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.

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.

Unsupervised malaria parasite detection based on phase spectrum.

PubMed

Fang, Yuming; Xiong, Wei; Lin, Weisi; Chen, Zhenzhong

2011-01-01

In this paper, we propose a novel method for malaria parasite detection based on phase spectrum. The method first obtains the amplitude spectrum and phase spectrum for blood smear images through Quaternion Fourier Transform (QFT). Then it gets the reconstructed image based on Inverse Quaternion Fourier transform (IQFT) on a constant amplitude spectrum and the original phase spectrum. The malaria parasite areas can be detected easily from the reconstructed blood smear images. Extensive experiments have demonstrated the effectiveness of this novel method.

Improved methods of performing coherent optical correlation

NASA Technical Reports Server (NTRS)

Husain-Abidi, A. S.

1972-01-01

Coherent optical correlators are described in which complex spatial filters are recorded by a quasi-Fourier transform method. The high-pass spatial filtering effects (due to the dynamic range of photographic films) normally encountered in Vander Lugt type complex filters are not present in this system. Experimental results for both transmittive as well as reflective objects are presented. Experiments are also performed by illuminating the object with diffused light. A correlator using paraboloidal mirror segments as the Fourier-transforming element is also described.

The Application of MP-FTS to Aperture Synthesis

NASA Astrophysics Data System (ADS)

Hattori, M.; Ohta, I. S.; Matsuo, H.; Shibata, Y.

2000-12-01

The application of the Martin-Puplett type Fourier transform spectrometer to aperture synthesis is considered. The configuration of the mirrors and beam splitters and the fundamental mathematical elements of the system are summarized. We show that the system can measure spectrally resolved spatial distribution of the Stokes parameters of sources as interfered signals. An original Martin-Puplett type Fourier transform spectrometer that can be applied to aperture synthesis in mm and sub-mm wave bands has been constructed. The preliminary results of our laboratory experiments are reported.

Characterization of ceramic matrix composite degradation using Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Henry, Christine; Criner, Amanda Keck; Imel, Megan; King, Derek

2018-04-01

Data collected with a handheld Fourier Transform Infrared (FTIR) device is analyzed and considered as a useful method for detecting and quantifying oxidation on the surface of ceramic matrix composite (CMC) materials. Experiments examine silicon carbide (SiC) coupons, looking for changes in chemical composition before and after thermal exposure. Using mathematical, physical and statistical models for FTIR reflectance data, this research seeks to quantify any detected spectral changes as an indicator of surface oxidation on the CMC coupon.

A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

ERIC Educational Resources Information Center

Debnath, Lokenath

2012-01-01

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

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.

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

Effect of ion clouds micromotion on measured signal in Fourier transform ion cyclotron resonance: Computer simulation.

PubMed

Vladimirov, Gleb; Kostyukevich, Yury; Kharybin, Oleg; Nikolaev, Eugene

2017-08-01

Particle-in-cell-based realistic simulation of Fourier transform ion cyclotron resonance experiments could be used to generate ion trajectories and a signal induced on the detection electrodes. It has been shown recently that there is a modulation of "reduced" cyclotron frequencies in ion cyclotron resonance signal caused by Coulomb interaction of ion clouds. In this work it was proposed to use this modulation in order to determine frequency difference between an ion of known m/z and all other ions generating signal in ion cyclotron resonance cell. It is shown that with an increase of number of ions in ion cyclotron resonance trap, the modulation index increases, which lead to a decrease in the accuracy of determination of peak intensities by super Fourier transform resolution methods such as filter diagonalization method.

The Fourier Transform in Chemistry-NMR, Part 3. Multiple-Pulse Experiments.

ERIC Educational Resources Information Center

Williams, Kathryn R.; King, Roy W.

1990-01-01

Described are six multipulse experiments with an emphasis on their application to common problems in chemistry. Exercises in relaxation time measurement, spin echoes, and polarization transfer are proposed. (CW)

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.

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.

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.

Fourier transform digital holographic adaptive optics imaging system

PubMed Central

Liu, Changgeng; Yu, Xiao; Kim, Myung K.

2013-01-01

A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541

Fractional finite Fourier transform.

PubMed

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Topics In Chemical Instrumentation: Fourier Transformations for Chemists Part I. Introduction to the Fourier Transform.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…

Simultaneous measurement of absolute strain and differential strain based on fiber Bragg grating Fabry-Perot sensor

NASA Astrophysics Data System (ADS)

Wang, Kuiru; Wang, Bo; Yan, Binbin; Sang, Xinzhu; Yuan, Jinhui; Peng, Gang-Ding

2013-10-01

We present a fiber Bragg grating Fabry-Perot (FBG-FP) sensor using the fast Fourier transform (FFT) demodulation for measuring the absolute strain and differential strain simultaneously. The amplitude and phase characteristics of Fourier transform spectrum have been studied. The relation between the amplitude of Fourier spectrum and the differential strain has been presented. We fabricate the fiber grating FP cavity sensor, and carry out the experiment on the measurement of absolute strain and differential strain. Experimental results verify the demodulation method, and show that this sensor has a good accuracy in the scope of measurement. The demodulating method can expand the number of multiplexed sensors combining with wavelength division multiplexing and time division multiplexing.

Fast frequency domain method to detect skew in a document image

NASA Astrophysics Data System (ADS)

Mehta, Sunita; Walia, Ekta; Dutta, Maitreyee

2015-12-01

In this paper, a new fast frequency domain method based on Discrete Wavelet Transform and Fast Fourier Transform has been implemented for the determination of the skew angle in a document image. Firstly, image size reduction is done by using two-dimensional Discrete Wavelet Transform and then skew angle is computed using Fast Fourier Transform. Skew angle error is almost negligible. The proposed method is experimented using a large number of documents having skew between -90° and +90° and results are compared with Moments with Discrete Wavelet Transform method and other commonly used existing methods. It has been determined that this method works more efficiently than the existing methods. Also, it works with typed, picture documents having different fonts and resolutions. It overcomes the drawback of the recently proposed method of Moments with Discrete Wavelet Transform that does not work with picture documents.

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.

The fractional Fourier transform and applications

NASA Technical Reports Server (NTRS)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

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.

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.

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

NASA Technical Reports Server (NTRS)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

PASSIVELY ESTIMATING INDEX OF REFRACTION FOR SPECULAR REFLECTORS USING POLARIMETRIC HYPERSPECTRAL IMAGING

DTIC Science & Technology

2016-12-22

23 6 Band-averaged radiance image with checkerboard is shown in the upper left. The 2-D Fourier transform of the image is...red is 1) that is multiplied by the Fourier transform of the original image. The inverse Fourier transform is then taken to get the final image with...Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 IFTS Imaging Fourier Transform Spectrometer

Microcomputer-Based Digital Signal Processing Laboratory Experiments.

ERIC Educational Resources Information Center

Tinari, Jr., Rocco; Rao, S. Sathyanarayan

1985-01-01

Describes a system (Apple II microcomputer interfaced to flexible, custom-designed digital hardware) which can provide: (1) Fast Fourier Transform (FFT) computation on real-time data with a video display of spectrum; (2) frequency synthesis experiments using the inverse FFT; and (3) real-time digital filtering experiments. (JN)

a Low-Cost Chirped-Pulse Fourier Transform Microwave Spectrometer for Undergraduate Physical Chemistry Lab

NASA Astrophysics Data System (ADS)

Carroll, Brandon; Finneran, Ian; Blake, Geoffrey

2014-06-01

We present the design and construction of a simple and low-cost waveguide chirped pulse Fourier transform microwave (CP-FTMW) spectrometer suitable for gas-phase rotational spectroscopy experiments in undergraduate physical chemistry labs as well as graduate level research. The spectrometer operates with modest bandwidth, using phased locked loop (PLL) microwave sources and a direct digital synthesis (DDS) chirp source, making it an affordable for undergraduate labs. The performance of the instrument is benchmarked by acquiring the pure rotational spectrum of the J = 1 - 0 transition OCS and its isotopologues from 11-12.5 GHz.

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

The paper analyzes the existing feature extraction methods. The characteristics of discrete Fourier transform and piecewise aggregation approximation are analyzed. Combining with the advantages of the two methods, a new piecewise discrete Fourier transform is proposed. And the method is used to analyze the lighting power of a large customer in this paper. The time series feature maps of four different cases are compared with the original data, discrete Fourier transform, piecewise aggregation approximation and piecewise discrete Fourier transform. This new method can reflect both the overall trend of electricity change and its internal changes in electrical analysis.

GIFTS EDU Ground-based Measurement Experiment

NASA Technical Reports Server (NTRS)

Zhou, Daniel K.; Smith, W. L., Sr.; Zollinger, L. J.; Huppi, R. J.; Reisse, R. A.; Larar, A. M.; Liu, X.; Tansock, J. J., Jr.; Jensen, S. M.; Revercomb, H. E.;

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",…

A fast algorithm for vertex-frequency representations of signals on graphs

PubMed Central

Jestrović, Iva; Coyle, James L.; Sejdić, Ervin

2016-01-01

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational complexity makes these algorithms impractical. We sought to develop a fast windowed graph Fourier transform and a fast graph S-transform requiring significantly shorter computation time. The proposed schemes have been tested with synthetic test graph signals and real graph signals derived from electroencephalography recordings made during swallowing. The results showed that the proposed schemes provide significantly lower computation time in comparison with the standard windowed graph Fourier transform and the fast graph S-transform. Also, the results showed that noise has no effect on the results of the algorithm for the fast windowed graph Fourier transform or on the graph S-transform. Finally, we showed that graphs can be reconstructed from the vertex-frequency representations obtained with the proposed algorithms. PMID:28479645

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.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

Atmospheric Chemistry Experiment (ACE) Measurements of Tropospheric and Stratospheric Chemistry and Long-Term Trends

NASA Technical Reports Server (NTRS)

Rinsland, Curtis P.; Bernath, Peter; Boone, Chris; Nassar, Ray

2007-01-01

We highlight chemistry and trend measurement results from the Atmospheric Chemistry Experiment (ACE) which is providing precise middle troposphere to the lower thermosphere measurements with a 0.02/cm resolution Fourier transform spectrometer covering 750-4400/cm

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

PubMed

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 2¹⁰ times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

Properties of the Magnitude Terms of Orthogonal Scaling Functions.

PubMed

Tay, Peter C; Havlicek, Joseph P; Acton, Scott T; Hossack, John A

2010-09-01

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.

Crystallinity Determination of Nylon 66 by Density Measurement and Fourier Transform Infrared (FTIR) Spectroscopy

ERIC Educational Resources Information Center

Vasanthan, N.

2012-01-01

Polymer science represents an important area in industrial and research laboratories for chemists and material scientists. However, experiments involving polymers are uncommon in chemistry and material science curricula; therefore, an experiment involving polymers has been developed. This experiment has been used to teach fabrication of polymer…

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.

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

[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.

Fourier removal of stripe artifacts in IRAS images

NASA Technical Reports Server (NTRS)

Van Buren, Dave

1987-01-01

By working in the Fourier plane, approximate removal of stripe artifacts in IRAS images can be effected. The image of interest is smoothed and subtracted from the original, giving the high-spatial-frequency part. This 'filtered' image is then clipped to remove point sources and then Fourier transformed. Subtracting the Fourier components contributing to the stripes in this image from the Fourier transform of the original and transforming back to the image plane yields substantial removal of the stripes.

NOTE: Calculating diffraction patterns

NASA Astrophysics Data System (ADS)

Rioux, Frank

2003-05-01

Following Marcella's approach to the double-slit experiment (Marcella T V 2002 Eur. J. Phys. 23 615-21), diffraction patterns for two-dimensional masks are calculated by Fourier transform of the Mask geometry into momentum space.

Electro-Optical Imaging Fourier-Transform Spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

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.

Geometric interpretations of the Discrete Fourier Transform (DFT)

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1984-01-01

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Using an NMR Spectrometer to Do Magnetic Resonance Imaging: An Undergraduate Physical Chemistry Laboratory Experiment

ERIC Educational Resources Information Center

Steinmetz, Wayne E.; Maher, M. Cyrus

2007-01-01

A conventional Fourier-transform NMR spectrometer with a triple-axis gradient probe can function as a MRI imager. In this experiment students gain hands-on experience with MRI while they learn about important principles underlying the practice of NMR, such as gradients, multi-dimensional spectroscopy, and relaxation. Students image a biological…

Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)

Determination of Fourier Transforms on an Instructional Analog Computer

ERIC Educational Resources Information Center

Anderson, Owen T.; Greenwood, Stephen R.

1974-01-01

An analog computer program to find and display the Fourier transform of some real, even functions is described. Oscilloscope traces are shown for Fourier transforms of a rectangular pulse, a Gaussian, a cosine wave, and a delayed narrow pulse. Instructional uses of the program are discussed briefly. (DT)

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.

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.

360° Fourier transform profilometry in surface reconstruction for fluorescence molecular tomography.

PubMed

Shi, Bi'er; Zhang, Bin; Liu, Fei; Luo, Jianwen; Bai, Jing

2013-05-01

Fluorescence molecular tomography (FMT) is an emerging tool in the observation of diseases. A fast and accurate surface reconstruction of the experimental object is needed as a boundary constraint for FMT reconstruction. In this paper, an automatic, noncontact, and 3-D surface reconstruction method named 360◦ Fourier transform profilometry (FTP) is proposed to reconstruct 3-D surface profiles for FMT system. This method can reconstruct 360◦ integrated surface profiles utilizing the single-frame FTP at different angles. Results show that the relative mean error of the surface reconstruction of this method is less than 1.4% in phantom experiments, and is no more than 2.9% in mouse experiments in vivo. Compared with the Radon transform method, the proposed method reduces the computation time by more than 90% with a minimal error increase. At last, a combined 360◦ FTP/FMT experiment is conducted on a nude mouse. Not only can the 360◦ FTP system operate with the FMT system simultaneously, but it can also help to monitor the status of animals. Moreover, the 360◦ FTP system is independent of FMT system and can be performed to reconstruct the surface by itself.

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

The scale of the Fourier transform: a point of view of the fractional Fourier transform

NASA Astrophysics Data System (ADS)

Jimenez, C. J.; Vilardy, J. M.; Salinas, S.; Mattos, L.; Torres, C. O.

2017-01-01

In this paper using the Fourier transform of order fractional, the ray transfer matrix for the symmetrical optical systems type ABCD and the formulae by Collins for the diffraction, we obtain explicitly the expression for scaled Fourier transform conventional; this result is the great importance in optical signal processing because it offers the possibility of scaling the size of output the Fourier distribution of the system, only by manipulating the distance of the diffraction object toward the thin lens, this research also emphasizes on practical limits when a finite spherical converging lens aperture is used. Digital simulation was carried out using the numerical platform of Matlab 7.1.

Motion detection using extended fractional Fourier transform and digital speckle photography.

PubMed

Bhaduri, Basanta; Tay, C J; Quan, C; Sheppard, Colin J R

2010-05-24

Digital speckle photography is a useful tool for measuring the motion of optically rough surfaces from the speckle shift that takes place at the recording plane. A simple correlation based digital speckle photographic system has been proposed that implements two simultaneous optical extended fractional Fourier transforms (EFRTs) of different orders using only a single lens and detector to simultaneously detect both the magnitude and direction of translation and tilt by capturing only two frames: one before and another after the object motion. The dynamic range and sensitivity of the measurement can be varied readily by altering the position of the mirror/s used in the optical setup. Theoretical analysis and experiment results are presented.

Experimental Research Into Generation of Acoustic Emission Signals in the Process of Friction of Hadfield Steel Single Crystals

NASA Astrophysics Data System (ADS)

Lychagin, D. V.; Filippov, A. V.; Novitskaia, O. S.; Kolubaev, E. A.; Sizova, O. V.

2016-08-01

The results of experimental research into dry sliding friction of Hadfield steel single crystals involving registration of acoustic emission are presented in the paper. The images of friction surfaces of Hadfield steel single crystals and wear grooves of the counterbody surface made after completion of three serial experiments conducted under similar conditions and friction regimes are given. The relation of the acoustic emission waveform envelope to the changing friction factor is revealed. Amplitude-frequency characteristics of acoustic emission signal frames are determined on the base of Fast Fourier Transform and Short Time Fourier Transform during the run-in stage of tribounits and in the process of stable friction.

Quaternion-Based Texture Analysis of Multiband Satellite Images: Application to the Estimation of Aboveground Biomass in the East Region of Cameroon.

PubMed

Djiongo Kenfack, Cedrigue Boris; Monga, Olivier; Mpong, Serge Moto; Ndoundam, René

2018-03-01

Within the last decade, several approaches using quaternion numbers to handle and model multiband images in a holistic manner were introduced. The quaternion Fourier transform can be efficiently used to model texture in multidimensional data such as color images. For practical application, multispectral satellite data appear as a primary source for measuring past trends and monitoring changes in forest carbon stocks. In this work, we propose a texture-color descriptor based on the quaternion Fourier transform to extract relevant information from multiband satellite images. We propose a new multiband image texture model extraction, called FOTO++, in order to address biomass estimation issues. The first stage consists in removing noise from the multispectral data while preserving the edges of canopies. Afterward, color texture descriptors are extracted thanks to a discrete form of the quaternion Fourier transform, and finally the support vector regression method is used to deduce biomass estimation from texture indices. Our texture features are modeled using a vector composed with the radial spectrum coming from the amplitude of the quaternion Fourier transform. We conduct several experiments in order to study the sensitivity of our model to acquisition parameters. We also assess its performance both on synthetic images and on real multispectral images of Cameroonian forest. The results show that our model is more robust to acquisition parameters than the classical Fourier Texture Ordination model (FOTO). Our scheme is also more accurate for aboveground biomass estimation. We stress that a similar methodology could be implemented using quaternion wavelets. These results highlight the potential of the quaternion-based approach to study multispectral satellite images.

Far Infrared Spectrometry of the Cosmic Background Radiation

DOE R&D Accomplishments Database

Mather, J. C.

1974-01-01

I describe two experiments to measure the cosmic background radiation near 1 mm wavelength. The first was a ground-based search for spectral lines, made with a Fabry-Perot interferometer and an InSb detector. The second is a measurement of the spectrum from 3 to 18 cm{sup -1}, made with a balloon-borne Fourier transform spectrometer. It is a polarizing Michelson interferometer, cooled in liquid helium, and operated with a germanium bolometer. I give the theory of operation, construction details, and experimental results. The first experiment was successfully completed but the second suffered equipment malfunction on its first flight. I describe the theory of Fourier transformations and give a new understanding of convolutional phase correction computations. I discuss for infrared bolometer calibration procedures, and tabulate test results on nine detectors. I describe methods of improving bolometer sensitivity with immersion optics and with conductive film blackening.

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.

Research about vibration characteristics of timing chain system based on short-time Fourier transform

NASA Astrophysics Data System (ADS)

Xi, Jiaxin; Liu, Ning

2017-09-01

Vibration characteristic of timing chain system is very important for an engine. In this study, we used a bush roller chain drive system as an example to explain how to use mulitybody dynamic techniques and short-time Fourier transform to investigate vibration characteristics of timing chain system. Multibody dynamic simulation data as chain tension force and external excitation sources curves were provided for short-time Fourier transform study. The study results of short-time Fourier transform illustrate that there are two main vibration frequency domain of timing chain system, one is the low frequency vibration caused by crankshaft sprocket velocity and camshaft sprocket torque. Another is vibration around 1000Hz lead by hydraulic tensioner. Hence, short-time Fourier transform method is useful for basic research of vibration characteristics for timing chain system.

Fourier transform mass spectrometry.

PubMed

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-07-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.

Fourier Transform Mass Spectrometry

PubMed Central

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-01-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

Properly used ''aliasing'' can give better resolution from fewer points in Fourier transform spectroscopy

NASA Astrophysics Data System (ADS)

D'Astous, Y.; Blanchard, M.

1982-05-01

In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)

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

Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Heisler, R.

1978-01-01

A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.

Representation of Complex Spectra in Auditory Cortex

DTIC Science & Technology

1997-01-01

predict the response to any broadband dynamic sound. Fourier Transform Inverse Transform ∫ [.] exp(±2πjΩx±2πjwt) 2 1 2 / 1 1 a 2 1 2 / 1 1 a...Systems Research University of Maryland Spectro-Temporal Transform Ω wx = log f t w = “ripple velocity” Ω = “ripple frequency” Fourier Transform Inverse ... Transform ∫ [.] exp(±2πjΩx±2πjwt) Real functions in the spectro-temporal domain give rise to complex conjugate symmetric functions in the Fourier

Measuring Heterogeneous Reaction Rates with ATR-FTIR Spectroscopy to Evaluate Chemical Fates in an Atmospheric Environment: A Physical Chemistry and Environmental Chemistry Laboratory Experiment

ERIC Educational Resources Information Center

Roberts, Jason E.; Zeng, Guang; Maron, Marta K.; Mach, Mindy; Dwebi, Iman; Liu, Yong

2016-01-01

This paper reports an undergraduate laboratory experiment to measure heterogeneous liquid/gas reaction kinetics (ozone-oleic acid and ozone-phenothrin) using a flow reactor coupled to an attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectrometer. The experiment is specially designed for an upper-level undergraduate Physical…

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

PubMed

Dovlo, Edem; Baddour, Natalie

2015-01-01

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

Automatic Fourier transform and self-Fourier beams due to parabolic potential

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

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn; Liu, Xing; Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fouriermore » transforms are the beams themselves.« less

Four Forms of the Fourier Transform - for Freshmen, using Matlab

NASA Astrophysics Data System (ADS)

Simons, F. J.; Maloof, A. C.

2016-12-01

In 2015, a Fall "Freshman Seminar" at Princeton University (http://geoweb.princeton.edu/people/simons/FRS-SESC.html) taught students to combine field observations of the natural world with quantitative modeling and interpretation, to answer questions like: "How have Earth and human histories been recorded in the geology of Princeton, the Catskills, France and Spain?" (where we took the students on a data-gathering field trip during Fall Break), and "What experiments and analysis can a first-year (possibly non-future-major) do to query such archives of the past?" In the classroom, through problem sets, and around campus, students gained practical experience collecting geological and geophysical data in a geographic context, and analyzing these data using statistical techniques such as regression, time-series and image analysis, with the programming language Matlab. In this presentation I will detail how we instilled basic Matlab skills for quantitative geoscience data analysis through a 6-week progression of topics and exercises. In the 6 weeks after the Fall Break trip, we strengthened these competencies to make our students fully proficient for further learning, as evidenced by their end-of-term independent research work.The particular case study is focused on introducing power-spectral analysis to Freshmen, in a way that even the least quantitative among them could functionally understand. Not counting (0) "inspection", the four ways by which we have successfully instilled the concept of power-spectral analysis in a hands-on fashion are (1) "correlation", (2) "inversion", (3) "stacking", and formal (4) "Fourier transformation". These four provide the main "mappings". Along the way, of course, we also make sure that the students understand that "power-spectral density estimation" is not the same as "Fourier transformation", nor that every Fourier transform has to be "Fast". Hence, concepts from analysis-of-variance techniques, regression, and hypothesis testing, arise in this context, and will be discussed.

A discrete Fourier transform for virtual memory machines

NASA Technical Reports Server (NTRS)

Galant, David C.

1992-01-01

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

A Simple Approach to Fourier Aliasing

ERIC Educational Resources Information Center

Foadi, James

2007-01-01

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and…

A general spectral transformation simultaneously including a Fourier transformation and a Laplace transformation

NASA Technical Reports Server (NTRS)

Marko, H.

1978-01-01

A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.

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)

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.

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.

