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information. Theory and Methods The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly-accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely-used calibrationless uniformly-undersampled trajectories. Results Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches. Conclusion The SENSE-LORAKS framework provides promising new opportunities for highly-accelerated MRI. PMID:27037836

A study on the application of Fourier series in IMRT treatment planning.

PubMed

Almeida-Trinidad, R; Garnica-Garza, H M

2007-12-01

In intensity-modulated radiotherapy, a set of x-ray fluence profiles is iteratively adjusted until a desired absorbed dose distribution is obtained. The purpose of this article is to present a method that allows the optimization of fluence profiles based on the Fourier series decomposition of an initial approximation to the profile. The method has the advantage that a new fluence profile can be obtained in a precise and controlled way with the tuning of only two parameters, namely the phase of the sine and cosine terms of one of the Fourier components, in contrast to the point-by-point tuning of the profile. Also, because the method uses analytical functions, the resultant profiles do not exhibit numerical artifacts. A test case consisting of a mathematical phantom with a target wrapped around a critical structure is discussed to illustrate the algorithm. It is shown that the degree of conformality of the absorbed dose distribution can be tailored by varying the number of Fourier terms made available to the optimization algorithm. For the test case discussed here, it is shown that the number of Fourier terms to be modified depends on the number of radiation beams incident on the target but it is in general in the order of 10 terms.

Program for the analysis of time series. [by means of fast Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Brown, T. J.; Brown, C. G.; Hardin, J. C.

1974-01-01

A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.

Polarization Ratio Determination with Two Identical Linearly Polarized Antennas

DTIC Science & Technology

2017-01-17

Fourier transform analysis of 21 measurements with one of the antennas rotating about its axis a circular polarization ratio is derived which can be...deter- mined directly from a discrete Fourier transform (DFT) of (5). However, leakage between closely spaced DFT bins requires improving the... Fourier transform and a mechanical antenna rotation to separate the principal and opposite circular polarization components followed by a basis

A Comparison of FTNMR and FTIR Techniques.

ERIC Educational Resources Information Center

Ahn, Myong-Ku

1989-01-01

Nuclear magnetic resonance and infrared are two spectroscopic methods that commonly use the Fourier transform technique. Discussed are the similarities and differences in the use of the Fourier transform in these two spectroscopic techniques. (CW)

Evaluation of the use of a singularity element in finite element analysis of center-cracked plates

NASA Technical Reports Server (NTRS)

Mendelson, A.; Gross, B.; Srawley, J., E.

1972-01-01

Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.

Fourier Analysis of Musical Intervals

ERIC Educational Resources Information Center

LoPresto, Michael C.

2008-01-01

Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace. A recent article in "The Physics Teacher" aptly demonstrated the use of MacScope in just such a manner as a way to teach Fourier analysis. A logical continuation of this project is to…

Using time-frequency analysis to determine time-resolved detonation velocity with microwave interferometry.

PubMed

Kittell, David E; Mares, Jesus O; Son, Steven F

2015-04-01

Two time-frequency analysis methods based on the short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were used to determine time-resolved detonation velocities with microwave interferometry (MI). The results were directly compared to well-established analysis techniques consisting of a peak-picking routine as well as a phase unwrapping method (i.e., quadrature analysis). The comparison is conducted on experimental data consisting of transient detonation phenomena observed in triaminotrinitrobenzene and ammonium nitrate-urea explosives, representing high and low quality MI signals, respectively. Time-frequency analysis proved much more capable of extracting useful and highly resolved velocity information from low quality signals than the phase unwrapping and peak-picking methods. Additionally, control of the time-frequency methods is mainly constrained to a single parameter which allows for a highly unbiased analysis method to extract velocity information. In contrast, the phase unwrapping technique introduces user based variability while the peak-picking technique does not achieve a highly resolved velocity result. Both STFT and CWT methods are proposed as improved additions to the analysis methods applied to MI detonation experiments, and may be useful in similar applications.

Study on sampling of continuous linear system based on generalized Fourier transform

NASA Astrophysics Data System (ADS)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

Cylindrical angular spectrum using Fourier coefficients of point light source and its application to fast hologram calculation.

PubMed

Oh, Seungtaik; Jeong, Il Kwon

2015-11-16

We will introduce a new simple analytic formula of the Fourier coefficient of the 3D field distribution of a point light source to generate a cylindrical angular spectrum which captures the object wave in 360° in the 3D Fourier space. Conceptually, the cylindrical angular spectrum can be understood as a cylindrical version of the omnidirectional spectral approach of Sando et al. Our Fourier coefficient formula is based on an intuitive observation that a point light radiates uniformly in all directions. Our formula is defined over all frequency vectors lying on the entire sphere in the 3D Fourier space and is more natural and computationally more efficient for all around recording of the object wave than that of the previous omnidirectional spectral method. A generalized frequency-based occlusion culling method for an arbitrary complex object is also proposed to enhance the 3D quality of a hologram. As a practical application of the cylindrical angular spectrum, an interactive hologram example is presented together with implementation details.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1990-09-18

to be published Proceedings: conference Chaos in Australia (February 1990). 5. On the Kadomtsev Petviashvili Equation and Associated Constraints by...Scattering Transfoni (IST). IST is a method which alows one to’solve nonlinear wave equations by solving certain related direct and inverse scattering...problems. We use these results to find solutions to nonlinear wave equations much like one uses Fourier analysis for linear problems. Moreover the