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates

PubMed Central

Dovlo, Edem; Baddour, Natalie

2015-01-01

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: • The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms. • The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform. • The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time. PMID:26150988

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.

Realistic Analytical Polyhedral MRI Phantoms

PubMed Central

Ngo, Tri M.; Fung, George S. K.; Han, Shuo; Chen, Min; Prince, Jerry L.; Tsui, Benjamin M. W.; McVeigh, Elliot R.; Herzka, Daniel A.

2015-01-01

Purpose Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing 3D analytical phantoms are unable to accurately model shapes of biomedical interest. It is demonstrated that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. Theory The derivations of the Fourier transform of a polygon and polyhedron are presented. Methods The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D/2D MRI acquisitions was described. Results Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D/2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing as compared to equivalent voxelized/rasterized phantoms. Conclusion Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. PMID:26479724

A Comparison of Optical versus Hardware Fourier Transforms.

DTIC Science & Technology

1983-10-31

AD- R136 223 A COMPRISON’OF OPTICAL ERSUS HARDWARE FOURIER i/i.TRANSFORMS(U) VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF PHYSICS S P...transform and its inverse filtered Fourier transform obtained with the Digital Image Processing (DIP) hardware system located at the School of Aerospace...transparencies, and provided to us by Dr. Ralph G. Allen, Director of the Laser Effects Branch (Division of Radiation Sciences). The DIP system consisted of: an

Fourier analysis and signal processing by use of the Moebius inversion formula

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Yu, Xiaoli; Shih, Ming-Tang; Tufts, Donald W.; Truong, T. K.

1990-01-01

A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Moebius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.

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.

The bioscouring performance of four polygalacturonase enzymes

USDA-ARS?s Scientific Manuscript database

Fourier Transform Infrared Attenuated Total Reflectance (FTIR-ATR) analyses of greige cotton fabrics bioscoured with a combination of ultrasound and endo- and exo-polygalacturonase enzymes obtained from Rhizopus sp. fungi were used in a fractional factorial design experiment to examine their perform...

Development of a parallel demodulation system used for extrinsic Fabry-Perot interferometer and fiber Bragg grating sensors.

PubMed

Jiang, Junfeng; Liu, Tiegen; Zhang, Yimo; Liu, Lina; Zha, Ying; Zhang, Fan; Wang, Yunxin; Long, Pin

2006-01-20

A parallel demodulation system for extrinsic Fabry-Perot interferometer (EFPI) and fiber Bragg grating (FBG) sensors is presented, which is based on a Michelson interferometer and combines the methods of low-coherence interference and a Fourier-transform spectrum. The parallel demodulation theory is modeled with Fourier-transform spectrum technology, and a signal separation method with an EFPI and FBG is proposed. The design of an optical path difference scanning and sampling method without a reference light is described. Experiments show that the parallel demodulation system has good spectrum demodulation and low-coherence interference demodulation performance. It can realize simultaneous strain and temperature measurements while keeping the whole system configuration less complex.

Hyperfine Structure in the Pure Rotational Spectrum of 208Pb35Cl

NASA Astrophysics Data System (ADS)

Dewberry, Christopher T.; Grubbs, Garry S., II; Etchison, Kerry C.; Cooke, Stephen A.

2010-06-01

Initially in our laboratory the pure rotational spectrum of the title molecule was studied using a Balle-Flygare Fourier transform microwave spectrometer. Analysis was troublesome and so the spectrum was remeasured using a chirped pulse Fourier transform microwave (CP-FTMW) spectrometer. The correct intensity aspect of the CP-FTMW experiment allowed successful quantum number assignments for the hyperfine structure for the correct isotopologue. Spectroscopic constants have been obtained from a fit to a data set consisting of our measurements combined with those of a prior study on the X_2^2Π3/2 → X_1^2Π_{1/2 fine structure transitions. K. Ziebarth, K. D. Setzer, O. Shestakov and E. H. Fink J. Mol. Spectrosc., 191 108, 1998.

Tutorial on Fourier space coverage for scattering experiments, with application to SAR

NASA Astrophysics Data System (ADS)

Deming, Ross W.

2010-04-01

The Fourier Diffraction Theorem relates the data measured during electromagnetic, optical, or acoustic scattering experiments to the spatial Fourier transform of the object under test. The theorem is well-known, but since it is based on integral equations and complicated mathematical expansions, the typical derivation may be difficult for the non-specialist. In this paper, the theorem is derived and presented using simple geometry, plus undergraduatelevel physics and mathematics. For practitioners of synthetic aperture radar (SAR) imaging, the theorem is important to understand because it leads to a simple geometric and graphical understanding of image resolution and sampling requirements, and how they are affected by radar system parameters and experimental geometry. Also, the theorem can be used as a starting point for imaging algorithms and motion compensation methods. Several examples are given in this paper for realistic scenarios.

Rapid update of discrete Fourier transform for real-time signal processing

NASA Astrophysics Data System (ADS)

Sherlock, Barry G.; Kakad, Yogendra P.

2001-10-01

In many identification and target recognition applications, the incoming signal will have properties that render it amenable to analysis or processing in the Fourier domain. In such applications, however, it is usually essential that the identification or target recognition be performed in real time. An important constraint upon real-time processing in the Fourier domain is the time taken to perform the Discrete Fourier Transform (DFT). Ideally, a new Fourier transform should be obtained after the arrival of every new data point. However, the Fast Fourier Transform (FFT) algorithm requires on the order of N log2 N operations, where N is the length of the transform, and this usually makes calculation of the transform for every new data point computationally prohibitive. In this paper, we develop an algorithm to update the existing DFT to represent the new data series that results when a new signal point is received. Updating the DFT in this way uses less computational order by a factor of log2 N. The algorithm can be modified to work in the presence of data window functions. This is a considerable advantage, because windowing is often necessary to reduce edge effects that occur because the implicit periodicity of the Fourier transform is not exhibited by the real-world signal. Versions are developed in this paper for use with the boxcar window, the split triangular, Hanning, Hamming, and Blackman windows. Generalization of these results to 2D is also presented.

Multitasking and microtasking experience on the NA S Cray-2 and ACF Cray X-MP

NASA Technical Reports Server (NTRS)

Raiszadeh, Farhad

1987-01-01

The fast Fourier transform (FFT) kernel of the NAS benchmark program has been utilized to experiment with the multitasking library on the Cray-2 and Cray X-MP/48, and microtasking directives on the Cray X-MP. Some performance figures are shown, and the state of multitasking software is described.

Fast Fourier Tranformation Algorithms: Experiments with Microcomputers.

DTIC Science & Technology

1986-07-01

is, functions a with a known, discrete Fourier transform A Such functions are given fn [I]. The functions, TF1 , TF2, and TF3, were used and are...the IBM PC, all with TF1 (Eq. 1). ’The compilers provided options to improve performance, as noted, for which a penalty in compiling time has to be...BASIC only. Series I In this series the procedures were as follows: (i) Calculate the input values for TF1 of ar and the modulus Iar (which is

Real-time frequency-to-time mapping based on spectrally-discrete chromatic dispersion.

PubMed

Dai, Yitang; Li, Jilong; Zhang, Ziping; Yin, Feifei; Li, Wangzhe; Xu, Kun

2017-07-10

Traditional photonics-assisted real-time Fourier transform (RTFT) usually suffers from limited chromatic dispersion, huge volume, or large time delay and attendant loss. In this paper we propose frequency-to-time mapping (FTM) by spectrally-discrete dispersion to increase frequency sensitivity greatly. The novel media has periodic ON/OFF intensity frequency response while quadratic phase distribution along disconnected channels, which de-chirps matched optical input to repeated Fourier-transform-limited output. Real-time FTM is then obtained within each period. Since only discrete phase retardation rather than continuously-changed true time delay is required, huge equivalent dispersion is then available by compact device. Such FTM is theoretically analyzed, and implementation by cascaded optical ring resonators is proposed. After a numerical example, our theory is demonstrated by a proof-of-concept experiment, where a single loop containing 0.5-meters-long fiber is used. FTM under 400-MHz unambiguous bandwidth and 25-MHz resolution is reported. Highly-sensitive and linear mapping is achieved with 6.25 ps/MHz, equivalent to ~4.6 × 10 4 -km standard single mode fiber. Extended instantaneous bandwidth is expected by ring cascading. Our proposal may provide a promising method for real-time, low-latency Fourier transform.

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.

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

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Theory and operational rules for the discrete Hankel transform.

PubMed

Baddour, Natalie; Chouinard, Ugo

2015-04-01

Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

Sequential measurement of conjugate variables as an alternative quantum state tomography.

PubMed

Di Lorenzo, Antonio

2013-01-04

It is shown how it is possible to reconstruct the initial state of a one-dimensional system by sequentially measuring two conjugate variables. The procedure relies on the quasicharacteristic function, the Fourier transform of the Wigner quasiprobability. The proper characteristic function obtained by Fourier transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasicharacteristic function of the two detectors and that unknown of the quantum system. This allows state reconstruction through the sequence (1) data collection, (2) Fourier transform, (3) algebraic operation, and (4) inverse Fourier transform. The strength of the measurement should be intermediate for the procedure to work.

Photonic fractional Fourier transformer with a single dispersive device.

PubMed

Cuadrado-Laborde, C; Carrascosa, A; Díez, A; Cruz, J L; Andres, M V

2013-04-08

In this work we used the temporal analog of spatial Fresnel diffraction to design a temporal fractional Fourier transformer with a single dispersive device, in this way avoiding the use of quadratic phase modulators. We demonstrate that a single dispersive passive device inherently provides the fractional Fourier transform of an incident optical pulse. The relationships linking the fractional Fourier transform order and scaling factor with the dispersion parameters are derived. We first provide some numerical results in order to prove the validity of our proposal, using a fiber Bragg grating as the dispersive device. Next, we experimentally demonstrate the feasibility of this proposal by using a spool of a standard optical fiber as the dispersive device.

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.

Signal processing applications of massively parallel charge domain computing devices

NASA Technical Reports Server (NTRS)

Fijany, Amir (Inventor); Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor)

1999-01-01

The present invention is embodied in a charge coupled device (CCD)/charge injection device (CID) architecture capable of performing a Fourier transform by simultaneous matrix vector multiplication (MVM) operations in respective plural CCD/CID arrays in parallel in O(1) steps. For example, in one embodiment, a first CCD/CID array stores charge packets representing a first matrix operator based upon permutations of a Hartley transform and computes the Fourier transform of an incoming vector. A second CCD/CID array stores charge packets representing a second matrix operator based upon different permutations of a Hartley transform and computes the Fourier transform of an incoming vector. The incoming vector is applied to the inputs of the two CCD/CID arrays simultaneously, and the real and imaginary parts of the Fourier transform are produced simultaneously in the time required to perform a single MVM operation in a CCD/CID array.

[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.

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.

Ground-Based Measurement Experiment and First Results with Geosynchronous-Imaging Fourier Transform Spectrometer Engineering Demonstration Unit

NASA Technical Reports Server (NTRS)

Zhou, Daniel K.; Smith, William L.; Bingham, Gail E.; Huppi, Ronald J.; Revercomb, Henry E.; Zollinger, Lori J.; Larar, Allen M.; Liu, Xu; Tansock, Joseph J.; Reisse, Robert A.;

Practical Sub-Nyquist Sampling via Array-Based Compressed Sensing Receiver Architecture

DTIC Science & Technology

2016-07-10

different array ele- ments at different sub-Nyquist sampling rates. Signal processing inspired by the sparse fast Fourier transform allows for signal...reconstruction algorithms can be computationally demanding (REF). The related sparse Fourier transform algorithms aim to reduce the processing time nec- essary to...compute the DFT of frequency-sparse signals [7]. In particular, the sparse fast Fourier transform (sFFT) achieves processing time better than the

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.

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.

The tropical forest and fire emissions experiment: Laboratory fire measurement and synthesis of campaign data

Treesearch

R. J. Yokelson; T. J. Christian; T. G. Karl; A. Guenther

2008-01-01

As part of the Tropical Forest and Fire Emissions Experiment (TROFFEE), tropical forest fuels were burned in a large, biomass-fire simulation facility and the smoke was characterized with open-path Fourier transform infrared spectroscopy (FTIR), proton-transfer reaction mass spectrometry (PTR-MS), gas chromatography (GC), GC/PTRMS, and filter sampling of the particles...

FTIR Determination of Pollutants in Automobile Exhaust: An Environmental Chemistry Experiment Comparing Cold-Start and Warm-Engine Conditions

ERIC Educational Resources Information Center

Medhurst, Laura L.

2005-01-01

An experiment developed from the Advanced Integrated Environmental Laboratory illustrates the differences in automobile exhaust before and after the engine is warmed, using gas-phase Fourier transform infrared spectroscopy (FTIR). The apparatus consists of an Avatar 360 FTIR spectrometer from Nicolet fitted with a variable path length gas cell,…

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

NASA Astrophysics Data System (ADS)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

[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.

Laboratory demonstration of image reconstruction for coherent optical system of modular imaging collectors (COSMIC)

NASA Technical Reports Server (NTRS)

Traub, W. A.

1984-01-01

The first physical demonstration of the principle of image reconstruction using a set of images from a diffraction-blurred elongated aperture is reported. This is an optical validation of previous theoretical and numerical simulations of the COSMIC telescope array (coherent optical system of modular imaging collectors). The present experiment utilizes 17 diffraction blurred exposures of a laboratory light source, as imaged by a lens covered by a narrow-slit aperture; the aperture is rotated 10 degrees between each exposure. The images are recorded in digitized form by a CCD camera, Fourier transformed, numerically filtered, and added; the sum is then filtered and inverse Fourier transformed to form the final image. The image reconstruction process is found to be stable with respect to uncertainties in values of all physical parameters such as effective wavelength, rotation angle, pointing jitter, and aperture shape. Future experiments will explore the effects of low counting rates, autoguiding on the image, various aperture configurations, and separated optics.

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.

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)

Detection of Fast Moving and Accelerating Targets Compensating Range and Doppler Migration

DTIC Science & Technology

2014-06-01

Radon -Fourier transform has been introduced to realize long- term coherent integration of the moving targets with range migration [8, 9]. Radon ...2010) Long-time coherent integration for radar target detection base on Radon -Fourier transform, in Proceedings of the IEEE Radar Conference, pp...432–436. 9. Xu, J., Yu, J., Peng, Y. & Xia, X. (2011) Radon -Fourier transform for radar target detection, I: Generalized Doppler filter bank, IEEE

An Improved Filtering Method for Quantum Color Image in Frequency Domain

NASA Astrophysics Data System (ADS)

Li, Panchi; Xiao, Hong

2018-01-01

In this paper we investigate the use of quantum Fourier transform (QFT) in the field of image processing. We consider QFT-based color image filtering operations and their applications in image smoothing, sharpening, and selective filtering using quantum frequency domain filters. The underlying principle used for constructing the proposed quantum filters is to use the principle of the quantum Oracle to implement the filter function. Compared with the existing methods, our method is not only suitable for color images, but also can flexibly design the notch filters. We provide the quantum circuit that implements the filtering task and present the results of several simulation experiments on color images. The major advantages of the quantum frequency filtering lies in the exploitation of the efficient implementation of the quantum Fourier transform.

Encoding plaintext by Fourier transform hologram in double random phase encoding using fingerprint keys

NASA Astrophysics Data System (ADS)

Takeda, Masafumi; Nakano, Kazuya; Suzuki, Hiroyuki; Yamaguchi, Masahiro

2012-09-01

It has been shown that biometric information can be used as a cipher key for binary data encryption by applying double random phase encoding. In such methods, binary data are encoded in a bit pattern image, and the decrypted image becomes a plain image when the key is genuine; otherwise, decrypted images become random images. In some cases, images decrypted by imposters may not be fully random, such that the blurred bit pattern can be partially observed. In this paper, we propose a novel bit coding method based on a Fourier transform hologram, which makes images decrypted by imposters more random. Computer experiments confirm that the method increases the randomness of images decrypted by imposters while keeping the false rejection rate as low as in the conventional method.

A Primer of Fourier Transform NMR.

ERIC Educational Resources Information Center

Macomber, Roger S.

1985-01-01

Fourier transform nuclear magnetic resonance (NMR) is a new spectroscopic technique that is often omitted from undergraduate curricula because of lack of instructional materials. Therefore, information is provided to introduce students to the technique of data collection and transformation into the frequency domain. (JN)

Geometric Representations for Discrete Fourier Transforms

NASA Technical Reports Server (NTRS)

Cambell, C. W.

1986-01-01

Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.

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.

Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles

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

Warshaw, S I

2001-07-15

In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resultedmore » from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.« less

A Short-Segment Fourier Transform Methodology

DTIC Science & Technology

2009-03-01

defined sampling of the continuous-valued discrete-time Fourier transform, superresolution in the frequency domain and allowance of Dirac delta functions associated with pure sinusoidal input data components.

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

Variables that Impact on the Results of Breath-Alcohol Tests

ERIC Educational Resources Information Center

Labianca, Dominick A.

2004-01-01

In a 2003 issue of the "Journal of Chemical Education," Kniesel and Bellamy describe a timely and pedagogically effective experiment involving breath-alcohol analysis using an FTIR (Fourier Transform Infrared Spectroscopy) spectrometer. The present article clarifies some of the information presented in the 2003 article.

Bringing NMR and IR Spectroscopy to High Schools

ERIC Educational Resources Information Center

Bonjour, Jessica L.; Hass, Alisa L.; Pollock, David W.; Huebner, Aaron; Frost, John A.

2017-01-01

Development of benchtop, portable Fourier transform nuclear magnetic resonance (NMR) and infrared (IR) spectrometers has opened up opportunities for creating university-high school partnerships that provide high school students with hands-on experience with NMR and IR instruments. With recent changes to the international baccalaureate chemistry…

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

NASA Technical Reports Server (NTRS)

Park, J. H.

1984-01-01

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

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.

Implementation of the semiclassical quantum Fourier transform in a scalable system.

PubMed

Chiaverini, J; Britton, J; Leibfried, D; Knill, E; Barrett, M D; Blakestad, R B; Itano, W M; Jost, J D; Langer, C; Ozeri, R; Schaetz, T; Wineland, D J

2005-05-13

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

[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.

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.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, C.L.

1996-07-23

An imaging Fourier transform spectrometer is described having a Fourier transform infrared spectrometer providing a series of images to a focal plane array camera. The focal plane array camera is clocked to a multiple of zero crossing occurrences as caused by a moving mirror of the Fourier transform infrared spectrometer and as detected by a laser detector such that the frame capture rate of the focal plane array camera corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer. The images are transmitted to a computer for processing such that representations of the images as viewed in the light of an arbitrary spectral ``fingerprint`` pattern can be displayed on a monitor or otherwise stored and manipulated by the computer. 2 figs.

The Shell Seeker: What Is the Quantity of Shell in the Lido di Venezia Sand? A Calibration DRIFTS Experiment

ERIC Educational Resources Information Center

Pezzolo, Alessandra De Lorenzi

2011-01-01

In this experiment, students are given a fanciful application of the standard addition method to evaluate the approximate quantity of the shell component in a sample of sand collected on the Lido di Venezia seashore. Several diffuse reflectance infrared Fourier transform (DRIFT) spectra are recorded from a sand sample before and after addition of…

Linear Transforms for Fourier Data on the Sphere: Application to High Angular Resolution Diffusion MRI of the Brain

PubMed Central

Haldar, Justin P.; Leahy, Richard M.

2013-01-01

This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors. PMID:23353603

Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes

NASA Astrophysics Data System (ADS)

Saksida, Pavle

2018-01-01

We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium.

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...

Reduction and coding of synthetic aperture radar data with Fourier transforms

NASA Technical Reports Server (NTRS)

Tilley, David G.

1995-01-01

Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

Use of the fractional Fourier transform in {pi}/2 converters of laser modes

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

Malyutin, A A

2004-02-28

The possibility of using the fractional Fourier transform (FrFT) in optical schemes for astigmatic {pi}/2 converters of Hermite-Gaussian modes to donut Laguerre-Gaussian modes is considered. Several schemes of converters based on the FrFT of the half-integer and irrational orders are presented. The lowest FrFT order than can be used in astigmatic mode converters is found. The properties of converters based on the fractional and ordinary Fourier transforms are compared. (laser beams)

Restoration algorithms for imaging through atmospheric turbulence

DTIC Science & Technology

2017-02-18

the Fourier spectrum of each frame. The reconstructed image is then obtained by taking the inverse Fourier transform of the average of all processed...with wipξq “ Gσp|Fpviqpξq|pq řM j“1Gσp|Fpvjqpξq|pq , where F denotes the Fourier transform (ξ are the frequencies) and Gσ is a Gaussian filter of...a combination of SIFT [26] and ORSA [14] algorithms) in order to remove affine transformations (translations, rotations and homothety). The authors

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 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.

Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.

PubMed

Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene

2017-08-01

Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.

Fast Fourier Transform algorithm design and tradeoffs

NASA Technical Reports Server (NTRS)

Kamin, Ray A., III; Adams, George B., III

1988-01-01

The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.

Reducing Noise by Repetition: Introduction to Signal Averaging

ERIC Educational Resources Information Center

Hassan, Umer; Anwar, Muhammad Sabieh

2010-01-01

This paper describes theory and experiments, taken from biophysics and physiological measurements, to illustrate the technique of signal averaging. In the process, students are introduced to the basic concepts of signal processing, such as digital filtering, Fourier transformation, baseline correction, pink and Gaussian noise, and the cross- and…

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…

INVESTIGATION OF OPEN-PATH FTIR FOR FAST DEPLOYMENT EMERGENCY RESPONSE TO CHEMICAL THREATS AND ACCIDENTS.

EPA Science Inventory

We have performed a series of experiments to determine the tradeoff in detection sensitivity for implementing design features for an Open-Path Fourier Transform Infrared (OP-FTIR) chemical analyzer that would be quick to deploy under emergency response conditions. The fast-deplo...

FIELD EVALUATION OF A METHOD FOR ESTIMATING GASEOUS FLUXES FROM AREA SOURCES USING OPEN-PATH FOURIER TRANSFORM INFRARED

EPA Science Inventory

The paper describes preliminary results from a field experiment designed to evaluate a new approach to quantifying gaseous fugitive emissions from area air pollution sources. The new approach combines path-integrated concentration data acquired with any path-integrated optical re...

One-shot profile inspection for surfaces with depth, color and reflectivity discontinuities.

PubMed

Su, Wei-Hung; Chen, Sih-Yue

2017-05-01

A one-shot technique for surfaces with depth, color, and reflectivity discontinuities is presented. It uses windowed Fourier transform to extract the fringe phases and a binary-encoded scheme to unwrap the phases. Experiments show that absolute phases could be obtained with high reliability.

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2013 CFR

2013-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2014 CFR

2014-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

Biological Applications Of Fourier Transform Infrared (FTIR) Or Bloody FTIR

NASA Astrophysics Data System (ADS)

Jakobsen, R. J.; Winters, S.; Gendreau, R. M.

1981-10-01

An ex vivo FT-IR/ATR experiment for studying blood protein adsorption at the molecular level is described. This experiment involves the use of live dogs pumping the blood through a arterial-veinal shunt to the ATR cell and back into the animal. The results from these live dog experiments are compared to results obtained using donated whole blood. These experiments demonstrate that FT-IR can be used to study aqueous, physiological, flowing solutions in real time with the sensitivity necessary to detect minor changes.

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

1997-01-01

Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

40 CFR Appendix B to Subpart Uuuuu - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2012 CFR

2012-07-01

... Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix B to... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

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.

Motion-induced error reduction by combining Fourier transform profilometry with phase-shifting profilometry.

PubMed

Li, Beiwen; Liu, Ziping; Zhang, Song

2016-10-03

We propose a hybrid computational framework to reduce motion-induced measurement error by combining the Fourier transform profilometry (FTP) and phase-shifting profilometry (PSP). The proposed method is composed of three major steps: Step 1 is to extract continuous relative phase maps for each isolated object with single-shot FTP method and spatial phase unwrapping; Step 2 is to obtain an absolute phase map of the entire scene using PSP method, albeit motion-induced errors exist on the extracted absolute phase map; and Step 3 is to shift the continuous relative phase maps from Step 1 to generate final absolute phase maps for each isolated object by referring to the absolute phase map with error from Step 2. Experiments demonstrate the success of the proposed computational framework for measuring multiple isolated rapidly moving objects.

Experimental geometry for simultaneous beam characterization and sample imaging allowing for pink beam Fourier transform holography or coherent diffractive imaging

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

Flewett, Samuel; Eisebitt, Stefan

2011-02-20

One consequence of the self-amplified stimulated emission process used to generate x rays in free electron lasers (FELs) is the intrinsic shot-to-shot variance in the wavelength and temporal coherence. In order to optimize the results from diffractive imaging experiments at FEL sources, it will be advantageous to acquire a means of collecting coherence and spectral information simultaneously with the diffraction pattern from the sample we wish to study. We present a holographic mask geometry, including a grating structure, which can be used to extract both temporal and spatial coherence information alongside the sample scatter from each individual FEL shot andmore » also allows for the real space reconstruction of the sample using either Fourier transform holography or iterative phase retrieval.« less

An Evaluation of the Environmental Fate and Behavior of Munitions Materiel (Tetryl and Polar Metabolites of TNT) in Soil and Plant Systems. Environmental Fate and Behavior of Tetryl

DTIC Science & Technology

1992-03-01

attempted to verify product identity and purity by GC with either Fourier transform infrared spectro.icopy (FTIR) or mass spectroscopy (MS) detection...ýl0 5 In-1 z U)-’i0oo -3g’i o -6o0 626o a i60 ito1 2i oo I ’ o [JfnVENUII8ER (cm- FIGURE 3,9. Fourier Transform Infrared Spectroscopy Spectrum of...Fourier Transform Infrared Spectroscopy Spectrum of Tetryl I-I F1U~IGUR Fourier Utransformlfret Spcrop S ectrum of TeasomtinPoutrl 0 , -39 i : : : -. . i

Maskelynite formation via solid-state transformation: Evidence of infrared and x-ray anisotropy

DOE PAGES

Jaret, Steven J.; Ehm, Lars; Woerner, William R.; ...

2015-03-24

We present optical microscopy, micro-Raman spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, high-energy X-ray total scattering experiments, and micro-Fourier transform infrared (micro-FTIR) spectroscopy on shocked labradorite from the Lonar Crater, India. We show that maskelynite of shock class 2 is structurally more similar to fused glass than to crystalline plagioclase. However, there are slight but significant differences – preservation of original pre-impact igneous zoning, anisotropy at Infrared wavelengths, X-ray anisotropy, and preservation of some intermediate range order – which are all consistent with a solid-state transformation formation of maskelynite.

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

Wavelets

NASA Astrophysics Data System (ADS)

Strang, Gilbert

1994-06-01

Several methods are compared that are used to analyze and synthesize a signal. Three ways are mentioned to transform a symphony: into cosine waves (Fourier transform), into pieces of cosines (short-time Fourier transform), and into wavelets (little waves that start and stop). Choosing the best basis, higher dimensions, fast wavelet transform, and Daubechies wavelets are discussed. High-definition television is described. The use of wavelets in identifying fingerprints in the future is related.

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.

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.

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)

A Graphical Presentation to Teach the Concept of the Fourier Transform

ERIC Educational Resources Information Center

Besalu, E.

2006-01-01

A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.

Novel hybrid optical correlator: theory and optical simulation.

PubMed

Casasent, D; Herold, R L

1975-02-01

The inverse transform of the product of two Fourier transform holograms is analyzed and shown to contain the correlation of the two images from which the holograms were formed. The theory, analysis, and initial experimental demonstration of the feasibility of a novel correlation scheme using this multiplied Fourier transform hologram system are presented.

Fast algorithm for chirp transforms with zooming-in ability and its applications.

PubMed

Deng, X; Bihari, B; Gan, J; Zhao, F; Chen, R T

2000-04-01

A general fast numerical algorithm for chirp transforms is developed by using two fast Fourier transforms and employing an analytical kernel. This new algorithm unifies the calculations of arbitrary real-order fractional Fourier transforms and Fresnel diffraction. Its computational complexity is better than a fast convolution method using Fourier transforms. Furthermore, one can freely choose the sampling resolutions in both x and u space and zoom in on any portion of the data of interest. Computational results are compared with analytical ones. The errors are essentially limited by the accuracy of the fast Fourier transforms and are higher than the order 10(-12) for most cases. As an example of its application to scalar diffraction, this algorithm can be used to calculate near-field patterns directly behind the aperture, 0 < or = z < d2/lambda. It compensates another algorithm for Fresnel diffraction that is limited to z > d2/lambdaN [J. Opt. Soc. Am. A 15, 2111 (1998)]. Experimental results from waveguide-output microcoupler diffraction are in good agreement with the calculations.

Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.

PubMed

Liang, Zhichun; Crepeau, Richard H; Freed, Jack H

2005-12-01

Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

Experimental image alignment system

NASA Technical Reports Server (NTRS)

Moyer, A. L.; Kowel, S. T.; Kornreich, P. G.

1980-01-01

A microcomputer-based instrument for image alignment with respect to a reference image is described which uses the DEFT sensor (Direct Electronic Fourier Transform) for image sensing and preprocessing. The instrument alignment algorithm which uses the two-dimensional Fourier transform as input is also described. It generates signals used to steer the stage carrying the test image into the correct orientation. This algorithm has computational advantages over algorithms which use image intensity data as input and is suitable for a microcomputer-based instrument since the two-dimensional Fourier transform is provided by the DEFT sensor.

Modulated Fourier Transform Raman Fiber-Optic Spectroscopy

NASA Technical Reports Server (NTRS)

Jensen, Brian J. (Inventor); Cooper, John B. (Inventor); Wise, Kent L. (Inventor)

2000-01-01

A modification to a commercial Fourier Transform (FT) Raman spectrometer is presented for the elimination of thermal backgrounds in the FT Raman spectra. The modification involves the use of a mechanical optical chopper to modulate the continuous wave laser, remote collection of the signal via fiber optics, and connection of a dual-phase digital-signal-processor (DSP) lock-in amplifier between the detector and the spectrometer's collection electronics to demodulate and filter the optical signals. The resulting Modulated Fourier Transform Raman Fiber-Optic Spectrometer is capable of completely eliminating thermal backgrounds at temperatures exceeding 300 C.

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.

A fast D.F.T. algorithm using complex integer transforms

NASA Technical Reports Server (NTRS)

Reed, I. S.; Truong, T. K.

1978-01-01

Winograd (1976) has developed a new class of algorithms which depend heavily on the computation of a cyclic convolution for computing the conventional DFT (discrete Fourier transform); this new algorithm, for a few hundred transform points, requires substantially fewer multiplications than the conventional FFT algorithm. Reed and Truong have defined a special class of finite Fourier-like transforms over GF(q squared), where q = 2 to the p power minus 1 is a Mersenne prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 61. In the present paper it is shown that Winograd's algorithm can be combined with the aforementioned Fourier-like transform to yield a new algorithm for computing the DFT. A fast method for accurately computing the DFT of a sequence of complex numbers of very long transform-lengths is thus obtained.

The conjecture concerning time variations in the solar neutrino flux

NASA Technical Reports Server (NTRS)

Haubold, H. J.; Gerth, E.

1985-01-01

The results of the Fourier transformation of the unequally-spaced time series of the recorded Ar-37 production rate of the solar neutrino experiment (runs 18 to 80, 1970 to 1983) are reviewed. Significance criteria for every period discovered by the harmonic analysis are determined. A Fourier synthesis of certain discovered harmonics are performed. It seems that the solar neutrino flux increases shock-like with a period of approximately 8.3 years and after that breaks down. Possible connections between the periods found by the harmonic analysis and several observed phenomena on the solar surface are indicated.

A High Resolution Fourier-Transform Spectrometer for the Measurement of Atmospheric Column Abundances

NASA Technical Reports Server (NTRS)

Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.

2000-01-01

A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).

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.

Radiometric Short-Term Fourier Transform analysis of photonic Doppler velocimetry recordings and detectivity limit

NASA Astrophysics Data System (ADS)

Prudhomme, G.; Berthe, L.; Bénier, J.; Bozier, O.; Mercier, P.

2017-01-01

Photonic Doppler Velocimetry is a plug-and-play and versatile diagnostic used in dynamic physic experiments to measure velocities. When signals are analyzed using a Short-Time Fourier Transform, multiple velocities can be distinguished: for example, the velocities of moving particle-cloud appear on spectrograms. In order to estimate the back-scattering fluxes of target, we propose an original approach "PDV Radiometric analysis" resulting in an expression of time-velocity spectrograms coded in power units. Experiments involving micron-sized particles raise the issue of detection limit; particle-size limit is very difficult to evaluate. From the quantification of noise sources, we derive an estimation of the spectrogram noise leading to a detectivity limit, which may be compared to the fraction of the incoming power which has been back-scattered by the particle and then collected by the probe. This fraction increases with their size. At last, some results from laser-shock accelerated particles using two different PDV systems are compared: it shows the improvement of detectivity with respect to the Effective Number of Bits (ENOB) of the digitizer.

A Novel Hybrid Error Criterion-Based Active Control Method for on-Line Milling Vibration Suppression with Piezoelectric Actuators and Sensors

PubMed Central

Zhang, Xingwu; Wang, Chenxi; Gao, Robert X.; Yan, Ruqiang; Chen, Xuefeng; Wang, Shibin

2016-01-01

Milling vibration is one of the most serious factors affecting machining quality and precision. In this paper a novel hybrid error criterion-based frequency-domain LMS active control method is constructed and used for vibration suppression of milling processes by piezoelectric actuators and sensors, in which only one Fast Fourier Transform (FFT) is used and no Inverse Fast Fourier Transform (IFFT) is involved. The correction formulas are derived by a steepest descent procedure and the control parameters are analyzed and optimized. Then, a novel hybrid error criterion is constructed to improve the adaptability, reliability and anti-interference ability of the constructed control algorithm. Finally, based on piezoelectric actuators and acceleration sensors, a simulation of a spindle and a milling process experiment are presented to verify the proposed method. Besides, a protection program is added in the control flow to enhance the reliability of the control method in applications. The simulation and experiment results indicate that the proposed method is an effective and reliable way for on-line vibration suppression, and the machining quality can be obviously improved. PMID:26751448

The (CH2)2O-H2O hydrogen bonded complex. Ab Initio calculations and Fourier transform infrared spectroscopy from neon matrix and a new supersonic jet experiment coupled to the infrared AILES beamline of synchrotron SOLEIL.

PubMed

Cirtog, M; Asselin, P; Soulard, P; Tremblay, B; Madebène, B; Alikhani, M E; Georges, R; Moudens, A; Goubet, M; Huet, T R; Pirali, O; Roy, P

2011-03-31

A series of hydrogen bonded complexes involving oxirane and water molecules have been studied. In this paper we report on the vibrational study of the oxirane-water complex (CH(2))(2)O-H(2)O. Neon matrix experiments and ab initio anharmonic vibrational calculations have been performed, providing a consistent set of vibrational frequencies and anharmonic coupling constants. The implementation of a new large flow supersonic jet coupled to the Bruker IFS 125 HR spectrometer at the infrared AILES beamline of the French synchrotron SOLEIL (Jet-AILES) enabled us to record first jet-cooled Fourier transform infrared spectra of oxirane-water complexes at different resolutions down to 0.2 cm(-1). Rovibrational parameters and a lower bound of the predissociation lifetime of 25 ps for the v(OH)(b) = 1 state have been derived from the rovibrational analysis of the ν(OH)(b) band contour recorded at respective rotational temperatures of 12 K (Jet-AILES) and 35 K (LADIR jet).

Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability

NASA Technical Reports Server (NTRS)

Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.

2007-01-01

The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.

Method for determining and displaying the spacial distribution of a spectral pattern of received light

DOEpatents

Bennett, Charles L.

1996-01-01

An imaging Fourier transform spectrometer (10, 210) having a Fourier transform infrared spectrometer (12) providing a series of images (40) to a focal plane array camera (38). The focal plane array camera (38) is clocked to a multiple of zero crossing occurrences as caused by a moving mirror (18) of the Fourier transform infrared spectrometer (12) and as detected by a laser detector (50) such that the frame capture rate of the focal plane array camera (38) corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer (12). The images (40) are transmitted to a computer (45) for processing such that representations of the images (40) as viewed in the light of an arbitrary spectral "fingerprint" pattern can be displayed on a monitor (60) or otherwise stored and manipulated by the computer (45).

Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion

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

Yükçü, Niyazi

Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical propertiesmore » of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.« less

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.

Component analyses of urinary nanocrystallites of uric acid stone formers by combination of high-resolution transmission electron microscopy, fast Fourier transformation, energy dispersive X-ray spectroscopy, X-ray diffraction and Fourier transform infrared spectroscopy.

PubMed

Sun, Xin-Yuan; Xue, Jun-Fa; Xia, Zhi-Yue; Ouyang, Jian-Ming

2015-06-01

This study aimed to analyse the components of nanocrystallites in urines of patients with uric acid (UA) stones. X-ray diffraction (XRD), Fourier transform infrared spectroscopy, high-resolution transmission electron microscopy (HRTEM), fast Fourier transformation (FFT) of HRTEM, and energy dispersive X-ray spectroscopy (EDS) were performed to analyse the components of these nanocrystallites. XRD and FFT showed that the main component of urinary nanocrystallites was UA, which contains a small amount of calcium oxalate monohydrate and phosphates. EDS showed the characteristic absorption peaks of C, O, Ca and P. The formation of UA stones was closely related to a large number of UA nanocrystallites in urine. A combination of HRTEM, FFT, EDS and XRD analyses could be performed accurately to analyse the components of urinary nanocrystallites.

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.

Single Channel Quantum Color Image Encryption Algorithm Based on HSI Model and Quantum Fourier Transform

NASA Astrophysics Data System (ADS)

Gong, Li-Hua; He, Xiang-Tao; Tan, Ru-Chao; Zhou, Zhi-Hong

2018-01-01

In order to obtain high-quality color images, it is important to keep the hue component unchanged while emphasize the intensity or saturation component. As a public color model, Hue-Saturation Intensity (HSI) model is commonly used in image processing. A new single channel quantum color image encryption algorithm based on HSI model and quantum Fourier transform (QFT) is investigated, where the color components of the original color image are converted to HSI and the logistic map is employed to diffuse the relationship of pixels in color components. Subsequently, quantum Fourier transform is exploited to fulfill the encryption. The cipher-text is a combination of a gray image and a phase matrix. Simulations and theoretical analyses demonstrate that the proposed single channel quantum color image encryption scheme based on the HSI model and quantum Fourier transform is secure and effective.

Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units.

PubMed

Watanabe, Yuuki; Maeno, Seiya; Aoshima, Kenji; Hasegawa, Haruyuki; Koseki, Hitoshi

2010-09-01

The real-time display of full-range, 2048?axial pixelx1024?lateral pixel, Fourier-domain optical-coherence tomography (FD-OCT) images is demonstrated. The required speed was achieved by using dual graphic processing units (GPUs) with many stream processors to realize highly parallel processing. We used a zero-filling technique, including a forward Fourier transform, a zero padding to increase the axial data-array size to 8192, an inverse-Fourier transform back to the spectral domain, a linear interpolation from wavelength to wavenumber, a lateral Hilbert transform to obtain the complex spectrum, a Fourier transform to obtain the axial profiles, and a log scaling. The data-transfer time of the frame grabber was 15.73?ms, and the processing time, which includes the data transfer between the GPU memory and the host computer, was 14.75?ms, for a total time shorter than the 36.70?ms frame-interval time using a line-scan CCD camera operated at 27.9?kHz. That is, our OCT system achieved a processed-image display rate of 27.23 frames/s.

A new Fourier transform based CBIR scheme for mammographic mass classification: a preliminary invariance assessment

NASA Astrophysics Data System (ADS)

Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin

2015-03-01

The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.

Linear transforms for Fourier data on the sphere: application to high angular resolution diffusion MRI of the brain.

PubMed

Haldar, Justin P; Leahy, Richard M

2013-05-01

This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors. Copyright © 2013 Elsevier Inc. All rights reserved.

Versatile application of indirect Fourier transformation to structure factor analysis: from X-ray diffraction of molecular liquids to small angle scattering of protein solutions.

PubMed

Fukasawa, Toshiko; Sato, Takaaki

2011-02-28

We highlight versatile applicability of a structure-factor indirect Fourier transformation (IFT) technique, hereafter called SQ-IFT. The original IFT aims at the pair distance distribution function, p(r), of colloidal particles from small angle scattering of X-rays (SAXS) and neutrons (SANS), allowing the conversion of the experimental form factor, P(q), into a more intuitive real-space spatial autocorrelation function. Instead, SQ-IFT is an interaction potential model-free approach to the 'effective' or 'experimental' structure factor to yield the pair correlation functions (PCFs), g(r), of colloidal dispersions like globular protein solutions for small-angle scattering data as well as the radial distribution functions (RDFs) of molecular liquids in liquid diffraction (LD) experiments. We show that SQ-IFT yields accurate RDFs of liquid H(2)O and monohydric alcohol reflecting their local intermolecular structures, in which q-weighted structure function, qH(q), conventionally utilized in many LD studies out of necessity of performing direct Fourier transformation, is no longer required. We also show that SQ-IFT applied to theoretically calculated structure factors for uncharged and charged colloidal dispersions almost perfectly reproduces g(r) obtained as a solution of the Ornstein-Zernike (OZ) equation. We further demonstrate the relevance of SQ-IFT in its practical applications, using SANS effective structure factors of lysozyme solutions reported in recent literatures which revealed the equilibrium cluster formation due to coexisting long range electrostatic repulsion and short range attraction between the proteins. Finally, we present SAXS experiments on human serum albumin (HSA) at different ionic strength and protein concentration, in which we discuss the real space picture of spatial distributions of the proteins via the interaction potential model-free route.

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.

Instrument Line Shape Modeling and Correction for Off-Axis Detectors in Fourier Transform Spectrometry

NASA Technical Reports Server (NTRS)

Bowman, K.; Worden, H.; Beer, R.

1999-01-01

Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.

Fourier Transform Mass Spectrometry.

ERIC Educational Resources Information Center

Gross, Michael L.; Rempel, Don L.

1984-01-01

Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)

Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR.

ERIC Educational Resources Information Center

Perkins, W. D.

1987-01-01

This is Part II in a series on Fourier transform infrared spectroscopy (FT-IR). Described are various advantages of FT-IR spectroscopy including energy advantages, wavenumber accuracy, constant resolution, polarization effects, and stepping at grating changes. (RH)

Robust Features Of Surface Electromyography Signal

NASA Astrophysics Data System (ADS)

Sabri, M. I.; Miskon, M. F.; Yaacob, M. R.

2013-12-01

Nowadays, application of robotics in human life has been explored widely. Robotics exoskeleton system are one of drastically areas in recent robotic research that shows mimic impact in human life. These system have been developed significantly to be used for human power augmentation, robotics rehabilitation, human power assist, and haptic interaction in virtual reality. This paper focus on solving challenges in problem using neural signals and extracting human intent. Commonly, surface electromyography signal (sEMG) are used in order to control human intent for application exoskeleton robot. But the problem lies on difficulty of pattern recognition of the sEMG features due to high noises which are electrode and cable motion artifact, electrode noise, dermic noise, alternating current power line interface, and other noise came from electronic instrument. The main objective in this paper is to study the best features of electromyography in term of time domain (statistical analysis) and frequency domain (Fast Fourier Transform).The secondary objectives is to map the relationship between torque and best features of muscle unit activation potential (MaxPS and RMS) of biceps brachii. This project scope use primary data of 2 male sample subject which using same dominant hand (right handed), age between 20-27 years old, muscle diameter 32cm to 35cm and using single channel muscle (biceps brachii muscle). The experiment conduct 2 times repeated task of contraction and relaxation of biceps brachii when lifting different load from no load to 3kg with ascending 1kg The result shows that Fast Fourier Transform maximum power spectrum (MaxPS) has less error than mean value of reading compare to root mean square (RMS) value. Thus, Fast Fourier Transform maximum power spectrum (MaxPS) show the linear relationship against torque experience by elbow joint to lift different load. As the conclusion, the best features is MaxPS because it has the lowest error than other features and show the linear relationship with torque experience by elbow joint to lift different load.

A fast Karhunen-Loeve transform for a class of random processes

NASA Technical Reports Server (NTRS)

Jain, A. K.

1976-01-01

It is shown that for a class of finite first-order Markov signals, the Karhunen-Loeve (KL) transform for data compression is a set of periodic sine functions if the boundary values of the signal are fixed or known. These sine functions are shown to be related to the Fourier transform so that a fast Fourier transform algorithm can be used to implement the KL transform. Extension to two dimensions with reference to images with separable contravariance function is shown.

Massively parallel X-ray holography

NASA Astrophysics Data System (ADS)

Marchesini, Stefano; Boutet, Sébastien; Sakdinawat, Anne E.; Bogan, Michael J.; Bajt, Saša; Barty, Anton; Chapman, Henry N.; Frank, Matthias; Hau-Riege, Stefan P.; Szöke, Abraham; Cui, Congwu; Shapiro, David A.; Howells, Malcolm R.; Spence, John C. H.; Shaevitz, Joshua W.; Lee, Joanna Y.; Hajdu, Janos; Seibert, Marvin M.

2008-09-01

Advances in the development of free-electron lasers offer the realistic prospect of nanoscale imaging on the timescale of atomic motions. We identify X-ray Fourier-transform holography as a promising but, so far, inefficient scheme to do this. We show that a uniformly redundant array placed next to the sample, multiplies the efficiency of X-ray Fourier transform holography by more than three orders of magnitude, approaching that of a perfect lens, and provides holographic images with both amplitude- and phase-contrast information. The experiments reported here demonstrate this concept by imaging a nano-fabricated object at a synchrotron source, and a bacterial cell with a soft-X-ray free-electron laser, where illumination by a single 15-fs pulse was successfully used in producing the holographic image. As X-ray lasers move to shorter wavelengths we expect to obtain higher spatial resolution ultrafast movies of transient states of matter.

Emotion recognition based on multiple order features using fractional Fourier transform

NASA Astrophysics Data System (ADS)

Ren, Bo; Liu, Deyin; Qi, Lin

2017-07-01

In order to deal with the insufficiency of recently algorithms based on Two Dimensions Fractional Fourier Transform (2D-FrFT), this paper proposes a multiple order features based method for emotion recognition. Most existing methods utilize the feature of single order or a couple of orders of 2D-FrFT. However, different orders of 2D-FrFT have different contributions on the feature extraction of emotion recognition. Combination of these features can enhance the performance of an emotion recognition system. The proposed approach obtains numerous features that extracted in different orders of 2D-FrFT in the directions of x-axis and y-axis, and uses the statistical magnitudes as the final feature vectors for recognition. The Support Vector Machine (SVM) is utilized for the classification and RML Emotion database and Cohn-Kanade (CK) database are used for the experiment. The experimental results demonstrate the effectiveness of the proposed method.

Ground cross-modal impedance as a tool for analyzing ground/plate interaction and ground wave propagation.