Extending Single-Molecule Microscopy Using Optical Fourier Processing

PubMed Central

2015-01-01

This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules. PMID:24745862

Extending single-molecule microscopy using optical Fourier processing.

PubMed

Backer, Adam S; Moerner, W E

2014-07-17

This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.

Application of Savitzky-Golay differentiation filters and Fourier functions to simultaneous determination of cefepime and the co-administered drug, levofloxacin, in spiked human plasma

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Omar; Abdel-Ghany, Maha F.; Nagi, Reham; Abdel-Fattah, Laila

2015-03-01

The present work is concerned with simultaneous determination of cefepime (CEF) and the co-administered drug, levofloxacin (LEV), in spiked human plasma by applying a new approach, Savitzky-Golay differentiation filters, and combined trigonometric Fourier functions to their ratio spectra. The different parameters associated with the calculation of Savitzky-Golay and Fourier coefficients were optimized. The proposed methods were validated and applied for determination of the two drugs in laboratory prepared mixtures and spiked human plasma. The results were statistically compared with reported HPLC methods and were found accurate and precise.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

PubMed

Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun

2009-05-01

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

Self tuning system for industrial surveillance

DOEpatents

Stephan, Wegerich W; Jarman, Kristin K.; Gross, Kenneth C.

2000-01-01

A method and system for automatically establishing operational parameters of a statistical surveillance system. The method and system performs a frequency domain transition on time dependent data, a first Fourier composite is formed, serial correlation is removed, a series of Gaussian whiteness tests are performed along with an autocorrelation test, Fourier coefficients are stored and a second Fourier composite is formed. Pseudorandom noise is added, a Monte Carlo simulation is performed to establish SPRT missed alarm probabilities and tested with a synthesized signal. A false alarm test is then emperically evaluated and if less than a desired target value, then SPRT probabilities are used for performing surveillance.

Determination of diosmin in pharmaceutical formulations using Fourier transform infrared spectrophotometry

PubMed Central

Bunaciu, Andrei A.; Udristioiu, Gabriela Elena; Ruţă, Lavinia L.; Fleschin, Şerban; Aboul-Enein, Hassan Y.

2009-01-01

A Fourier transform infrared (FT-IR) spectrometric method was developed for the rapid, direct measurement of diosmin in different pharmaceutical drugs. Conventional KBr-spectra were compared for best determination of active substance in commercial preparations. The Beer–Lambert law and two chemometric approaches, partial least squares (PLS) and principal component regression (PCR+) methods, were tried in data processing. PMID:23960715

Technique for the metrology calibration of a Fourier transform spectrometer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spencer, Locke D.; Naylor, David A

2008-11-10

A method is presented for using a Fourier transform spectrometer (FTS) to calibrate the metrology of a second FTS. This technique is particularly useful when the second FTS is inside a cryostat or otherwise inaccessible.

Fourier functional analysis for unsteady aerodynamic modeling

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Chin, Suei

1991-01-01

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

Fourier Transform Infrared Absorption Spectroscopy for Quantitative Analysis of Gas Mixtures at Low Temperatures for Homeland Security Applications.

PubMed

Meier, D C; Benkstein, K D; Hurst, W S; Chu, P M

2017-05-01

Performance standard specifications for point chemical vapor detectors are established in ASTM E 2885-13 and ASTM E 2933-13. The performance evaluation of the detectors requires the accurate delivery of known concentrations of the chemical target to the system under test. Referee methods enable the analyte test concentration and associated uncertainties in the analyte test concentration to be validated by independent analysis, which is especially important for reactive analytes. This work extends the capability of a previously demonstrated method for using Fourier transform infrared (FT-IR) absorption spectroscopy for quantitatively evaluating the composition of vapor streams containing hazardous materials at Acute Exposure Guideline Levels (AEGL) to include test conditions colder than laboratory ambient temperatures. The described method covers the use of primary reference spectra to establish analyte concentrations, the generation of secondary reference spectra suitable for measuring analyte concentrations under specified testing environments, and the use of additional reference spectra and spectral profile strategies to mitigate the uncertainties due to impurities and water condensation within the low-temperature (7 °C, -5 °C) test cell. Important benefits of this approach include verification of the test analyte concentration with characterized uncertainties by in situ measurements co-located with the detector under test, near-real-time feedback, and broad applicability to toxic industrial chemicals.