PubMed

Grau, L; Laulagnet, B

2015-05-01

An analytical approach is investigated to model ground-plate interaction based on modal decomposition and the two-dimensional Fourier transform. A finite rectangular plate subjected to flexural vibration is coupled with the ground and modeled with the Kirchhoff hypothesis. A Navier equation represents the stratified ground, assumed infinite in the x- and y-directions and free at the top surface. To obtain an analytical solution, modal decomposition is applied to the structure and a Fourier Transform is applied to the ground. The result is a new tool for analyzing ground-plate interaction to resolve this problem: ground cross-modal impedance. It allows quantifying the added-stiffness, added-mass, and added-damping from the ground to the structure. Similarity with the parallel acoustic problem is highlighted. A comparison between the theory and the experiment shows good matching. Finally, specific cases are investigated, notably the influence of layer depth on plate vibration.

Preparation and characterization of novel carbon dioxide adsorbents based on polyethylenimine-modified Halloysite nanotubes.

PubMed

Cai, Haohao; Bao, Feng; Gao, Jie; Chen, Tao; Wang, Si; Ma, Rui

2015-01-01

New nano-sized carbon dioxide (CO2) adsorbents based on Halloysite nanotubes impregnated with polyethylenimine (PEI) were designed and synthesized, which were excellent adsorbents for the capture of CO2 at room temperature and had relatively high CO2 adsorption capacity. The prepared adsorbents were characterized by various techniques such as Fourier transform infrared spectrometry, gel permeation chromatography, dynamic light scattering, thermogravimetry, thermogravimetry-Fourier transform-infrared spectrometry, scanning electron microscopy and transmission electron microscopy. The adsorption characteristics and capacity were studied at room temperature, the highest CO2 adsorption capacity of 156.6 mg/g-PEI was obtained and the optimal adsorption capacity can reach a maximum value of 54.8 mg/g-adsorbent. The experiment indicated that this kind of adsorbent has a high stability at 80°C and PEI-impregnated adsorbents showed good reversibility and stability during cyclic adsorption-regeneration tests.

Synchrotron-based far-infrared spectroscopy of furan: Rotational analysis of the ν 14 , ν 11 , ν 18 and ν 19 vibrational levels

NASA Astrophysics Data System (ADS)

Tokaryk, D. W.; Culligan, S. D.; Billinghurst, B. E.; van Wijngaarden, J. A.

2011-11-01

Four vibrational levels of the five-membered ring molecule furan (C 4H 4O) have been rotationally analyzed from far-infrared Fourier transform spectra obtained at the Canadian Light Source synchrotron. We found that the low-lying ν14 and ν11 levels at 602.9 and 599.6 cm -1 interact through a second-order Coriolis resonance. This perturbation was characterized through a coupled analysis of the ν14 and ν18 fundamental spectra and the ν18- ν11 band. The ν19 fundamental spectrum was analyzed as well, and the data for all observed bands were combined with previously reported microwave transitions to produce the final fit. The spectra are an excellent demonstration of the high quality of data that can be obtained when far-infrared synchrotron radiation is used as the radiation source in Fourier transform spectroscopy experiments.

Techniques of noninvasive optical tomographic imaging

NASA Astrophysics Data System (ADS)

Rosen, Joseph; Abookasis, David; Gokhler, Mark

2006-01-01

Recently invented methods of optical tomographic imaging through scattering and absorbing media are presented. In one method, the three-dimensional structure of an object hidden between two biological tissues is recovered from many noisy speckle pictures obtained on the output of a multi-channeled optical imaging system. Objects are recovered from many speckled images observed by a digital camera through two stereoscopic microlens arrays. Each microlens in each array generates a speckle image of the object buried between the layers. In the computer each image is Fourier transformed jointly with an image of the speckled point-like source captured under the same conditions. A set of the squared magnitudes of the Fourier-transformed pictures is accumulated to form a single average picture. This final picture is again Fourier transformed, resulting in the three-dimensional reconstruction of the hidden object. In the other method, the effect of spatial longitudinal coherence is used for imaging through an absorbing layer with different thickness, or different index of refraction, along the layer. The technique is based on synthesis of multiple peak spatial degree of coherence. This degree of coherence enables us to scan simultaneously different sample points on different altitudes, and thus decreases the acquisition time. The same multi peak degree of coherence is also used for imaging through the absorbing layer. Our entire experiments are performed with a quasi-monochromatic light source. Therefore problems of dispersion and inhomogeneous absorption are avoided.

Coherence Conversion for Optimized Resolution in Optical Measurements - Example of Femtosecond Time Resolution Using the Transverse Coherence of 100-Picosecond X-Rays

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

Adams, Bernhard W.

2015-01-01

A way is proposed to obtain a femtosecond time resolution over a picosecond range in x-ray spectroscopic measurements where the light source and the detector are much slower than that. It is based on the invariance of the modulus of the Fourier transform to object translations. The method geometrically correlates time in the sample with x-ray amplitudes over a spatial coordinate, and then takes the optical Fourier transform through far-field diffraction. Thus, explicitly time-invariant intensities that encode the time evolution of the sample can be measured with a slow detector. This corresponds to a phase-space transformation that converts the transversemore » coherence to become effective in the longitudinal direction. Because synchrotron-radiation sources have highly anisotropic coherence properties with about $10^5$ longitudinal electromagnetic-field modes at 1 eV bandwidth, but only tens to hundreds transverse modes, coherence conversion can drastically improve the time resolution. Reconstruction of the femtosecond time evolution in the sample from the Fourier intensities is subject to a phase ambiguity that is well-known in crystallography. However, a way is presented to resolve it that is not available in that discipline. Finally, data from a demonstration experiment are presented. The same concept can be used to obtain attosecond time resolution with an x-ray free-electron laser.« less

[FREQUENCY-TEMPORAL STRUCTURE OF HUMAN ELECTROENCEPHALOGRAM IN THE CONDITION OF ARTIFICIAL HYPOGRAVITY: DRY IMMERSION MODEL].

PubMed

Kuznetsova, G D; Gabova, A V; Lazarev, I E; Obukhov, Iu V; Obukhov, K Iu; Morozov, A A; Kulikov, M A; Shchatskova, A B; Vasil'eva, O N; Tomilovskaia, E S

2015-01-01

Frequency-temporal electroencephalogram (EEG) reactions to hypogravity were studied in 7 male subjects at the age of 20 to 27 years. The experiment was conducted using dry immersion (DI) as the best known method of simulating the space microgravity effects on the Earth. This hypogravity model reproduces hypokinesia, i.e. the weight-bearing and mechanic load removal, which is typical of microgravity. EEG was recorded by Neuroscan-2 (Compumedics) before the experiment (baseline data) and at the end of day 2 in DI. Comparative analysis of the EEG frequency-temporal structure was performed with the use of 2 techniques: Fourier transform and modified wavelet analysis. The Fourier transform elicited that after 2 days in DI the main shifts occurring to the EEG spectral composition are a decline in the alpha power and a slight though reliable growth of theta power. Similar frequency shifts were detected in the same records analyzed using the wavelet transform. According to wavelet analysis, during DI shifts in EEG frequency spectrum are accompanied by frequency desorganization of the EEG dominant rhythm and gross impairment of total stability of the electrical activity with time. Wavelet transform provides an opportunity to quantify changes in the frequency-temporal structure of the electrical activity of the brain. Quantitative evidence of frequency desorganization and temporal instability of EEG wavelet spectrograms may be the key to the understanding of mechanisms that drive functional disorders in the brain cortex in the conditions of hypogravity.

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.

Generalized fiber Fourier optics.

PubMed

Cincotti, Gabriella

2011-06-15

A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.

QUANTITATIVE FOURIER TRANSFORM INFRARED SPECTROSCOPIC INVESTIGATION OF HUMIC SUBSTANCE FUNCTIONAL GROUP COMPOSITION

EPA Science Inventory

Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...

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.

[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.

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.

A 2D Fourier tool for the analysis of photo-elastic effect in large granular assemblies

NASA Astrophysics Data System (ADS)

Leśniewska, Danuta

2017-06-01

Fourier transforms are the basic tool in constructing different types of image filters, mainly those reducing optical noise. Some DIC or PIV software also uses frequency space to obtain displacement fields from a series of digital images of a deforming body. The paper presents series of 2D Fourier transforms of photo-elastic transmission images, representing large pseudo 2D granular assembly, deforming under varying boundary conditions. The images related to different scales were acquired using the same image resolution, but taken at different distance from the sample. Fourier transforms of images, representing different stages of deformation, reveal characteristic features at the three (`macro-`, `meso-` and `micro-`) scales, which can serve as a data to study internal order-disorder transition within granular materials.

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.

Partial Fourier techniques in single-shot cross-term spatiotemporal encoded MRI.

PubMed

Zhang, Zhiyong; Frydman, Lucio

2018-03-01

Cross-term spatiotemporal encoding (xSPEN) is a single-shot approach with exceptional immunity to field heterogeneities, the images of which faithfully deliver 2D spatial distributions without requiring a priori information or using postacquisition corrections. xSPEN, however, suffers from signal-to-noise ratio penalties due to its non-Fourier nature and due to diffusion losses-especially when seeking high resolution. This study explores partial Fourier transform approaches that, acting along either the readout or the spatiotemporally encoded dimensions, reduce these penalties. xSPEN uses an orthogonal (e.g., z) gradient to read, in direct space, the low-bandwidth (e.g., y) dimension. This substantially changes the nature of partial Fourier acquisitions vis-à-vis conventional imaging counterparts. A suitable theoretical analysis is derived to implement these procedures, along either the spatiotemporally or readout axes. Partial Fourier single-shot xSPEN images were recorded on preclinical and human scanners. Owing to their reduction in the experiments' acquisition times, this approach provided substantial sensitivity gains vis-à-vis previous implementations for a given targeted in-plane resolution. The physical origins of these gains are explained. Partial Fourier approaches, particularly when implemented along the low-bandwidth spatiotemporal dimension, provide several-fold sensitivity advantages at minimal costs to the execution and processing of the single-shot experiments. Magn Reson Med 79:1506-1514, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

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.

Fourier transform spectroscopy of cotton and cotton trash

USDA-ARS?s Scientific Manuscript database

Fourier Transform techniques have been shown to have higher signal-to-noise capabilities, higher throughput, negligible stray light, continuous spectra, and higher resolution. In addition, FT spectroscopy affords for frequencies in spectra to be measured all at once and more precise wavelength calib...

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)

ENVIRONMENTAL ANALYSIS BY AB INITIO QUANTUM MECHANICAL COMPUTATION AND GAS CHROMATOGRAPHY/FOURIER TRANSFORM INFRARED SPECTROMETRY.

EPA Science Inventory

Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...

A method to perform a fast fourier transform with primitive image transformations.

PubMed

Sheridan, Phil

2007-05-01

The Fourier transform is one of the most important transformations in image processing. A major component of this influence comes from the ability to implement it efficiently on a digital computer. This paper describes a new methodology to perform a fast Fourier transform (FFT). This methodology emerges from considerations of the natural physical constraints imposed by image capture devices (camera/eye). The novel aspects of the specific FFT method described include: 1) a bit-wise reversal re-grouping operation of the conventional FFT is replaced by the use of lossless image rotation and scaling and 2) the usual arithmetic operations of complex multiplication are replaced with integer addition. The significance of the FFT presented in this paper is introduced by extending a discrete and finite image algebra, named Spiral Honeycomb Image Algebra (SHIA), to a continuous version, named SHIAC.

Detection and volume estimation of embolic air in the middle cerebral artery using transcranial Doppler sonography.

PubMed

Bunegin, L; Wahl, D; Albin, M S

1994-03-01

Cerebral embolism has been implicated in the development of cognitive and neurological deficits following bypass surgery. This study proposes methodology for estimating cerebral air embolus volume using transcranial Doppler sonography. Transcranial Doppler audio signals of air bubbles in the middle cerebral artery obtained from in vivo experiments were subjected to a fast-Fourier transform analysis. Audio segments when no air was present as well as artifact resulting from electrocautery and sensor movement were also subjected to fast-Fourier transform analysis. Spectra were compared, and frequency and power differences were noted and used for development of audio band-pass filters for isolation of frequencies associated with air emboli. In a bench model of the middle cerebral artery circulation, repetitive injections of various air volumes between 0.5 and 500 microL were made. Transcranial Doppler audio output was band-pass filtered, acquired digitally, then subjected to a fast-Fourier transform power spectrum analysis and power spectrum integration. A linear least-squares correlation was performed on the data. Fast-Fourier transform analysis of audio segments indicated that frequencies between 250 and 500 Hz are consistently dominant in the spectrum when air emboli are present. Background frequencies appear to be below 240 Hz, and artifact resulting from sensor movement and electrocautery appears to be below 300 Hz. Data from the middle cerebral artery model filtered through a 307- to 450-Hz band-pass filter yielded a linear relation between emboli volume and the integrated value of the power spectrum near 40 microL. Detection of emboli less than 0.5 microL was inconsistent, and embolus volumes greater than 40 microL were indistinguishable from one another. The preliminary technique described in this study may represent a starting point from which automated detection and volume estimation of cerebral emboli might be approached.

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

Algebraic signal processing theory: 2-D spatial hexagonal lattice.

PubMed

Pünschel, Markus; Rötteler, Martin

2007-06-01

We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper.

Development of a High-Throughput Microwave Imaging System for Concealed Weapons Detection

DTIC Science & Technology

2016-07-15

hardware. Index Terms—Microwave imaging, multistatic radar, Fast Fourier Transform (FFT). I. INTRODUCTION Near-field microwave imaging is a non-ionizing...configuration, but its computational demands are extreme. Fast Fourier Transform (FFT) imaging has long been used to efficiently construct images sampled with...Simulated image of 25 point scatterers imaged at range 1.5m, with array layout depicted in Fig. 3. Left: image formed with Equation (5) ( Fourier

Analysis techniques for residual acceleration data

NASA Technical Reports Server (NTRS)

Rogers, Melissa J. B.; Alexander, J. Iwan D.; Snyder, Robert S.

1990-01-01

Various aspects of residual acceleration data are of interest to low-gravity experimenters. Maximum and mean values and various other statistics can be obtained from data as collected in the time domain. Additional information may be obtained through manipulation of the data. Fourier analysis is discussed as a means of obtaining information about dominant frequency components of a given data window. Transformation of data into different coordinate axes is useful in the analysis of experiments with different orientations and can be achieved by the use of a transformation matrix. Application of such analysis techniques to residual acceleration data provides additional information than what is provided in a time history and increases the effectiveness of post-flight analysis of low-gravity experiments.

Formulation of the rotational transformation of wave fields and their application to digital holography.

PubMed

Matsushima, Kyoji

2008-07-01

Rotational transformation based on coordinate rotation in Fourier space is a useful technique for simulating wave field propagation between nonparallel planes. This technique is characterized by fast computation because the transformation only requires executing a fast Fourier transform twice and a single interpolation. It is proved that the formula of the rotational transformation mathematically satisfies the Helmholtz equation. Moreover, to verify the formulation and its usefulness in wave optics, it is also demonstrated that the transformation makes it possible to reconstruct an image on arbitrarily tilted planes from a wave field captured experimentally by using digital holography.

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

EVALUATION OF A PORTABLE FOURIER TRANSFORM INFRARED GAS ANALYZER FOR MEASUREMENTS OF AIR TOXICS IN POLLUTION PREVENTION RESEARCH

EPA Science Inventory

A portable Fourier transform infrared gas analyzer with a photoacoustic detector performed reliably during pollution prevention research at two industrial facilities. It exhibited good agreement (within approximately 6%) with other analytical instruments (dispersive infrared and ...

PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY

EPA Science Inventory

Open-path Fourier transform infrared (OP-FT1R) spectroscopy is an accepted technology for measuring gaseous air contaminants. OP-FT1R absorbance spectra acquired during changing aerosols conditions reveal related changes in very broad baseline features. Usually, this shearing of ...

Gravity data inversion to determine 3D topographycal density contrast of Banten area, Indonesia based on fast Fourier transform

NASA Astrophysics Data System (ADS)

Windhari, Ayuty; Handayani, Gunawan

2015-04-01

The 3D inversion gravity anomaly to estimate topographical density using a matlab source code from gridded data provided by Parker Oldenburg algorithm based on fast Fourier transform was computed. We extend and improved the source code of 3DINVERT.M invented by Gomez Ortiz and Agarwal (2005) using the relationship between Fourier transform of the gravity anomaly and the sum of the Fourier transform from the topography density. We gave density contrast between the two media to apply the inversion. FFT routine was implemented to construct amplitude spectrum to the given mean depth. The results were presented as new graphics of inverted topography density, the gravity anomaly due to the inverted topography and the difference between the input gravity data and the computed ones. It terminates when the RMS error is lower than pre-assigned value used as convergence criterion or until maximum of iterations is reached. As an example, we used the matlab program on gravity data of Banten region, Indonesia.

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.

Wavelength-encoded tomography based on optical temporal Fourier transform

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

Zhang, Chi; Wong, Kenneth K. Y., E-mail: kywong@eee.hku.hk

We propose and demonstrate a technique called wavelength-encoded tomography (WET) for non-invasive optical cross-sectional imaging, particularly beneficial in biological system. The WET utilizes time-lens to perform the optical Fourier transform, and the time-to-wavelength conversion generates a wavelength-encoded image of optical scattering from internal microstructures, analogous to the interferometery-based imaging such as optical coherence tomography. Optical Fourier transform, in principle, comes with twice as good axial resolution over the electrical Fourier transform, and will greatly simplify the digital signal processing after the data acquisition. As a proof-of-principle demonstration, a 150 -μm (ideally 36 μm) resolution is achieved based on a 7.5-nm bandwidth swept-pump,more » using a conventional optical spectrum analyzer. This approach can potentially achieve up to 100-MHz or even higher frame rate with some proven ultrafast spectrum analyzer. We believe that this technique is innovative towards the next-generation ultrafast optical tomographic imaging application.« less

The limit distribution in the q-CLT for q\\,\\geqslant \\,1 is unique and can not have a compact support

NASA Astrophysics Data System (ADS)

Umarov, Sabir; Tsallis, Constantino

2016-10-01

In a paper by Umarov et al (2008 Milan J. Math. 76 307-28), a generalization of the Fourier transform, called the q-Fourier transform, was introduced and applied for the proof of a q-generalized central limit theorem (q-CLT). Subsequently, Hilhorst illustrated (2009 Braz. J. Phys. 39 371-9 2010 J. Stat. Mech. P10023) that the q-Fourier transform for q\\gt 1, is not invertible in the space of density functions. Indeed, using an invariance principle, he constructed a family of densities with the same q-Fourier transform and noted that ‘as a consequence, the q-CLT falls short of achieving its stated goal’. The distributions constructed there have compact support. We prove now that the limit distribution in the q-CLT is unique and can not have a compact support. This result excludes all the possible counterexamples which can be constructed using the invariance principle and fills the gap mentioned by Hilhorst.

A new hybrid electrospray Fourier transform mass spectrometer: design and performance characteristics.

PubMed

O'connor, Peter B; Pittman, Jason L; Thomson, Bruce A; Budnik, Bogdan A; Cournoyer, Jason C; Jebanathirajah, Judith; Lin, Cheng; Moyer, Susanne; Zhao, Cheng

2006-01-01

A new hybrid electrospray quadrupole Fourier transform mass spectrometry (FTMS) instrument design is shown and characterized. This instrument involves coupling an electrospray source and mass-resolving quadrupole, ion accumulation, and collision cell linear ion trap system developed by MDS Sciex with a home-built ion guide and ion cyclotron resonance (ICR) cell. The iterative progression of this design is shown. The final design involves a set of hexapole ion guides to transfer the ions from the accumulation/collision trap through the magnetic field gradient and into the cell. These hexapole ion guides are separated by a thin gate valve and two conduction limits to maintain the required <10(-9) mbar vacuum for FTICR. Low-attomole detection limits for a pure peptide are shown, 220 000 resolving power in broadband mode and 820 000 resolving power in narrow-band mode are demonstrated, and mass accuracy in the <2 ppm range is routinely available provided the signal is abundant, cleanly resolved, and internally calibrated. This instrument design provides high experimental flexibility, allowing Q2 CAD, SORI-CAD, IRMPD, and ECD experiments with selected ion accumulation as well as experiments such as nozzle skimmer dissociation. Initial top-down mass spectrometry experiments on a protein is shown using ECD.

Application of the fractional Fourier transform to image reconstruction in MRI.

PubMed

Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo

2012-07-01

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.

Nonlinear response of dense colloidal suspensions under oscillatory shear: mode-coupling theory and Fourier transform rheology experiments.

PubMed

Brader, J M; Siebenbürger, M; Ballauff, M; Reinheimer, K; Wilhelm, M; Frey, S J; Weysser, F; Fuchs, M

2010-12-01

Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.

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.

Angular acceptance analysis of an infrared focal plane array with a built-in stationary Fourier transform spectrometer.

PubMed

Gillard, Frédéric; Ferrec, Yann; Guérineau, Nicolas; Rommeluère, Sylvain; Taboury, Jean; Chavel, Pierre

2012-06-01

Stationary Fourier transform spectrometry is an interesting concept for building reliable field or embedded spectroradiometers, especially for the mid- and far- IR. Here, a very compact configuration of a cryogenic stationary Fourier transform IR (FTIR) spectrometer is investigated, where the interferometer is directly integrated in the focal plane array (FPA). We present a theoretical analysis to explain and describe the fringe formation inside the FTIR-FPA structure when illuminated by an extended source positioned at a finite distance from the detection plane. The results are then exploited to propose a simple front lens design compatible with a handheld package.

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.

Direct generation of abruptly focusing vortex beams using a 3/2 radial phase-only pattern.

PubMed

Davis, Jeffrey A; Cottrell, Don M; Zinn, Jonathan M

2013-03-20

Abruptly focusing Airy beams have previously been generated using a radial cubic phase pattern that represents the Fourier transform of the Airy beam. The Fourier transform of this pattern is formed using a system length of 2f, where f is the focal length of the Fourier transform lens. In this work, we directly generate these abruptly focusing Airy beams using a 3/2 radial phase pattern encoded onto a liquid crystal display. The resulting optical system is much shorter. In addition, we can easily produce vortex patterns at the focal point of these beams. Experimental results match theoretical predictions.

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

DOE PAGES

Vogman, G. V.; Shumlak, U.

2011-10-13

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. As a result, these measurements are used to gain a better understanding of Z-pinch equilibria.« less

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

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

Vogman, G. V.; Shumlak, U.

2011-10-15

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. These measurements are used to gain a better understanding of Z-pinch equilibria.« less

Determination of Structural Parameters from EXAFS (Extended X-Ray Absorption Fine Structure): Application to Solutions and Catalysts.

DTIC Science & Technology

1984-05-23

the disorder was accurately known. Inverse Transform To isolate the EAFS contribution due to a single feature in the Fourier transform, the inverse ...is associated with setting the "fold" components to 27 zero in r-space. An inverse transform (real part) of the major feature of the Fig. 4 Fourier...phase of the resulting inverse transform represents only any differences between the material being studied and the reference. This residual is

Fourier-transform imaging of cotton and botanical and field trash mixtures

USDA-ARS?s Scientific Manuscript database

Botanical and field cotton trash comingled with cotton lint can greatly reduce the marketability and quality of cotton. Trash can be found comingled with cotton lint during harvesting, ginning, and processing, thus this study is of interest. Attenuated Total Reflectance-Fourier Transform Infrared (A...

Detection and classification of salmonella serotypes using spectral signatures collected by fourier transform infrared (FT-IR) spectroscopy

USDA-ARS?s Scientific Manuscript database

Spectral signatures of Salmonella serotypes namely Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky were collected using Fourier transform infrared spectroscopy (FT-IR). About 5-10 µL of Salmonella suspensions with concentrations of 1...

Identification and characterization of salmonella serotypes using DNA spectral characteristics by fourier transform infrared (FT-IR) spectroscopy

USDA-ARS?s Scientific Manuscript database

Analysis of DNA samples of Salmonella serotypes (Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky) were performed using Fourier transform infrared spectroscopy (FT-IR) spectrometer by placing directly in contact with a diamond attenua...

Is Fourier analysis performed by the visual system or by the visual investigator.

PubMed

Ochs, A L

1979-01-01

A numerical Fourier transform was made of the pincushion grid illusion and the spectral components orthogonal to the illusory lines were isolated. Their inverse transform creates a picture of the illusion. The spatial-frequency response of cortical, simple receptive field neurons similarly filters the grid. A complete set of these neurons thus approximates a two-dimensional Fourier analyzer. One cannot conclude, however, that the brain actually uses frequency-domain information to interpret visual images.

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.

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.

Feature Extraction for Bearing Prognostics and Health Management (PHM) - A Survey (Preprint)

DTIC Science & Technology

2008-05-01

Envelope analysis • Cepstrum analysis • Higher order spectrum • Short-time Fourier Transform (STFT) • Wigner - Ville distribution ( WVD ) • Empirical mode...techniques are the short-time Fourier transform (STFT), the Wigner - Ville distribution , and the wavelet transform. In this paper we categorize wavelets...diagnosis have shown in many publications, for example, [22]. b) Wigner – Ville distribution : The afore-mentioned STFT is conceptually simple. However

Limitations and potential of spectral subtractions in fourier-transform infrared (FTIR) spectroscopy of soil samples

USDA-ARS?s Scientific Manuscript database

Soil science research is increasingly applying Fourier transform infrared (FTIR) spectroscopy for analysis of soil organic matter (SOM). However, the compositional complexity of soils and the dominance of the mineral component can limit spectroscopic resolution of SOM and other minor components. The...

Detection of starch adulteration in onion powder by FT-NIR and FT-IR spectroscopy

USDA-ARS?s Scientific Manuscript database

Adulteration of onion powder with cornstarch was identified by Fourier transform near-infrared (FT-NIR) and Fourier transform infrared (FT-IR) spectroscopy. The reflectance spectra of 180 pure and adulterated samples (1–35 wt% starch) were collected and preprocessed to generate calibration and predi...

Coordinate axes, location of origin, and redundancy for the one and two-dimensional discrete Fourier transform

NASA Technical Reports Server (NTRS)

Ioup, G. E.; Ioup, J. W.

1985-01-01

Appendix 4 of the Study of One- and Two-Dimensional Filtering and Deconvolution Algorithms for a Streaming Array Computer discusses coordinate axes, location of origin, and redundancy for the one- and two-dimensional Fourier transform for complex and real data.

3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography

Treesearch

Michael C. Martin; Charlotte Dabat-Blondeau; Miriam Unger; Julia Sedlmair; Dilworth Y. Parkinson; Hans A. Bechtel; Barbara Illman; Jonathan M. Castro; Marco Keiluweit; David Buschke; Brenda Ogle; Michael J. Nasse; Carol J. Hirschmugl

2013-01-01

We report Fourier transform infrared spectro-microtomography, a nondestructive three-dimensional imaging approach that reveals the distribution of distinctive chemical compositions throughout an intact biological or materials sample. The method combines mid-infrared absorption contrast with computed tomographic data acquisition and reconstruction to enhance chemical...

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...

Applications of Fourier transform infrared spectroscopy to quality control of the epoxy matrix

NASA Technical Reports Server (NTRS)

Antoon, M. K.; Starkey, K. M.; Koenig, J. L.

1979-01-01

The object of the paper is to demonstrate the utility of Fourier transform infrared (FT-IR) difference spectra for investigating the composition of a neat epoxy resin, hardener, and catalysts. The composition and degree of cross-linking of the cured matrix is also considered.

A statistical evaluation of spectral fingerprinting methods using analysis of variance and principal component analysis

USDA-ARS?s Scientific Manuscript database

Six methods were compared with respect to spectral fingerprinting of a well-characterized series of broccoli samples. Spectral fingerprints were acquired for finely-powdered solid samples using Fourier transform-infrared (IR) and Fourier transform-near infrared (NIR) spectrometry and for aqueous met...

Machine Learning-Aided, Robust Wideband Spectrum Sensing for Cognitive Radios

DTIC Science & Technology

2015-06-12

to even Approved for public release; distribution is unlimited. 2 on the order of a giga -Hertz (GHz). Due to wide bandwidth and noncontiguous...Frequency Band CS Compressive Sampling DFT Discrete Fourier Transform EMI Electro Magnetic Interference FFT Fast Fourier Transform GHz Giga Hertz Hz Hertz

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…

New developments in photoacoustics

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

Rosencwaig, A.

1981-07-01

There have been several important new developments in the fields of photoacoustics and photoacoustic spectroscopy. Photoactoustic techniques are now being used in ferromagnetic and electron spin resonance experiments, and there have been rapid advances in Fourier-transform infrared photoacoustic spectroscopy. In addition, the calorimetric aspects of photoacoustics are now being extensively exploited for phase transition studies, and to perform thermal-wave imaging and microscopy.

ATR-FTIR Spectroscopy in the Undergraduate Chemistry Laboratory: Part II--A Physical Chemistry Laboratory Experiment on Surface Adsorption

ERIC Educational Resources Information Center

Schuttlefield, Jennifer D.; Larsen, Sarah C.; Grassian, Vicki H.

2008-01-01

Attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectroscopy is a useful technique for measuring the infrared spectra of solids and liquids as well as probing adsorption on particle surfaces. The use of FTIR-ATR spectroscopy in organic and inorganic chemistry laboratory courses as well as in undergraduate research was presented…

Digital Holographic Logic

NASA Technical Reports Server (NTRS)

Preston, K., Jr.

1972-01-01

The characteristics of the holographic logic computer are discussed. The holographic operation is reviewed from the Fourier transform viewpoint, and the formation of holograms for use in performing digital logic are described. The operation of the computer with an experiment in which the binary identity function is calculated is discussed along with devices for achieving real-time performance. An application in pattern recognition using neighborhood logic is presented.

Reduced field-of-view imaging for single-shot MRI with an amplitude-modulated chirp pulse excitation and Fourier transform reconstruction.

PubMed

Li, Jing; Zhang, Miao; Chen, Lin; Cai, Congbo; Sun, Huijun; Cai, Shuhui

2015-06-01

We employ an amplitude-modulated chirp pulse to selectively excite spins in one or more regions of interest (ROIs) to realize reduced field-of-view (rFOV) imaging based on single-shot spatiotemporally encoded (SPEN) sequence and Fourier transform reconstruction. The proposed rFOV imaging method was theoretically analyzed and illustrated with numerical simulation and tested with phantom experiments and in vivo rat experiments. In addition, point spread function was applied to demonstrate the feasibility of the proposed method. To evaluate the proposed method, the rFOV results were compared with those obtained using the EPI method with orthogonal RF excitation. The simulation and experimental results show that the proposed method can image one or two separated ROIs along the SPEN dimension in a single shot with higher spatial resolution, less sensitive to field inhomogeneity, and practically no aliasing artifacts. In addition, the proposed method may produce rFOV images with comparable signal-to-noise ratio to the rFOV EPI images. The proposed method is promising for the applications under severe susceptibility heterogeneities and for imaging separate ROIs simultaneously. Copyright © 2015 Elsevier Inc. All rights reserved.

[Measurements of stable isotopes in atmospheric CO2 and H2O by open-path Fourier transform infrared spectrometry].

PubMed

Wang, Wei; Liu, Wen-Qing; Zhang, Tian-Shu

2013-08-01

The development of spectroscopic techniques has offered continuous measurement of stable isotopes in the ambient air. The method of measuring environmental stable isotopes based on Fourier transform infrared spectrometry (FTIR) is described. In order to verify the feasibility of the method for continuous measurement of the stable isotopes, an open-path FTIR system was used to measure stable isotopes of CO2 and H2O in ambient air directly in a seven-day field experiment, including 12CO2, 3CO2, H2 16O and HD16 O. Also, the time course of carbon isotopic ratio delta13 C and deuterium isotope composition deltaD was calculated. The measurement precision is about 1.08 per thousand for delta13 C and 1.32 per thousand for deltaD. The measured stable isotopes of CO2 and H2O were analyzed on different time scales by Keeling plot methods, and the deuterium isotopic ratios of evapotranspiration were determined. The results of the field experiment demonstrate the potential of the open-path FTIR system for continuous measurement of stable isotopes in the air.

Ruthenium trisbipyridine as a candidate for gas-phase spectroscopic studies in a Fourier transform mass spectrometer

DOE PAGES

Scott, Jill R.; Ham, Jason E.; Durham, Bill; ...

2004-01-01

Metal polypyridines are excellent candidates for gas-phase optical experiments where their intrinsic properties can be studied without complications due to the presence of solvent. The fluorescence lifetimes of [Ru(bpy) 3 ] 1+ trapped in an optical detection cell within a Fourier transform mass spectrometer were obtained using matrix-assisted laser desorption/ionization to generate the ions with either 2,5-dihydroxybenzoic acid (DHB) or sinapinic acid (SA) as matrix. All transients acquired, whether using DHB or SA for ion generation, were best described as approximately exponential decays. The rate constant for transients derived using DHB as matrix was 4×10 7 s −1 , whilemore » the rate constant using SA was 1×10 7 s −1 . Some suggestions of multiple exponential decay were evident although limited by the quality of the signals. Photodissociation experiments revealed that [Ru(bpy) 3 ] 1+ generated using DHB can decompose to [Ru(bpy) 2 ] 1+ , whereas ions generated using SA showed no decomposition. Comparison of the mass spectra with the fluorescence lifetimes illustrates the promise of incorporating optical detection with trapped ion mass spectrometry techniques.« less

The Effect of Substrate Emissivity on the Spectral Emission of a Hot-Gas Overlayer

DTIC Science & Technology

2015-12-30

unlimited. Unclassified Unlimited Unclassified Unlimited Unclassified Unlimited Unclassified Unlimited 19 Harold D. Ladouceur (202) 767-3558 Fourier ...13 REFERENCES………………………………………………………………………………….………..14 E-1 EXECUTIVE SUMMARY Fourier transform infrared...Raman spectroscopy, ambient x-ray photoelectron spectroscopy, near- infrared thermal imaging, and Fourier transform infrared emission spectroscopy

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.

Products of multiple Fourier series with application to the multiblade transformation

NASA Technical Reports Server (NTRS)

Kunz, D. L.

1981-01-01

A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.

Diffraction Theory and Almost Periodic Distributions

NASA Astrophysics Data System (ADS)

Strungaru, Nicolae; Terauds, Venta

2016-09-01

We introduce and study the notions of translation bounded tempered distributions, and autocorrelation for a tempered distribution. We further introduce the spaces of weakly, strongly and null weakly almost periodic tempered distributions and show that for weakly almost periodic tempered distributions the Eberlein decomposition holds. For translation bounded measures all these notions coincide with the classical ones. We show that tempered distributions with measure Fourier transform are weakly almost periodic and that for this class, the Eberlein decomposition is exactly the Fourier dual of the Lebesgue decomposition, with the Fourier-Bohr coefficients specifying the pure point part of the Fourier transform. We complete the project by looking at few interesting examples.

Fast acquisition of multidimensional NMR spectra of solids and mesophases using alternative sampling methods.

PubMed

Lesot, Philippe; Kazimierczuk, Krzysztof; Trébosc, Julien; Amoureux, Jean-Paul; Lafon, Olivier

2015-11-01

Unique information about the atom-level structure and dynamics of solids and mesophases can be obtained by the use of multidimensional nuclear magnetic resonance (NMR) experiments. Nevertheless, the acquisition of these experiments often requires long acquisition times. We review here alternative sampling methods, which have been proposed to circumvent this issue in the case of solids and mesophases. Compared to the spectra of solutions, those of solids and mesophases present some specificities because they usually display lower signal-to-noise ratios, non-Lorentzian line shapes, lower spectral resolutions and wider spectral widths. We highlight herein the advantages and limitations of these alternative sampling methods. A first route to accelerate the acquisition time of multidimensional NMR spectra consists in the use of sparse sampling schemes, such as truncated, radial or random sampling ones. These sparsely sampled datasets are generally processed by reconstruction methods differing from the Discrete Fourier Transform (DFT). A host of non-DFT methods have been applied for solids and mesophases, including the G-matrix Fourier transform, the linear least-square procedures, the covariance transform, the maximum entropy and the compressed sensing. A second class of alternative sampling consists in departing from the Jeener paradigm for multidimensional NMR experiments. These non-Jeener methods include Hadamard spectroscopy as well as spatial or orientational encoding of the evolution frequencies. The increasing number of high field NMR magnets and the development of techniques to enhance NMR sensitivity will contribute to widen the use of these alternative sampling methods for the study of solids and mesophases in the coming years. Copyright © 2015 John Wiley & Sons, Ltd.

MRS3D: 3D Spherical Wavelet Transform on the Sphere

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2011-12-01

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. We present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We tested the 3D wavelet transform and as a toy-application, applied a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and found we can successfully remove noise without much loss to the large scale structure. The new spherical 3D isotropic wavelet transform, called MRS3D, is ideally suited to analysing and denoising future 3D spherical cosmological surveys; it uses a novel discrete spherical Fourier-Bessel Transform. MRS3D is based on two packages, IDL and Healpix and can be used only if these two packages have been installed.

Wavelet based detection of manatee vocalizations

NASA Astrophysics Data System (ADS)

Gur, Berke M.; Niezrecki, Christopher

2005-04-01

The West Indian manatee (Trichechus manatus latirostris) has become endangered partly because of watercraft collisions in Florida's coastal waterways. Several boater warning systems, based upon manatee vocalizations, have been proposed to reduce the number of collisions. Three detection methods based on the Fourier transform (threshold, harmonic content and autocorrelation methods) were previously suggested and tested. In the last decade, the wavelet transform has emerged as an alternative to the Fourier transform and has been successfully applied in various fields of science and engineering including the acoustic detection of dolphin vocalizations. As of yet, no prior research has been conducted in analyzing manatee vocalizations using the wavelet transform. Within this study, the wavelet transform is used as an alternative to the Fourier transform in detecting manatee vocalizations. The wavelet coefficients are analyzed and tested against a specified criterion to determine the existence of a manatee call. The performance of the method presented is tested on the same data previously used in the prior studies, and the results are compared. Preliminary results indicate that using the wavelet transform as a signal processing technique to detect manatee vocalizations shows great promise.

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.

Analytical properties of time-of-flight PET data.

PubMed

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M

2008-06-07

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the 'bow-tie' property of the 2D Radon transform to the time-of-flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data.

Analytical properties of time-of-flight PET data

NASA Astrophysics Data System (ADS)

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M.

2008-06-01

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the 'bow-tie' property of the 2D Radon transform to the time-of-flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data.

Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram.

PubMed

Barnett, Patrick D; Strange, K Alicia; Angel, S Michael

2017-06-01

This work describes a method of applying the Fourier transform to the two-dimensional Fizeau fringe patterns generated by the spatial heterodyne Raman spectrometer (SHRS), a dispersive interferometer, to correct the effects of certain types of optical alignment errors. In the SHRS, certain types of optical misalignments result in wavelength-dependent and wavelength-independent rotations of the fringe pattern on the detector. We describe here a simple correction technique that can be used in post-processing, by applying the Fourier transform in a row-by-row manner. This allows the user to be more forgiving of fringe alignment and allows for a reduction in the mechanical complexity of the SHRS.

The investigation of the bio-oil produced by hydrothermal liquefaction of Spirulina platensis using ultrahigh resolution Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Kostyukevich, Yury; Vlaskin, Mikhail; Vladimirov, Gleb; Zherebker, Alexander; Kononikhin, Alexey; Popov, Igor; Nikolaev, Eugene

2017-04-01

We report the investigation of the hydrothermal liquefaction products of the Spirulina platensis microalgae by using the Fourier transform ion cyclotron resonance mass spectrometry. The hydrothermal liquefaction produced two fractions: one with boiling temperature below 300℃ and the dense residue that remained in the reactor. It was observed that N 2 and N classes of compounds that dominate in the positive ESI Fourier transform ion cyclotron resonance spectra for both fractions, and that the light fraction is considerably more saturated then the heavy one. The performed hydrogen/deuterium exchange reaction indicated the presence of the onium compounds in the bio-oil.

The application of digital signal processing techniques to a teleoperator radar system

NASA Technical Reports Server (NTRS)

Pujol, A.

1982-01-01

A digital signal processing system was studied for the determination of the spectral frequency distribution of echo signals from a teleoperator radar system. The system consisted of a sample and hold circuit, an analog to digital converter, a digital filter, and a Fast Fourier Transform. The system is interfaced to a 16 bit microprocessor. The microprocessor is programmed to control the complete digital signal processing. The digital filtering and Fast Fourier Transform functions are implemented by a S2815 digital filter/utility peripheral chip and a S2814A Fast Fourier Transform chip. The S2815 initially simulates a low-pass Butterworth filter with later expansion to complete filter circuit (bandpass and highpass) synthesizing.

Color image cryptosystem using Fresnel diffraction and phase modulation in an expanded fractional Fourier transform domain

NASA Astrophysics Data System (ADS)

Chen, Hang; Liu, Zhengjun; Chen, Qi; Blondel, Walter; Varis, Pierre

2018-05-01

In this letter, what we believe is a new technique for optical color image encryption by using Fresnel diffraction and a phase modulation in an extended fractional Fourier transform domain is proposed. Different from the RGB component separation based method, the color image is converted into one component by improved Chirikov mapping. The encryption system is addressed with Fresnel diffraction and phase modulation. A pair of lenses is placed into the fractional Fourier transform system for the modulation of beam propagation. The structure parameters of the optical system and parameters in Chirikov mapping serve as extra keys. Some numerical simulations are given to test the validity of the proposed cryptosystem.

Metasurface Enabled Wide-Angle Fourier Lens.

PubMed

Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo

2018-06-01

Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Ultra-Wideband Radar Transient Detection using Time-Frequency and Wavelet Transforms.

DTIC Science & Technology

1992-12-01

if p==2, mesh(flipud(abs(spdatamatrix).A2)) end 2. Wigner - Ville Distribution function P = wvd (data,winlenstep,begintheendp) % Filename: wvd.m % Title...short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution , and time-scale methods, such as the a trous...such as the short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution [1], and time-scale methods, such

SAR image formation with azimuth interpolation after azimuth transform

DOEpatents

Doerry,; Armin W. , Martin; Grant D. , Holzrichter; Michael, W [Albuquerque, NM

2008-07-08

Two-dimensional SAR data can be processed into a rectangular grid format by subjecting the SAR data to a Fourier transform operation, and thereafter to a corresponding interpolation operation. Because the interpolation operation follows the Fourier transform operation, the interpolation operation can be simplified, and the effect of interpolation errors can be diminished. This provides for the possibility of both reducing the re-grid processing time, and improving the image quality.

Delineation of First-Order Elastic Property Closures for Hexagonal Metals Using Fast Fourier Transforms

PubMed Central

Landry, Nicholas W.; Knezevic, Marko

2015-01-01

Property closures are envelopes representing the complete set of theoretically feasible macroscopic property combinations for a given material system. In this paper, we present a computational procedure based on fast Fourier transforms (FFTs) for delineation of elastic property closures for hexagonal close packed (HCP) metals. The procedure consists of building a database of non-zero Fourier transforms for each component of the elastic stiffness tensor, calculating the Fourier transforms of orientation distribution functions (ODFs), and calculating the ODF-to-elastic property bounds in the Fourier space. In earlier studies, HCP closures were computed using the generalized spherical harmonics (GSH) representation and an assumption of orthotropic sample symmetry; here, the FFT approach allowed us to successfully calculate the closures for a range of HCP metals without invoking any sample symmetry assumption. The methodology presented here facilitates for the first time computation of property closures involving normal-shear coupling stiffness coefficients. We found that the representation of these property linkages using FFTs need more terms compared to GSH representations. However, the use of FFT representations reduces the computational time involved in producing the property closures due to the use of fast FFT algorithms. Moreover, FFT algorithms are readily available as opposed to GSH codes. PMID:28793566

Optical joint transform correlation on the DMD. [deformable mirror device

NASA Technical Reports Server (NTRS)

Knopp, Jerome; Juday, Richard D.

1989-01-01

Initial experimental investigation of the deformable mirror device (DMD) in a joint optical transform correlation is reported. The inverted cloverleaf version of the DMD, in which form the DMD is phase-mostly but of limited phase range, is used. Binarized joint Fourier transforms were calculated for similar and dissimilar objects and written onto the DMD. Inverse Fourier transform was done in a diffraction order for which the DMD shows phase-mostly modulation. Matched test objects produced sharp correlation, distinct objects did not. Further studies are warranted and they are outlined.

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.

Fourier transform wavefront control with adaptive prediction of the atmosphere.

PubMed

Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre

2007-09-01

Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.

PLANE-INTEGRATED OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROMETRY METHODOLOGY FOR ANAEROBIC SWINE LAGOON EMISSION MEASUREMENTS

EPA Science Inventory

Emissions of ammonia and methane from an anaerobic lagoon at a swine animal feeding operation were evaluated five times over a period of two years. The plane-integrated (PI) open-path Fourier transform infrared spectrometry (OP-FTIR) methodology was used to transect the plume at ...

Turbulence excited frequency domain damping measurement and truncation effects

NASA Technical Reports Server (NTRS)

Soovere, J.

1976-01-01

Existing frequency domain modal frequency and damping analysis methods are discussed. The effects of truncation in the Laplace and Fourier transform data analysis methods are described. Methods for eliminating truncation errors from measured damping are presented. Implications of truncation effects in fast Fourier transform analysis are discussed. Limited comparison with test data is presented.

Comparison and validation of Fourier transform infrared spectroscopic methods for monitoring secondary cell wall cellulose from cotton fibers

USDA-ARS?s Scientific Manuscript database

The amount of secondary cell wall (SCW) cellulose in the fiber affects the quality and commercial value of cotton. Accurate assessments of SCW cellulose are essential for improving cotton fibers. Fourier Transform Infrared (FT-IR) spectroscopy enables distinguishing SCW from other cell wall componen...

CHARACTERIZATION OF AMBIENT PM2.5 AEROSOL AT A SOUTHEASTERN US SITE: FOURIER TRANSFORM INFRARED ANALYSIS OR PARTICLE PHASE

EPA Science Inventory

During a field study in the summer of 2000 in the Research Triangle Park (RTP), aerosol samples were collected using a five stage cascade impactor and subsequently analyzed using Fourier Transform Infrared Spectroscopy (FTIR). The impaction surfaces were stainless steel disks....

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.

Topics in Chemical Instrumentation: Fourier Transform-Infrared Spectroscopy: Part I. Instrumentation.

ERIC Educational Resources Information Center

Perkins, W. D.

1986-01-01

Discusses: (1) the design of the Fourier Transform-Infrared Spectroscopy (FT-IR) spectrometer; (2) the computation of the spectrum from the interferogram; and (3) the use of apodization. (Part II will discuss advantages of FT-IR over dispersive techniques and show applications of FT-IR to difficult spectroscopic measurements.) (JN)

Diffuse-reflectance fourier-transform mid-infrared spectroscopy as a method of characterizing changes in soil organic matter

USDA-ARS?s Scientific Manuscript database

Diffuse-Reflectance Fourier-Transform Mid-Infrared Spectroscopy (MidIR) can identify the presence of important organic functional groups in soil organic matter (SOM). Soils contain myriad organic and inorganic components that absorb in the MidIR so spectral interpretation needs to be validated in or...

Secondary cell wall development in cotton fibers as examined with attenuated total reflection Fourier transform infrared spectroscopy

USDA-ARS?s Scientific Manuscript database

Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-IR) spectroscopy. The selected harvesting points coincide with secondary cell wall (SCW) development in the fibers. Progressive but moderat...

Development of secondary cell wall in cotton fibers as examined with Fourier transform-infrared spectroscopy

USDA-ARS?s Scientific Manuscript database

Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...

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.

Vibrational spectroscopy and DFT calculations of flavonoid derriobtusone A

NASA Astrophysics Data System (ADS)

Marques, A. N. L.; Mendes Filho, J.; Freire, P. T. C.; Santos, H. S.; Albuquerque, M. R. J. R.; Bandeira, P. N.; Leite, R. V.; Braz-Filho, R.; Gusmão, G. O. M.; Nogueira, C. E. S.; Teixeira, A. M. R.

2017-02-01

Flavonoids are secondary metabolites of plants which perform various functions. One subclass of flavonoid is auronol that can present immunostimulating activity. In this work Fourier-Transform Infrared with Attenuated Total Reflectance (FTIR-ATR) and Fourier-Transform Raman (FT-Raman) spectra of an auronol, derriobtusone A (C18H12O4), were obtained at room temperature. Theoretical calculations using Density Functional Theory (DFT) were performed in order to assign the normal modes and to interpret the spectra of the derriobtusone A molecule. The FTIR-ATR and FT-Raman spectra of the crystal, were recorded at room temperature in the regions 600 cm-1 to 4000 cm-1 and 40 cm-1 to 4000 cm-1, respectively. The normal modes of vibrations were obtained using Density Functional Theory with B3LYP functional and 6-31G+ (d,p) basis set. The calculated frequencies are in good agreement with those obtained experimentally. Detailed assignments of the normal modes present in both the Fourier-Transform infrared and the Fourier-Transform Raman spectra of the crystal are given.

An alternative path to the boundary: The CFT as the Fourier space of AdS

NASA Astrophysics Data System (ADS)

Tolfree, Ian M.

2009-12-01

In this thesis we shed new light on the conjectured duality between an n + 1 dimensional theory of gravity in anti de Sitter space (AdS) and an n dimensional conformal field theory (CFT) by showing that the CFT can be interpreted as the Fourier space of AdS. We then make use of this to gain insight into the nature of black hole entropy. In the first part of this thesis, we give an introduction to the ideas of and review the basics of the AdS/CFT. In the next section we make use of well known integral geometry techniques to derive the Fourier transformation of a function on AdS and see it is a function with compact support on the boundary. Comparing this to the literature, we find that the Green's functions from the literature are actually the Fourier weights of the transformation and that the boundary values of fields appearing in the correspondence are the Fourier coefficients of the transformation. One is thus left to interpret the CFT as the quantized version of a classical theory in AdS and the dual operator as the Fourier coefficients. Group theoretic considerations are discussed in relation to the transformation and its potential use in constructing QCD like theories. In the last section, we then build upon this to study the BTZ black hole. Named after its authors, Banados, Teitelboim and Zanelli, the BTZ black hole is a three dimensional (two space plus one time dimension) black hole in anti de Sitter space. Following standard procedures for modifying Fourier Transformations to accommodate quotient spaces we arrive at a mapping in a black hole background consistent with known results that yields the exact micro-states of a scalar field in a black hole background. We find that the micro-states are the Fourier coefficients on the boundary, which transform under the principal series representation of SL(2, R). Using the knowledge of how to represent a bulk scalar field in the CFT, and knowing how a black hole interacts with a scalar field, we deduce the possible representations of a black hole in the CFT. We find that the black hole micro-states live on the boundary, not on the horizon, and correspond to the possible emission modes of the black hole.

Analysis of photonic Doppler velocimetry data based on the continuous wavelet transform

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

Liu Shouxian; Wang Detian; Li Tao

2011-02-15

The short time Fourier transform (STFT) cannot resolve rapid velocity changes in most photonic Doppler velocimetry (PDV) data. A practical analysis method based on the continuous wavelet transform (CWT) was presented to overcome this difficulty. The adaptability of the wavelet family predicates that the continuous wavelet transform uses an adaptive time window to estimate the instantaneous frequency of signals. The local frequencies of signal are accurately determined by finding the ridge in the spectrogram of the CWT and then are converted to target velocity according to the Doppler effects. A performance comparison between the CWT and STFT is demonstrated bymore » a plate-impact experiment data. The results illustrate that the new method is automatic and adequate for analysis of PDV data.« less

A technique for phase correction in Fourier transform spectroscopy

NASA Astrophysics Data System (ADS)

Artsang, P.; Pongchalee, P.; Palawong, K.; Buisset, C.; Meemon, P.

2018-03-01

Fourier transform spectroscopy (FTS) is a type of spectroscopy that can be used to analyze components in the sample. The basic setup that is commonly used in this technique is "Michelson interferometer". The interference signal obtained from interferometer can be Fourier transformed into the spectral pattern of the illuminating light source. To experimentally study the concept of the Fourier transform spectroscopy, the project started by setup the Michelson interferometer in the laboratory. The implemented system used a broadband light source in near infrared region (0.81-0.89 μm) and controlled the movable mirror by using computer controlled motorized translation stage. In the early study, there is no sample the interference path. Therefore, the theoretical spectral results after the Fourier transformation of the captured interferogram must be the spectral shape of the light source. One main challenge of the FTS is to retrieve the correct phase information of the inferferogram that relates with the correct spectral shape of the light source. One main source of the phase distortion in FTS that we observed from our system is the non-linear movement of the movable reference mirror of the Michelson interferometer. Therefore, to improve the result, we coupled a monochromatic light source to the implemented interferometer. We simultaneously measured the interferograms of the monochromatic and broadband light sources. The interferogram of the monochromatic light source was used to correct the phase of the interferogram of the broadband light source. The result shows significant improvement in the computed spectral shape.

Three-dimensional Fourier transform evaluation of sequences of spatially and temporally modulated speckle interferograms.

PubMed

Trillo, C; Doval, A F; López-Vázquez, J C

2010-07-05

Phase evaluation methods based on the 2D spatial Fourier transform of a speckle interferogram with spatial carrier usually assume that the Fourier spectrum of the interferogram has a trimodal distribution, i. e. that the side lobes corresponding to the interferential terms do not overlap the other two spectral terms, which are related to the intensity of the object and reference beams, respectively. Otherwise, part of the spectrum of the object beam is inside the inverse-transform window of the selected interference lobe and induces an error in the resultant phase map. We present a technique for the acquisition and processing of speckle interferogram sequences that separates the interference lobes from the other spectral terms when the aforementioned assumption does not apply and regardless of the temporal bandwidth of the phase signal. It requires the recording of a sequence of interferograms with spatial and temporal carriers, and their processing with a 3D Fourier transform. In the resultant 3D spectrum, the spatial and temporal carriers separate the conjugate interferential terms from each other and from the term related to the object beam. Experimental corroboration is provided through the measurement of the amplitude of surface acoustic waves in plates with a double-pulsed TV holography setup. The results obtained with the proposed method are compared to those obtained with the processing of individual interferograms with the regular spatial-carrier 2D Fourier transform method.

Amyloid Hydrogen Bonding Polymorphism Evaluated by (15)N{(17)O}REAPDOR Solid-State NMR and Ultra-High Resolution Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

PubMed

Wei, Juan; Antzutkin, Oleg N; Filippov, Andrei V; Iuga, Dinu; Lam, Pui Yiu; Barrow, Mark P; Dupree, Ray; Brown, Steven P; O'Connor, Peter B

2016-04-12

A combined approach, using Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) and solid-state NMR (Nuclear Magnetic Resonance), shows a high degree of polymorphism exhibited by Aβ species in forming hydrogen-bonded networks. Two Alzheimer's Aβ peptides, Ac-Aβ(16-22)-NH2 and Aβ(11-25), selectively labeled with (17)O and (15)N at specific amino acid residues were investigated. The total amount of peptides labeled with (17)O as measured by FTICR-MS enabled the interpretation of dephasing observed in (15)N{(17)O}REAPDOR solid-state NMR experiments. Specifically, about one-third of the Aβ peptides were found to be involved in the formation of a specific >C═(17)O···H-(15)N hydrogen bond with their neighbor peptide molecules, and we hypothesize that the rest of the molecules undergo ± n off-registry shifts in their hydrogen bonding networks.

Transient excitation and data processing techniques employing the fast fourier transform for aeroelastic testing

NASA Technical Reports Server (NTRS)

Jennings, W. P.; Olsen, N. L.; Walter, M. J.

1976-01-01

The development of testing techniques useful in airplane ground resonance testing, wind tunnel aeroelastic model testing, and airplane flight flutter testing is presented. Included is the consideration of impulsive excitation, steady-state sinusoidal excitation, and random and pseudorandom excitation. Reasons for the selection of fast sine sweeps for transient excitation are given. The use of the fast fourier transform dynamic analyzer (HP-5451B) is presented, together with a curve fitting data process in the Laplace domain to experimentally evaluate values of generalized mass, model frequencies, dampings, and mode shapes. The effects of poor signal to noise ratios due to turbulence creating data variance are discussed. Data manipulation techniques used to overcome variance problems are also included. The experience is described that was gained by using these techniques since the early stages of the SST program. Data measured during 747 flight flutter tests, and SST, YC-14, and 727 empennage flutter model tests are included.

Light scattering properties of kidney epithelial cells and nuclei

NASA Astrophysics Data System (ADS)

Vitol, Elina A.; Kurzweg, Timothy P.; Nabet, Bahram

2006-02-01

Enlargement of mammalian cells nuclei due to the cancerous inflammation can be detected early through noninvasive optical techniques. We report on the results of cellular experiments, aimed towards the development of a fiber optic endoscopic probe used for precancerous detection of Barrett's esophagus. We previously presented white light scattering results from tissue phantoms (polystyrene polybead microspheres). In this paper, we discuss light scattering properties of epithelial MDCK (Madine-Darby Canine Kidney) cells and cell nuclei suspensions. A bifurcated optical fiber is used for experimental illumination and signal detection. The resulting scattering spectra from the cells do not exhibit the predicted Mie theory oscillatory behavior inherent to ideally spherical scatterers, such as polystyrene microspheres. However, we are able to demonstrate that the Fourier transform spectra of the cell suspensions are well correlated with the Fourier transform spectra of cell nuclei, concluding that the dominate scatterer in the backscattering region is the nucleus. This correlation experimentally illustrates that in the backscattering region, the cell nuclei are the main scatterer in the cells of the incident light.

Hosting a Fourier Transform Spectrometer (FTS) on CubeSat Spacecraft Platforms for Global Measurements of Three-Dimensional Winds

NASA Astrophysics Data System (ADS)

Scott, D. K.; Neilsen, T. L.; Weston, C.; Frazier, C.; Smith, T.; Shumway, A.

2015-12-01

Global measurements of vertically-resolved atmospheric wind profiles offer the potential for improved weather forecasts and superior predictions of atmospheric wind patterns. A small-satellite constellation that uses a Fourier Transform Spectrometer (FTS) instrument onboard 12U CubeSats can provide measurements of global tropospheric wind profiles from space at a very low cost. These small satellites are called FTS CubeSats. This presentation will describe a spacecraft concept that provides a stable, robust platform to host the FTS payload. Of importance to the payload are power, data, station keeping, thermal, and accommodations that enable high spectral measurements to be made from a LEO orbit. The spacecraft concept draws on Space Dynamics Laboratory (SDL) heritage and the recent success of the Dynamic Ionosphere Cubesat Experiment (DICE) and HyperAngular Rainbow Polarimeter (HARP) missions. Working with team members, SDL built a prototype observatory (spacecraft and payload) for testing and proof of concept.

Fast neutral beam ion source coupled to a Fourier transform ion cyclotron resonance mass spectrometer

NASA Astrophysics Data System (ADS)

Hill, Nicholas C.; Limbach, Patrick A.; Shomo, Ronald E., II; Marshall, Alan G.; Appelhans, Anthony D.; Delmore, James E.

1991-11-01

The coupling of an autoneutralizing SF-6 fast ion-beam gun to a Fourier transform ion cyclotron resonance (FT/ICR) mass spectrometer is described. The fast neutral beam provides for secondary-ion-type FT/ICR mass analysis [e.g., production of abundant pseudomolecular (M+H)+ ions] of involatile samples without the need for external ion injection, since ions are formed at the entrance to the ICR ion trap. The design, construction, and testing of the hybrid instrument are described. The feasibility of the experiment (for both broadband and high-resolution FT/ICR positive-ion mass spectra) is demonstrated with tetra-butylammonium bromide and a Tylenol■ sample. The ability to analyze high molecular weight polymers with high mass resolution is demonstrated for Teflon■. All of the advantages of the fast neutral beam ion source previously demonstrated with quadrupole mass analysis are preserved, and the additional advantages of FT/ICR mass analysis (e.g., high mass resolving power, ion trapping) are retained.

Simulation of Near-Edge X-ray Absorption Fine Structure with Time-Dependent Equation-of-Motion Coupled-Cluster Theory.

PubMed

Nascimento, Daniel R; DePrince, A Eugene

2017-07-06

An explicitly time-dependent (TD) approach to equation-of-motion (EOM) coupled-cluster theory with single and double excitations (CCSD) is implemented for simulating near-edge X-ray absorption fine structure in molecular systems. The TD-EOM-CCSD absorption line shape function is given by the Fourier transform of the CCSD dipole autocorrelation function. We represent this transform by its Padé approximant, which provides converged spectra in much shorter simulation times than are required by the Fourier form. The result is a powerful framework for the blackbox simulation of broadband absorption spectra. K-edge X-ray absorption spectra for carbon, nitrogen, and oxygen in several small molecules are obtained from the real part of the absorption line shape function and are compared with experiment. The computed and experimentally obtained spectra are in good agreement; the mean unsigned error in the predicted peak positions is only 1.2 eV. We also explore the spectral signatures of protonation in these molecules.

Experimental validation of spatial Fourier transform-based multiple sound zone generation with a linear loudspeaker array.

PubMed

Okamoto, Takuma; Sakaguchi, Atsushi

2017-03-01

Generating acoustically bright and dark zones using loudspeakers is gaining attention as one of the most important acoustic communication techniques for such uses as personal sound systems and multilingual guide services. Although most conventional methods are based on numerical solutions, an analytical approach based on the spatial Fourier transform with a linear loudspeaker array has been proposed, and its effectiveness has been compared with conventional acoustic energy difference maximization and presented by computer simulations. To describe the effectiveness of the proposal in actual environments, this paper investigates the experimental validation of the proposed approach with rectangular and Hann windows and compared it with three conventional methods: simple delay-and-sum beamforming, contrast maximization, and least squares-based pressure matching using an actually implemented linear array of 64 loudspeakers in an anechoic chamber. The results of both the computer simulations and the actual experiments show that the proposed approach with a Hann window more accurately controlled the bright and dark zones than the conventional methods.

Investigations of the functional states of dendritic cells under different conditioned microenvironments by Fourier transformed infrared spectroscopy.

PubMed

Dong, Rong; Long, Jinhua; Xu, Xiaoli; Zhang, Chunlin; Wen, Zongyao; Li, Long; Yao, Weijuan; Zeng, Zhu

2014-01-10

Dendritic cells are potent and specialized antigen presenting cells, which play a crucial role in initiating and amplifying both the innate and adaptive immune responses. The dendritic cell-based vaccination against cancer has been clinically achieved promising successes. But there are still many challenges in its clinical application, especially for how to identify the functional states. The CD14+ monocytes were isolated from human peripheral blood after plastic adherence and purified to approximately 98% with cocktail immunomagnetic beads. The immature dendritic cells and mature dendritic cells were induced by traditional protocols. The resulting dendritic cells were cocultured with normal cells and cancer cells. The functional state of dendritic cells including immature dendritic cells (imDCs) and mature dendritic cells (mDCs) under different conditioned microenvironments were investigated by Fourier transformed infrared spectroscopy (FTIR) and molecular biological methods. The results of Fourier transformed infrared spectroscopy showed that the gene transcription activity and energy states of dendritic cells were specifically suppressed by tumor cells (P < 0.05 or 0.01). The expression levels of NF-kappa B (NF-κB) in dendritic cells were also specifically inhibited by tumor-derived factors (P < 0.05 or 0.01). Moreover, the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were closely correlated with the expression levels of NF-κB (R2:0.69 and R2:0.81, respectively). Our results confirmed that the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were positively correlated with the expression levels of NF-κB, suggesting that Fourier transformed infrared spectroscopy technology could be clinically applied to identify the functional states of dendritic cell when performing dendritic cell-based vaccination. It's significant for the simplification and standardization of dendritic cell-based vaccination clinical preparation protocols.

The Twist Tensor Nuclear Norm for Video Completion.

PubMed

Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui

2017-12-01

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.

Theory of Wavelet-Based Coarse-Graining Hierarchies for Molecular Dynamics

DTIC Science & Technology

2017-04-01

resolution. ............................................... 15 Fig. 6 Fourier transform of the y-component of 1,000 atoms in crystalline PE (100,800 atoms...of magnitude of optimal representation. . 16 Fig. 7 Top row: Fourier transform of the y-component of a 100,800 atom crystalline PE sampled at 1 fs. 3... transform of the z-component of alanine dipeptide in vacuum excluding zero frequency to allow detail at other frequencies. MD at 500 K and 1 atm. Left

Single-pixel non-imaging object recognition by means of Fourier spectrum acquisition

NASA Astrophysics Data System (ADS)

Chen, Huichao; Shi, Jianhong; Liu, Xialin; Niu, Zhouzhou; Zeng, Guihua

2018-04-01

Single-pixel imaging has emerged over recent years as a novel imaging technique, which has significant application prospects. In this paper, we propose and experimentally demonstrate a scheme that can achieve single-pixel non-imaging object recognition by acquiring the Fourier spectrum. In an experiment, a four-step phase-shifting sinusoid illumination light is used to irradiate the object image, the value of the light intensity is measured with a single-pixel detection unit, and the Fourier coefficients of the object image are obtained by a differential measurement. The Fourier coefficients are first cast into binary numbers to obtain the hash value. We propose a new method of perceptual hashing algorithm, which is combined with a discrete Fourier transform to calculate the hash value. The hash distance is obtained by calculating the difference of the hash value between the object image and the contrast images. By setting an appropriate threshold, the object image can be quickly and accurately recognized. The proposed scheme realizes single-pixel non-imaging perceptual hashing object recognition by using fewer measurements. Our result might open a new path for realizing object recognition with non-imaging.

Development of Imaging Fourier-Transform Spectroscopy for the Characterization of Turbulent Jet Flames

DTIC Science & Technology

2014-09-18

Spatially resolved infrared spectra of jet exhaust from an F109 turbofan engine...Appendix E contains a conference proceeding in its entirety [32]. This proceeding summarizes analysis of a turbofan engine exhaust via the Hyper-Cam and...demonstrated in a separate experiment. Recently, exhaust from an F109 turbofan engine was imaged with the IFTS[32]. Examination of the time-averaged

Discrete Fourier Transform in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

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.

Electro-optic imaging Fourier transform spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)

2009-01-01

An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.

Geometry and dynamics in the fractional discrete Fourier transform.

PubMed

Wolf, Kurt Bernardo; Krötzsch, Guillermo

2007-03-01

The N x N Fourier matrix is one distinguished element within the group U(N) of all N x N unitary matrices. It has the geometric property of being a fourth root of unity and is close to the dynamics of harmonic oscillators. The dynamical correspondence is exact only in the N-->infinity contraction limit for the integral Fourier transform and its fractional powers. In the finite-N case, several options have been considered in the literature. We compare their fidelity in reproducing the classical harmonic motion of discrete coherent states.

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.

Computing the Power-Density Spectrum for an Engineering Model

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1982-01-01

Computer program for calculating of power-density spectrum (PDS) from data base generated by Advanced Continuous Simulation Language (ACSL) uses algorithm that employs fast Fourier transform (FFT) to calculate PDS of variable. Accomplished by first estimating autocovariance function of variable and then taking FFT of smoothed autocovariance function to obtain PDS. Fast-Fourier-transform technique conserves computer resources.

Using Mathematical Software to Introduce Fourier Transforms in Physical Chemistry to Develop Improved Understanding of Their Applications in Analytical Chemistry

ERIC Educational Resources Information Center

Miller, Tierney C.; Richardson, John N.; Kegerreis, Jeb S.

2016-01-01

This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to…

Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform

ERIC Educational Resources Information Center

Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

2010-01-01

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…

Rapid identification and classification of Listeria spp. and serotype assignment of Listeria monocytogenes using fourier transform-infrared spectroscopy and artificial neural network analysis

USDA-ARS?s Scientific Manuscript database

The use of Fourier Transform-Infrared Spectroscopy (FT-IR) in conjunction with Artificial Neural Network software, NeuroDeveloper™ was examined for the rapid identification and classification of Listeria species and serotyping of Listeria monocytogenes. A spectral library was created for 245 strains...

COMPARISON OF AN INNOVATIVE NONLINEAR ALGORITHM TO CLASSICAL LEAST SQUARES FOR ANALYZING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTRA COLLECTED AT A CONCENTRATED SWINE PRODUCTION FACILITY

EPA Science Inventory

Open-path Fourier transform infrared (OP/FTIR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric gases at an integrated swine production facility. The concentration-pathlength products of the target gases at this site often exceeded th...

APPLICATION OF STANDARDIZED QUALITY CONTROL PROCEDURES TO OPEN-PATH FOURIER TRANSFORM INFRARED DATA COLLECTED AT A CONCENTRATED SWINE PRODUCTION FACILITY

EPA Science Inventory

Open-path Fourier transform infrared (OP/FT-IR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric eases at a concentrated swine production facility. A total of 2200 OP/FT-IR spectra were acquired along nine different monitoring paths d...

“Self-absorption” phenomenon in near-infrared Fourier transform Raman spectroscopy of cellulosic and lignocellulosic materials

Treesearch

Umesh P. Agarwal; Nancy Kawai

2005-01-01

While cellulosic and lignocellulosic materials have been studied using conventional Raman spectroscopy, availability of near-infrared (NIR) Fourier transform (FT) Raman instrumentation has made studying these materials much more convenient. This is especially true because the problem of laser-induced fluorescence can be avoided or minimized in FT- Raman (NIR Raman)...

Propagation Characteristics Of Weakly Guiding Optical Fibers

NASA Technical Reports Server (NTRS)

Manshadi, Farzin

1992-01-01

Report discusses electromagnetic propagation characteristics of weakly guiding optical-fiber structures having complicated shapes with cross-sectional dimensions of order of wavelength. Coupling, power-dividing, and transition dielectric-waveguide structures analyzed. Basic data computed by scalar-wave, fast-Fourier-transform (SW-FFT) technique, based on numerical solution of scalar version of wave equation by forward-marching fast-Fourier-transform method.

Analytical Properties of Time-of-Flight PET Data

PubMed Central

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M.

2015-01-01

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the “bow-tie” property of the 2D Radon transform to the time of flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data. PMID:18460746

Electro-optic Imaging Fourier Transform Spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin

2005-01-01

JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-O IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 micron (1000-4000/cm) to allow high-resolution, high-speed hyperspectral imaging applications. One application will be the remote sensing of the measurement of a large number of different atmospheric gases simultaneously in the same airmass. Due to the use of a combination of birefringent phase retarders and multiple achromatic phase switches to achieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventional Fourier transform spectrometer but without any moving parts. In this paper, the principle of operations, system architecture and recent experimental progress will be presented.

Electro-optic Imaging Fourier Transform Spectrometer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin

2005-01-01

JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-0IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 pm (1000 -4000 cm-') to allow high-resolution, high-speed hyperspectral imaging applications [l-51. One application will be theremote sensing of the measurement of a large number of different atmospheric gases simultaneously in the sameairmass. Due to the use of a combination of birefiingent phase retarders and multiple achromatic phase switches toachieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventionalFourier transform spectrometer but without any moving parts. In this paper, the principle of operations, systemarchitecture and recent experimental progress will be presen.

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.

Fourier transform infrared microspectroscopy for the analysis of the biochemical composition of C. elegans worms.

PubMed

Sheng, Ming; Gorzsás, András; Tuck, Simon

2016-01-01

Changes in intermediary metabolism have profound effects on many aspects of C. elegans biology including growth, development and behavior. However, many traditional biochemical techniques for analyzing chemical composition require relatively large amounts of starting material precluding the analysis of mutants that cannot be grown in large amounts as homozygotes. Here we describe a technique for detecting changes in the chemical compositions of C. elegans worms by Fourier transform infrared microspectroscopy. We demonstrate that the technique can be used to detect changes in the relative levels of carbohydrates, proteins and lipids in one and the same worm. We suggest that Fourier transform infrared microspectroscopy represents a useful addition to the arsenal of techniques for metabolic studies of C. elegans worms.

The short time Fourier transform and local signals

NASA Astrophysics Data System (ADS)

Okumura, Shuhei

In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

Four Fourier transform spectrometers and the Arctic polar vortex: instrument intercomparison and ACE-FTS validation at Eureka during the IPY springs of 2007 and 2008

NASA Astrophysics Data System (ADS)

Batchelor, R. L.; Kolonjari, F.; Lindenmaier, R.; Mittermeier, R. L.; Daffer, W.; Fast, H.; Manney, G.; Strong, K.; Walker, K. A.

2009-11-01

The Canadian Arctic Atmospheric Chemistry Experiment Validation Campaigns have been carried out at Eureka, Nunavut (80.05° N, 86.42° W) during the polar sunrise period since 2004. During the International Polar Year (IPY) springs of 2007 and 2008, three ground-based Fourier transform infrared (FTIR) spectrometers were operated simultaneously. This paper presents a comparison of trace gas measurements of stratospherically important species involved in ozone depletion, namely O3, HCl, ClONO2, HNO3 and HF, recorded with these three spectrometers. Total column densities of the gases measured with the new Canadian Network for the Detection of Atmospheric Change (CANDAC) Bruker 125HR are shown to agree to within 3.5% with the existing Environment Canada Bomem DA8 measurements. After smoothing both of these sets of measurements to account for the lower spectral resolution of the University of Waterloo Portable Atmospheric Research Interferometric Spectrometer for the Infrared (PARIS-IR), the measurements were likewise shown to agree with PARIS-IR to within 7%. Concurrent measurements of these gases were also made with the satellite-based Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) during overpasses of Eureka during these time periods. While one of the mandates of the ACE satellite mission is to study ozone depletion in the polar spring, previous validation exercises have identified the highly variable polar vortex conditions of the spring period to be a challenge for validation efforts. In this work, comparisons between the CANDAC Bruker 125HR and ACE-FTS have been used to develop strict criteria that allow the ground- and satellite-based instruments to be confidently compared. When these criteria are taken into consideration, there is shown to be no significant bias between the ACE-FTS and ground-based FTIR spectrometer for any of these gases.

The extended Fourier transform for 2D spectral estimation.

PubMed

Armstrong, G S; Mandelshtam, V A

2001-11-01

We present a linear algebraic method, named the eXtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson. 147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solution of an ill-conditioned problem, which requires regularization. The regularization depends on a parameter, q, that essentially controls the resolution. By varying q from 0 to infinity one can "tune" the spectrum between a high-resolution spectral estimate and the finite DFT. The optimal value of q is chosen according to how well the data fits the form of a sum of complex sinusoids and, in particular, the signal-to-noise ratio. Both 1D and 2D XFT are presented with applications to experimental NMR signals. Copyright 2001 Academic Press.

Replica Fourier Tansforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

NASA Astrophysics Data System (ADS)

de Dominicis, C.; Carlucci, D. M.; Temesvári, T.

1997-01-01

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices M^{α β;γ^δ}, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work. On montre que l'analyse d'objets vivant sur un arbre ultramétrique, en particulier, la diagonalisation par blocs d'une matrice M^{α β;γ^δ} dépendant de 4-répliques, se simplifie de façon dramatique si l'on introduit les opérations appropriées sur ces objets. Ce sont les Transformées de Fourier de Répliques sur un arbre ultramétrique. Ces transformations sont définies et utilisées dans le présent travail.

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.

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.

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.

Transfer Functions Via Laplace- And Fourier-Borel Transforms

NASA Technical Reports Server (NTRS)

Can, Sumer; Unal, Aynur

1991-01-01

Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.

Extreme ultraviolet interferometry

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

Goldberg, Kenneth A.

EUV lithography is a promising and viable candidate for circuit fabrication with 0.1-micron critical dimension and smaller. In order to achieve diffraction-limited performance, all-reflective multilayer-coated lithographic imaging systems operating near 13-nm wavelength and 0.1 NA have system wavefront tolerances of 0.27 nm, or 0.02 waves RMS. Owing to the highly-sensitive resonant reflective properties of multilayer mirrors and extraordinarily tight tolerances set forth for their fabrication, EUV optical systems require at-wavelength EUV interferometry for final alignment and qualification. This dissertation discusses the development and successful implementation of high-accuracy EUV interferometric techniques. Proof-of-principle experiments with a prototype EUV point-diffraction interferometer for themore » measurement of Fresnel zoneplate lenses first demonstrated sub-wavelength EUV interferometric capability. These experiments spurred the development of the superior phase-shifting point-diffraction interferometer (PS/PDI), which has been implemented for the testing of an all-reflective lithographic-quality EUV optical system. Both systems rely on pinhole diffraction to produce spherical reference wavefronts in a common-path geometry. Extensive experiments demonstrate EUV wavefront-measuring precision beyond 0.02 waves RMS. EUV imaging experiments provide verification of the high-accuracy of the point-diffraction principle, and demonstrate the utility of the measurements in successfully predicting imaging performance. Complementary to the experimental research, several areas of theoretical investigation related to the novel PS/PDI system are presented. First-principles electromagnetic field simulations of pinhole diffraction are conducted to ascertain the upper limits of measurement accuracy and to guide selection of the pinhole diameter. Investigations of the relative merits of different PS/PDI configurations accompany a general study of the most significant sources of systematic measurement errors. To overcome a variety of experimental difficulties, several new methods in interferogram analysis and phase-retrieval were developed: the Fourier-Transform Method of Phase-Shift Determination, which uses Fourier-domain analysis to improve the accuracy of phase-shifting interferometry; the Fourier-Transform Guided Unwrap Method, which was developed to overcome difficulties associated with a high density of mid-spatial-frequency blemishes and which uses a low-spatial-frequency approximation to the measured wavefront to guide the phase unwrapping in the presence of noise; and, finally, an expedient method of Gram-Schmidt orthogonalization which facilitates polynomial basis transformations in wave-front surface fitting procedures.« less

Coherent time-stretch transformation for real-time capture of wideband signals.

PubMed

Buckley, Brandon W; Madni, Asad M; Jalali, Bahram

2013-09-09

Time stretch transformation of wideband waveforms boosts the performance of analog-to-digital converters and digital signal processors by slowing down analog electrical signals before digitization. The transform is based on dispersive Fourier transformation implemented in the optical domain. A coherent receiver would be ideal for capturing the time-stretched optical signal. Coherent receivers offer improved sensitivity, allow for digital cancellation of dispersion-induced impairments and optical nonlinearities, and enable decoding of phase-modulated optical data formats. Because time-stretch uses a chirped broadband (>1 THz) optical carrier, a new coherent detection technique is required. In this paper, we introduce and demonstrate coherent time stretch transformation; a technique that combines dispersive Fourier transform with optically broadband coherent detection.

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.

Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

NASA Astrophysics Data System (ADS)

Stupin, Daniil D.; Koniakhin, Sergei V.; Verlov, Nikolay A.; Dubina, Michael V.

2017-05-01

The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

Utility of Higher Harmonics in Electrospray Ionization Fourier Transform Electrostatic Linear Ion Trap Mass Spectrometry.

PubMed

Dziekonski, Eric T; Johnson, Joshua T; McLuckey, Scott A

2017-04-18

Mass resolution (M/ΔM fwhm) is observed to linearly increase with harmonic order in a Fourier transform electrostatic linear ion trap (ELIT) mass spectrometer. This behavior was predicted by Grosshans and Marshall for frequency-multiple detection in a Fourier transform ion cyclotron resonance mass spectrometer only for situations when the prominent mechanism for signal decay is ion ejection from the trap. As the analyzer pressure in our ELIT chamber is relatively high, such that collisional scattering and collision-induced dissociation are expected to underlie much of the ion loss, we sought to explore the relationship between harmonic order and mass resolution. Mass resolutions of 36 900 (fundamental), 75 850 (2nd harmonic), and 108 200 (3rd harmonic) were obtained for GdO + (avg. m/z 173.919) with a transient length of 300 ms. To demonstrate that the mass resolution was truly increasing with harmonic order, the unresolved isotopes at the fundamental distribution of cytochrome c +8 (m/z ∼ 1549) were nearly baseline, resolved at the third harmonic (mass resolution ≈ 23 000) with a transient length of only 200 ms. This experiment demonstrates that, when the ion density is sufficiently low, ions with frequency differences of less than 4 Hz remain uncoalesced. Higher harmonics can be used to increase the effective mass resolution for a fixed transient length and thereby may enable the resolution of closely spaced masses, determination of a protein ion's charge state, and study of the onset of peak coalescence when the resolution at the fundamental frequency is insufficient.

Research on fast Fourier transforms algorithm of huge remote sensing image technology with GPU and partitioning technology.

PubMed

Yang, Xue; Li, Xue-You; Li, Jia-Guo; Ma, Jun; Zhang, Li; Yang, Jan; Du, Quan-Ye

2014-02-01

Fast Fourier transforms (FFT) is a basic approach to remote sensing image processing. With the improvement of capacity of remote sensing image capture with the features of hyperspectrum, high spatial resolution and high temporal resolution, how to use FFT technology to efficiently process huge remote sensing image becomes the critical step and research hot spot of current image processing technology. FFT algorithm, one of the basic algorithms of image processing, can be used for stripe noise removal, image compression, image registration, etc. in processing remote sensing image. CUFFT function library is the FFT algorithm library based on CPU and FFTW. FFTW is a FFT algorithm developed based on CPU in PC platform, and is currently the fastest CPU based FFT algorithm function library. However there is a common problem that once the available memory or memory is less than the capacity of image, there will be out of memory or memory overflow when using the above two methods to realize image FFT arithmetic. To address this problem, a CPU and partitioning technology based Huge Remote Fast Fourier Transform (HRFFT) algorithm is proposed in this paper. By improving the FFT algorithm in CUFFT function library, the problem of out of memory and memory overflow is solved. Moreover, this method is proved rational by experiment combined with the CCD image of HJ-1A satellite. When applied to practical image processing, it improves effect of the image processing, speeds up the processing, which saves the time of computation and achieves sound result.

[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.

Kinetics and Product Branching Fractions of Reactions between a Cation and a Radical: Ar+ + CH3 and O2+ + CH3 (Postprint)

DTIC Science & Technology

2015-01-13

Gross group using a Chen nozzle coupled to a Fourier transform ion cyclotron reso- nance (FT-ICR) mass spectrometer for reactions of the benzyl radical...reactions: A Fourier transform ion cyclotron resonance study of allyl radical reacting with aromatic radical cations. Int. J. Mass Spectrom. 2009, 287, 8

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

Color and surface chemistry changes of extracted wood flour after heating at 120 °C

Treesearch

Yao Chen; Mandla A. Tshabalala; Jianmin Gao; Nicole M. Stark

2013-01-01

To investigate the effect of heat on color and surface chemistry of wood flour (WF), unextracted, extracted and delignified samples of commercial WF were heated at 120 °C for 24 h and analyzed by colorimetry, diffuse reflectance visible (DRV), attenuated total reflectance Fourier transform infrared (ATR-FTIR) and Fourier transform Raman (FT-Raman) spectroscopies....

Characterization of southern yellow pine bark layers by Attenuated Total Reflectance (ATR) and Fourier Transform Infrared (FT-IR) Spectroscopy

Treesearch

Thomas L. Eberhardt

2009-01-01

The outer bark (rhytidome) of the southern yellow pines is a complex structure comprised of alternating layers of obliterated phloem and periderm tissues, with the latter comprised of three layers, those being phellem, phellogen, and phelloderm. An attenuated total reflectance (ATR) sampling accessory, coupled with a Fourier transform infrared (FTIR) spectrometer,...

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

Molecular Isotopic Distribution Analysis (MIDAs) with Adjustable Mass Accuracy

NASA Astrophysics Data System (ADS)

Alves, Gelio; Ogurtsov, Aleksey Y.; Yu, Yi-Kuo

2014-01-01

In this paper, we present Molecular Isotopic Distribution Analysis (MIDAs), a new software tool designed to compute molecular isotopic distributions with adjustable accuracies. MIDAs offers two algorithms, one polynomial-based and one Fourier-transform-based, both of which compute molecular isotopic distributions accurately and efficiently. The polynomial-based algorithm contains few novel aspects, whereas the Fourier-transform-based algorithm consists mainly of improvements to other existing Fourier-transform-based algorithms. We have benchmarked the performance of the two algorithms implemented in MIDAs with that of eight software packages (BRAIN, Emass, Mercury, Mercury5, NeutronCluster, Qmass, JFC, IC) using a consensus set of benchmark molecules. Under the proposed evaluation criteria, MIDAs's algorithms, JFC, and Emass compute with comparable accuracy the coarse-grained (low-resolution) isotopic distributions and are more accurate than the other software packages. For fine-grained isotopic distributions, we compared IC, MIDAs's polynomial algorithm, and MIDAs's Fourier transform algorithm. Among the three, IC and MIDAs's polynomial algorithm compute isotopic distributions that better resemble their corresponding exact fine-grained (high-resolution) isotopic distributions. MIDAs can be accessed freely through a user-friendly web-interface at http://www.ncbi.nlm.nih.gov/CBBresearch/Yu/midas/index.html.

GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography.

PubMed

Xu, Daguang; Huang, Yong; Kang, Jin U

2014-06-16

We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).

Determination of Spectroscopic Properties of Atmospheric Molecules from High Resolution Vacuum Ultraviolet Cross Section and Wavelength Measurements

NASA Technical Reports Server (NTRS)

Parkinson, W. H.; Yoshino, K.

1997-01-01

An account is given of progress during the period 8/l/96-7/31/97 on work on (a) cross section measurements of O2 S-R using a Fourier transform spectrometer (FTS) at the Photon Factory in Japan; (b) the determination of the predissociation linewidths of the Schumann-Runge bands (S-R) of 02; (c) cross section measurements of 02 Herzberg bands using a Fourier transform spectrometer (FTS) at Imperial College; and (d) cross section measurements of H2O in the wavelength region 120-188 nm. The experimental investigations are effected at high resolution with a 6.65 m scanning spectrometer and with the Fourier transform spectrometer. Below 175 nm, synchrotron radiation is most suitable for cross section measurements in combination with spectrometers at the Photon Factory Japan. Cross section measurements of the Doppler limited bands depend on using the very high resolution, available with the Fourier transform spectrometer, (0.025/cm resolution). All of these spectroscopic measurements are needed for accurate calculations of the production of atomic oxygen, the penetration of solar radiation into the Earth's atmosphere, and photochemistry of minor molecules.

Molecular Isotopic Distribution Analysis (MIDAs) with adjustable mass accuracy.

PubMed

Alves, Gelio; Ogurtsov, Aleksey Y; Yu, Yi-Kuo

2014-01-01

In this paper, we present Molecular Isotopic Distribution Analysis (MIDAs), a new software tool designed to compute molecular isotopic distributions with adjustable accuracies. MIDAs offers two algorithms, one polynomial-based and one Fourier-transform-based, both of which compute molecular isotopic distributions accurately and efficiently. The polynomial-based algorithm contains few novel aspects, whereas the Fourier-transform-based algorithm consists mainly of improvements to other existing Fourier-transform-based algorithms. We have benchmarked the performance of the two algorithms implemented in MIDAs with that of eight software packages (BRAIN, Emass, Mercury, Mercury5, NeutronCluster, Qmass, JFC, IC) using a consensus set of benchmark molecules. Under the proposed evaluation criteria, MIDAs's algorithms, JFC, and Emass compute with comparable accuracy the coarse-grained (low-resolution) isotopic distributions and are more accurate than the other software packages. For fine-grained isotopic distributions, we compared IC, MIDAs's polynomial algorithm, and MIDAs's Fourier transform algorithm. Among the three, IC and MIDAs's polynomial algorithm compute isotopic distributions that better resemble their corresponding exact fine-grained (high-resolution) isotopic distributions. MIDAs can be accessed freely through a user-friendly web-interface at http://www.ncbi.nlm.nih.gov/CBBresearch/Yu/midas/index.html.

A Discussion of the Discrete Fourier Transform Execution on a Typical Desktop PC

NASA Technical Reports Server (NTRS)

White, Michael J.

2006-01-01

This paper will discuss and compare the execution times of three examples of the Discrete Fourier Transform (DFT). The first two examples will demonstrate the direct implementation of the algorithm. In the first example, the Fourier coefficients are generated at the execution of the DFT. In the second example, the coefficients are generated prior to execution and the DFT coefficients are indexed at execution. The last example will demonstrate the Cooley- Tukey algorithm, better known as the Fast Fourier Transform. All examples were written in C executed on a PC using a Pentium 4 running at 1.7 Ghz. As a function of N, the total complex data size, the direct implementation DFT executes, as expected at order of N2 and the FFT executes at order of N log2 N. At N=16K, there is an increase in processing time beyond what is expected. This is not caused by implementation but is a consequence of the effect that machine architecture and memory hierarchy has on implementation. This paper will include a brief overview of digital signal processing, along with a discussion of contemporary work with discrete Fourier processing.

Photomorphic analysis techniques: An interim spatial analysis using satellite remote sensor imagery and historical data

NASA Technical Reports Server (NTRS)

Keuper, H. R.; Peplies, R. W.; Gillooly, R. P.

1977-01-01

The use of machine scanning and/or computer-based techniques to provide greater objectivity in the photomorphic approach was investigated. Photomorphic analysis and its application in regional planning are discussed. Topics included: delineation of photomorphic regions; inadequacies of existing classification systems; tonal and textural characteristics and signature analysis techniques; pattern recognition and Fourier transform analysis; and optical experiments. A bibliography is included.

Environmentally Benign Repair of Composites Using High Temperature Cyanate Ester Nanocomposites

DTIC Science & Technology

2010-10-01

temperature by magnetic stirring. Thermogravimetric analysis (TG) measurements were performed on a TG model Q50 (TA Instruments, Inc.) to determine the...standard 1259-85. These experiments were also compared with thermogravimetric analysis (TGA) in both dynamic heating and isothermal conditions. The...characterized with thermogravimetric analysis (TG) and Fourier transform infrared spectroscopy (FT-IR). For the TG, about 20 mg of sample was placed in

Stress wave calculations in composite plates using the fast Fourier transform.

NASA Technical Reports Server (NTRS)

Moon, F. C.

1973-01-01

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform

PubMed Central

Chan, Kenny K. H.; Tang, Shuo

2010-01-01

The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551

Multichannel Dynamic Fourier-Transform IR Spectrometer

NASA Astrophysics Data System (ADS)

Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.

2017-09-01

A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.

Portable device for generation of ultra-pure water vapor feeds

NASA Astrophysics Data System (ADS)

Velin, P.; Stenman, U.; Skoglundh, M.; Carlsson, P.-A.

2017-11-01

A portable device for the generation of co-feeds of water vapor has been designed, constructed, and evaluated for flexible use as an add-on component to laboratory chemical reactors. The vapor is formed by catalytic oxidation of hydrogen, which benefits the formation of well-controlled minute concentrations of ultra-pure water. Analysis of the effluent stream by on-line mass spectrometry and Fourier transform infrared spectroscopy confirms that water vapor can be, with high precision, generated both rapidly and steadily over extended periods in the range of 100 ppm to 3 vol. % (limited by safety considerations) using a total flow of 100 to 1500 ml/min at normal temperature and pressure. Further, the device has been used complementary to a commercial water evaporator and mixing system to span water concentrations up to 12 vol. %. Finally, an operando diffuse reflective infrared Fourier transform spectroscopic measurement of palladium catalysed methane oxidation in the absence and presence of up to 1.0 vol. % water has been carried out to demonstrate the applicability of the device for co-feeding well-controlled low concentrations of water vapor to a common type of spectroscopic experiment. The possibilities of creating isotopically labeled water vapor as well as using tracer gases for dynamic experiments are discussed.

Portable device for generation of ultra-pure water vapor feeds.

PubMed

Velin, P; Stenman, U; Skoglundh, M; Carlsson, P-A

2017-11-01

A portable device for the generation of co-feeds of water vapor has been designed, constructed, and evaluated for flexible use as an add-on component to laboratory chemical reactors. The vapor is formed by catalytic oxidation of hydrogen, which benefits the formation of well-controlled minute concentrations of ultra-pure water. Analysis of the effluent stream by on-line mass spectrometry and Fourier transform infrared spectroscopy confirms that water vapor can be, with high precision, generated both rapidly and steadily over extended periods in the range of 100 ppm to 3 vol. % (limited by safety considerations) using a total flow of 100 to 1500 ml/min at normal temperature and pressure. Further, the device has been used complementary to a commercial water evaporator and mixing system to span water concentrations up to 12 vol. %. Finally, an operando diffuse reflective infrared Fourier transform spectroscopic measurement of palladium catalysed methane oxidation in the absence and presence of up to 1.0 vol. % water has been carried out to demonstrate the applicability of the device for co-feeding well-controlled low concentrations of water vapor to a common type of spectroscopic experiment. The possibilities of creating isotopically labeled water vapor as well as using tracer gases for dynamic experiments are discussed.

The angular difference function and its application to image registration.

PubMed

Keller, Yosi; Shkolnisky, Yoel; Averbuch, Amir

2005-06-01

The estimation of large motions without prior knowledge is an important problem in image registration. In this paper, we present the angular difference function (ADF) and demonstrate its applicability to rotation estimation. The ADF of two functions is defined as the integral of their spectral difference along the radial direction. It is efficiently computed using the pseudopolar Fourier transform, which computes the discrete Fourier transform of an image on a near spherical grid. Unlike other Fourier-based registration schemes, the suggested approach does not require any interpolation. Thus, it is more accurate and significantly faster.

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.

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…

Fourier Spectroscopy: A Simple Analysis Technique

ERIC Educational Resources Information Center

Oelfke, William C.

1975-01-01

Presents a simple method of analysis in which the student can integrate, point by point, any interferogram to obtain its Fourier transform. The manual technique requires no special equipment and is based on relationships that most undergraduate physics students can derive from the Fourier integral equations. (Author/MLH)

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

NASA Technical Reports Server (NTRS)

Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.

1977-01-01

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.

Determination of Carbon Dioxide, Carbon Monoxide, and Methane Concentrations in Cigarette Smoke by Fourier Transform Infrared Spectroscopy

ERIC Educational Resources Information Center

Tan, T. L.; Lebron, G. B.

2012-01-01

The integrated absorbance areas of vibrational bands of CO[subscript 2], CO, and CH[subscript 4] gases in cigarette smoke were measured from Fourier transform infrared (FTIR) spectra to derive the partial pressures of these gases at different smoke times. The quantity of the three gas-phase components of cigarette smoke at different smoke times…

To See the World in a Grain of Sand: Recognizing the Origin of Sand Specimens by Diffuse Reflectance Infrared Fourier Transform Spectroscopy and Multivariate Exploratory Data Analysis

ERIC Educational Resources Information Center

Pezzolo, Alessandra De Lorenzi

2011-01-01

The diffuse reflectance infrared Fourier transform (DRIFT) spectra of sand samples exhibit features reflecting their composition. Basic multivariate analysis (MVA) can be used to effectively sort subsets of homogeneous specimens collected from nearby locations, as well as pointing out similarities in composition among sands of different origins.…

Double Fourier Series Solution of Poisson’s Equation on a Sphere.

DTIC Science & Technology

1980-10-29

algebraic systems, the solution of these systems, and the inverse transform of the solution in Fourier space back to physi- cal space. 6. Yee, S. Y. K...Multiply each count in steps (2) through (5) by K] 7. Inverse transform um(0j j = 1, J - 1, to obtain u k; set u(P) = u 0 (P). [K(J - 1) log 2 K

Using multiple calibration sets to improve the quantitative accuracy of partial least squares (PLS) regression on open-path fourier transform infrared (OP/FT-IR) spectra of ammonia over wide concentration ranges

USDA-ARS?s Scientific Manuscript database

A technique of using multiple calibration sets in partial least squares regression (PLS) was proposed to improve the quantitative determination of ammonia from open-path Fourier transform infrared spectra. The spectra were measured near animal farms, and the path-integrated concentration of ammonia...

Fast restoration approach for motion blurred image based on deconvolution under the blurring paths

NASA Astrophysics Data System (ADS)

Shi, Yu; Song, Jie; Hua, Xia

2015-12-01

For the real-time motion deblurring, it is of utmost importance to get a higher processing speed with about the same image quality. This paper presents a fast Richardson-Lucy motion deblurring approach to remove motion blur which rotates blurred image under blurring paths. Hence, the computational time is reduced sharply by using one-dimensional Fast Fourier Transform in one-dimensional Richardson-Lucy method. In order to obtain accurate transformational results, interpolation method is incorporated to fetch the gray values. Experiment results demonstrate that the proposed approach is efficient and effective to reduce motion blur under the blur paths.

A two-dimensional time domain near zone to far zone transformation

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Ryan, Deirdre; Beggs, John H.; Kunz, Karl S.

1991-01-01

A time domain transformation useful for extrapolating three dimensional near zone finite difference time domain (FDTD) results to the far zone was presented. Here, the corresponding two dimensional transform is outlined. While the three dimensional transformation produced a physically observable far zone time domain field, this is not convenient to do directly in two dimensions, since a convolution would be required. However, a representative two dimensional far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required, it can be obtained by inverse Fourier transform of the final frequency domain result.

A two-dimensional time domain near zone to far zone transformation

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Ryan, Deirdre; Beggs, John H.; Kunz, Karl S.

1991-01-01

In a previous paper, a time domain transformation useful for extrapolating 3-D near zone finite difference time domain (FDTD) results to the far zone was presented. In this paper, the corresponding 2-D transform is outlined. While the 3-D transformation produced a physically observable far zone time domain field, this is not convenient to do directly in 2-D, since a convolution would be required. However, a representative 2-D far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required it can be obtained by inverse Fourier transform of the final frequency domain result.

A Review of Maximum Entropy Spectral Analysis and Applications to Fourier Spectroscopy.

DTIC Science & Technology

1985-04-03

1 From Pythagoras to Fourier 3 2. 2 The Periodogram as Introduced by Sir Arthur Schuster 6 2. 3 The Slutzky Effect and the Work of Yule 7 2.4 The...Transform 27 4. 2 The Z-Transform Convolution Theorem 29 4. 3 The Wiener -Khintchmne , Theorem 31 4.4 The Z-Transform of el. 3 5. A COMPARISON BETWEEN...the Convolution I’heoreni, the Wiene i-Khintrbitte Theorem , aind the conventional ;pp roach of Il1ac km in and Tuke-,. Finally, it should he

On Weak and Strong 2k- bent Boolean Functions

DTIC Science & Technology

2016-01-01

U.S.A. Email: pstanica@nps.edu Abstract—In this paper we introduce a sequence of discrete Fourier transforms and define new versions of bent...denotes the complex conjugate of z. An important tool in our analysis is the discrete Fourier transform , known in Boolean functions literature, as Walsh...Hadamard, or Walsh–Hadamard transform , which is the func- tion Wf : Fn2 → C, defined by Wf (u) = 2− n 2 ∑ x∈Vn (−1)f(x)⊕u·x. Any f ∈ Bn can be

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical expression for an elliptical Gaussian beam (EGB) truncated by an elliptical aperture and passing through a fractional Fourier transform system is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of truncated EGBs than the usual way by using the integral formula directly, and the efficiency of numerical calculation is significantly improved.

A pipeline design of a fast prime factor DFT on a finite field

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, In-Shek; Shao, H. M.; Reed, Irving S.; Shyu, Hsuen-Chyun

1988-01-01

A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented.

Qualitative and semiquantitative Fourier transformation using a noncoherent system.

PubMed

Rogers, G L

1979-09-15

A number of authors have pointed out that a system of zone plates combined with a diffuse source, transparent input, lens, and focusing screen will display on the output screen the Fourier transform of the input. Strictly speaking, the transform normally displayed is the cosine transform, and the bipolar output is superimposed on a dc gray level to give a positive-only intensity variation. By phase-shifting one zone plate the sine transform is obtained. Temporal modulation is possible. It is also possible to redesign the system to accept a diffusely reflecting input at the cost of introducing a phase gradient in the output. Results are given of the sine and cosine transforms of a small circular aperture. As expected, the sine transform is a uniform gray. Both transforms show unwanted artifacts beyond 0.1 rad off-axis. An analysis shows this is due to unwanted circularly symmetrical moire patterns between the zone plates.

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.

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.

[Spatial domain display for interference image dataset].

PubMed

Wang, Cai-Ling; Li, Yu-Shan; Liu, Xue-Bin; Hu, Bing-Liang; Jing, Juan-Juan; Wen, Jia

2011-11-01

The requirements of imaging interferometer visualization is imminent for the user of image interpretation and information extraction. However, the conventional researches on visualization only focus on the spectral image dataset in spectral domain. Hence, the quick show of interference spectral image dataset display is one of the nodes in interference image processing. The conventional visualization of interference dataset chooses classical spectral image dataset display method after Fourier transformation. In the present paper, the problem of quick view of interferometer imager in image domain is addressed and the algorithm is proposed which simplifies the matter. The Fourier transformation is an obstacle since its computation time is very large and the complexion would be even deteriorated with the size of dataset increasing. The algorithm proposed, named interference weighted envelopes, makes the dataset divorced from transformation. The authors choose three interference weighted envelopes respectively based on the Fourier transformation, features of interference data and human visual system. After comparing the proposed with the conventional methods, the results show the huge difference in display time.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL CORRELATIONS

PubMed Central

BAJAJ, CHANDRAJIT; BAUER, BENEDIKT; BETTADAPURA, RADHAKRISHNA; VOLLRATH, ANTJE

2013-01-01

The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (R, t), R ∈ SO(3), t ∈ ℝ3 that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transform to achieve a speedup either with respect to the sought translation or rotation. We present PFcorr, a new exhaustive solution, based on the non-equispaced SO(3) Fourier transform, to the rigid-body correlation problem; unlike previous solutions, ours achieves a combination of translational and rotational speedups without requiring equispaced grids. PFcorr can be straightforwardly applied to a variety of problems in protein structure prediction and refinement that involve correlations under rigid-body motions of the protein. Additionally, we show how it applies, along with an appropriate flexibility model, to analogs of the above problems in which the flexibility of the protein is relevant. PMID:24379643

Methods for performing fast discrete curvelet transforms of data

DOEpatents

Candes, Emmanuel; Donoho, David; Demanet, Laurent

2010-11-23

Fast digital implementations of the second generation curvelet transform for use in data processing are disclosed. One such digital transformation is based on unequally-spaced fast Fourier transforms (USFFT) while another is based on the wrapping of specially selected Fourier samples. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. Both implementations are fast in the sense that they run in about O(n.sup.2 log n) flops for n by n Cartesian arrays or about O(N log N) flops for Cartesian arrays of size N=n.sup.3; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity.

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.

A novel collinear optical system with annulus mirrors for holographic disc driver

NASA Astrophysics Data System (ADS)

Wang, Ye

2008-12-01

This paper focus on a novel collinear lens system with annulus mirrors for holographic disc driver, both information beam and reference beam are use same laser beam. The expanded and parallel laser beam, center part of it as the information beam then through Fourier transform lens, the beam around center part as a reference beam. On this axis, the ring reference beam reflected by two annulus shaped mirrors, then became a convergent beam, together with the information beam which through the first Fourier transform lens then produce holographic pattern to be write into the holographic disc behind of them, this lens system with two mirrors made the angle between information beam and reference beam more wide, can improved the multiplex level of holographic storage. Pair of Fourier transform lens with advance performance is designed in this paper.

Colorectal Cancer and Colitis Diagnosis Using Fourier Transform Infrared Spectroscopy and an Improved K-Nearest-Neighbour Classifier.

PubMed

Li, Qingbo; Hao, Can; Kang, Xue; Zhang, Jialin; Sun, Xuejun; Wang, Wenbo; Zeng, Haishan

2017-11-27

Combining Fourier transform infrared spectroscopy (FTIR) with endoscopy, it is expected that noninvasive, rapid detection of colorectal cancer can be performed in vivo in the future. In this study, Fourier transform infrared spectra were collected from 88 endoscopic biopsy colorectal tissue samples (41 colitis and 47 cancers). A new method, viz., entropy weight local-hyperplane k-nearest-neighbor (EWHK), which is an improved version of K-local hyperplane distance nearest-neighbor (HKNN), is proposed for tissue classification. In order to avoid limiting high dimensions and small values of the nearest neighbor, the new EWHK method calculates feature weights based on information entropy. The average results of the random classification showed that the EWHK classifier for differentiating cancer from colitis samples produced a sensitivity of 81.38% and a specificity of 92.69%.

FFTDC2: a one-dimensional Fourier transform with forward and inverse data conditioning for non-complex data

USGS Publications Warehouse

Bracken, Robert E.

2004-01-01

A subroutine (FFTDC2) coded in Fortran 77 is described, which performs a Fast Fourier Transform or Discrete Fourier Transform together with necessary conditioning steps of trend removal, extension, and windowing. The source code for the entire library of required subroutines is provided with the digital release of this report. But, there is only one required entry point, the subroutine call to FFTDC2; all the other subroutines are operationally transparent to the user. Complete instructions for use of FFTDC2.F (as well as for all the other subroutines) and some practical theoretical discussions are included as comments at the beginning of the source code. This subroutine is intended to be an efficient tool for the programmer in a variety of production-level signal-processing applications.

Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra.

PubMed

Desbiens, Raphaël; Tremblay, Pierre; Genest, Jérôme; Bouchard, Jean-Pierre

2006-01-20

The instrument line shape (ILS) of a Fourier-transform spectrometer is expressed in a matrix form. For all line shape effects that scale with wavenumber, the ILS matrix is shown to be transposed in the spectral and interferogram domains. The novel representation of the ILS matrix in the interferogram domain yields an insightful physical interpretation of the underlying process producing self-apodization. Working in the interferogram domain circumvents the problem of taking into account the effects of finite optical path difference and permits a proper discretization of the equations. A fast algorithm in O(N log2 N), based on the fractional Fourier transform, is introduced that permits the application of a constant resolving power line shape to theoretical spectra or forward models. The ILS integration formalism is validated with experimental data.

Randomly displaced phase distribution design and its advantage in page-data recording of Fourier transform holograms.

PubMed

Emoto, Akira; Fukuda, Takashi

2013-02-20

For Fourier transform holography, an effective random phase distribution with randomly displaced phase segments is proposed for obtaining a smooth finite optical intensity distribution in the Fourier transform plane. Since unitary phase segments are randomly distributed in-plane, the blanks give various spatial frequency components to an image, and thus smooth the spectrum. Moreover, by randomly changing the phase segment size, spike generation from the unitary phase segment size in the spectrum can be reduced significantly. As a result, a smooth spectrum including sidebands can be formed at a relatively narrow extent. The proposed phase distribution sustains the primary functions of a random phase mask for holographic-data recording and reconstruction. Therefore, this distribution is expected to find applications in high-density holographic memory systems, replacing conventional random phase mask patterns.

A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

DOE PAGES

Xu, Kuan; Austin, Anthony P.; Wei, Ke

2017-12-21

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N) 2), where N is the number of degrees of freedom used in each of the Fourier extensions.

A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

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

Xu, Kuan; Austin, Anthony P.; Wei, Ke

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N) 2), where N is the number of degrees of freedom used in each of the Fourier extensions.

Large amplitude Fourier transformed ac voltammetry at a rotating disc electrode: a versatile technique for covering Levich and flow rate insensitive regimes in a single experiment.

PubMed

Bano, Kiran; Kennedy, Gareth F; Zhang, Jie; Bond, Alan M

2012-04-14

The theory for large amplitude Fourier transformed ac voltammetry at a rotating disc electrode is described. Resolution of time domain data into dc and ac harmonic components reveals that the mass transport for the dc component is controlled by convective-diffusion, while the background free higher order harmonic components are flow rate insensitive and mainly governed by linear diffusion. Thus, remarkable versatility is available; Levich behaviour of the dc component limiting current provides diffusion coefficient values and access to higher harmonics allows fast electrode kinetics to be probed. Two series of experiments (dc and ac voltammetry) have been required to extract these parameters; here large amplitude ac voltammetry with RDE methodology is used to demonstrate that kinetics and diffusion coefficient information can be extracted from a single experiment. To demonstrate the power of this approach, theoretical and experimental comparisons of data obtained for the reversible [Ru(NH(3))(6)](3+/2+) and quasi-reversible [Fe(CN)(6)](3-/4-) electron transfer processes are presented over a wide range of electrode rotation rates and with different concentrations and electrode materials. Excellent agreement of experimental and simulated data is achieved, which allows parameters such as electron transfer rate, diffusion coefficient, uncompensated resistance and others to be determined using a strategically applied approach that takes into account the different levels of sensitivity of each parameter to the dc or the ac harmonic.

Separation and determination of estrogen in the water environment by high performance liquid chromatography-fourier transform infrared spectroscopy

PubMed Central

Zheng, Bei; Li, Wentao; Li, Hongyan; Liu, Lin; Lei, Pei; Ge, Xiaopeng; Yu, Zhiyong; Zhou, Yiqi

2016-01-01

The components for connecting high-performance liquid chromatography (HPLC) with Fourier-transform infrared spectroscopy (FTIR) were investigated to determine estrogen in the water environment, including heating for atomization, solvent removal, sample deposition, drive control, spectrum collection, chip swap, cleaning and drying. Results showed that when the atomization temperature was increased to 388 K, the interference of mobile phase components (methanol, H2O, acetonitrile, and NaH2PO4) were completely removed in the IR measurement of estrogen, with 0.999 of similarity between IR spectra obtained after separation and corresponding to the standard IR spectra. In experiments with varying HPLC injection volumes, high similarity for IR spectra was obtained at 20 ul injection volume at 0.01 mg/L BPA while a useful IR spectrum for 10 ng/L BPA was obtained at 80 ul injection volume. In addition, estrogen concentrations in the natural water samples were calculated semi-quantitatively from the peak intensities of IR spectrum in the mid-infrared region. PMID:27577974

Absorption Mode FT-ICR Mass Spectrometry Imaging

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

Smith, Donald F.; Kilgour, David P.; Konijnenburg, Marco

2013-12-03

Fourier transform ion cyclotron resonance mass spectrometry offers the highest mass resolving power for molecular imaging experiments. This high mass resolving power ensures that closely spaced peaks at the same nominal mass are resolved for proper image generation. Typically higher magnetic fields are used to increase mass resolving power. However, a gain in mass resolving power can also be realized by phase correction of the data for absorption mode display. In addition to mass resolving power, absorption mode offers higher mass accuracy and signal-to-noise ratio over the conventional magnitude mode. Here we present the first use of absorption mode formore » Fourier transform ion cyclotron resonance mass spectrometry imaging. The Autophaser algorithm is used to phase correct each spectrum (pixel) in the image and then these parameters are used by the Chameleon work-flow based data processing software to generate absorption mode ?Datacubes? for image and spectral viewing. Absorption mode reveals new mass and spatial features that are not resolved in magnitude mode and results in improved selected ion image contrast.« less

High-performance compression and double cryptography based on compressive ghost imaging with the fast Fourier transform

NASA Astrophysics Data System (ADS)

Leihong, Zhang; Zilan, Pan; Luying, Wu; Xiuhua, Ma

2016-11-01

To solve the problem that large images can hardly be retrieved for stringent hardware restrictions and the security level is low, a method based on compressive ghost imaging (CGI) with Fast Fourier Transform (FFT) is proposed, named FFT-CGI. Initially, the information is encrypted by the sender with FFT, and the FFT-coded image is encrypted by the system of CGI with a secret key. Then the receiver decrypts the image with the aid of compressive sensing (CS) and FFT. Simulation results are given to verify the feasibility, security, and compression of the proposed encryption scheme. The experiment suggests the method can improve the quality of large images compared with conventional ghost imaging and achieve the imaging for large-sized images, further the amount of data transmitted largely reduced because of the combination of compressive sensing and FFT, and improve the security level of ghost images through ciphertext-only attack (COA), chosen-plaintext attack (CPA), and noise attack. This technique can be immediately applied to encryption and data storage with the advantages of high security, fast transmission, and high quality of reconstructed information.

Separation and determination of estrogen in the water environment by high performance liquid chromatography-fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Zheng, Bei; Li, Wentao; Li, Hongyan; Liu, Lin; Lei, Pei; Ge, Xiaopeng; Yu, Zhiyong; Zhou, Yiqi

2016-08-01

The components for connecting high-performance liquid chromatography (HPLC) with Fourier-transform infrared spectroscopy (FTIR) were investigated to determine estrogen in the water environment, including heating for atomization, solvent removal, sample deposition, drive control, spectrum collection, chip swap, cleaning and drying. Results showed that when the atomization temperature was increased to 388 K, the interference of mobile phase components (methanol, H2O, acetonitrile, and NaH2PO4) were completely removed in the IR measurement of estrogen, with 0.999 of similarity between IR spectra obtained after separation and corresponding to the standard IR spectra. In experiments with varying HPLC injection volumes, high similarity for IR spectra was obtained at 20 ul injection volume at 0.01 mg/L BPA while a useful IR spectrum for 10 ng/L BPA was obtained at 80 ul injection volume. In addition, estrogen concentrations in the natural water samples were calculated semi-quantitatively from the peak intensities of IR spectrum in the mid-infrared region.

Comparison of Fourier transform infrared spectrometry and 2,4-dinitrophenylhydrazine impinger techniques for the measurement of formaldehyde in vehicle exhaust

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

Haack, L.P.; LaCourse, D.L.; Korniski, T.J.

1986-01-01

Experiments were conducted to validate a Fourier transform infrared (FT-IR) sampling and analysis system for measurement of trace gases in vehicle exhaust utilizing gasoline-, gasohol-, diesel-, and methanol-fueled vehicles as the emission source and formaldehyde (HCHO) as the test molecule. The 2,4-dinitrophenylhydrazine impinger method was chosen as the reference method. Diluted exhaust was drawn continuously though the FT-IR cell and measured every 3 s. The FT-IR signals were averaged over a complete driving-test cycle and compared to the concentration determined from concurrent impinger sampling. By impinger measurements it was shown that HCHO losses between the tailpipe and the FT-IR cellmore » were on the order of only 5%, independent of vehicle type or HCHO concentration (0.02-8.5 ppm). Comparisons between FT-IR and impinger measurements on 43 tests of methanol-fueled vehicles under transient conditions (diluted-exhaust HCHO 0.28-8.5 ppm) showed FT-IR/impinger = 1.055 +/- 0.095. 19 references, 5 figures, 5 tables.« less

Rotation invariant features for wear particle classification

NASA Astrophysics Data System (ADS)

Arof, Hamzah; Deravi, Farzin

1997-09-01

This paper investigates the ability of a set of rotation invariant features to classify images of wear particles found in used lubricating oil of machinery. The rotation invariant attribute of the features is derived from the property of the magnitudes of Fourier transform coefficients that do not change with spatial shift of the input elements. By analyzing individual circular neighborhoods centered at every pixel in an image, local and global texture characteristics of an image can be described. A number of input sequences are formed by the intensities of pixels on concentric rings of various radii measured from the center of each neighborhood. Fourier transforming the sequences would generate coefficients whose magnitudes are invariant to rotation. Rotation invariant features extracted from these coefficients were utilized to classify wear particle images that were obtained from a number of different particles captured at different orientations. In an experiment involving images of 6 classes, the circular neighborhood features obtained a 91% recognition rate which compares favorably to a 76% rate achieved by features of a 6 by 6 co-occurrence matrix.

Research of transmissive near infrared spectroscopy for non-invasive blood glucose measurement

NASA Astrophysics Data System (ADS)

Yang, Wenming; Liao, Ningfang; Li, Yasheng; Shao, Liwei; Huang, Dehuang

2016-10-01

Near infrared (NIR) has prospectively applied in non-invasive blood glucose measurement due to glucose absorption among the 1.0-2.5m spectral bands. However, this significant technology is hard to be developed because of other blood components and low signal-to-noise ratio (SNR). In this work, we presented a non-invasive glucose measurement system using Fourier transform spectrometer which will work in fingertips or other human body tissues. A refrigerated InGaAs detector with high quantum efficiency performing well in the range of 1.0-1.7μm wavelength is used to acquire transmissive radiation. Preliminary experiment investigations were set up to test glucose levels of aqueous solutions with different concentrations. The analytical modeling of the interferogram data is based on arithmetic Fourier transform and supported by the curvilineal characterization. Experimental results show the variation of light intensity among different glucose concentrations and emphasize the obvious absorption of glucose in NIR wave-range. This study confirms the suitability that NIR can be developed in non-invasive glucose measurement.

Fourier transform infrared spectroscopy microscopic imaging classification based on spatial-spectral features

NASA Astrophysics Data System (ADS)

Liu, Lian; Yang, Xiukun; Zhong, Mingliang; Liu, Yao; Jing, Xiaojun; Yang, Qin

2018-04-01

The discrete fractional Brownian incremental random (DFBIR) field is used to describe the irregular, random, and highly complex shapes of natural objects such as coastlines and biological tissues, for which traditional Euclidean geometry cannot be used. In this paper, an anisotropic variable window (AVW) directional operator based on the DFBIR field model is proposed for extracting spatial characteristics of Fourier transform infrared spectroscopy (FTIR) microscopic imaging. Probabilistic principal component analysis first extracts spectral features, and then the spatial features of the proposed AVW directional operator are combined with the former to construct a spatial-spectral structure, which increases feature-related information and helps a support vector machine classifier to obtain more efficient distribution-related information. Compared to Haralick’s grey-level co-occurrence matrix, Gabor filters, and local binary patterns (e.g. uniform LBPs, rotation-invariant LBPs, uniform rotation-invariant LBPs), experiments on three FTIR spectroscopy microscopic imaging datasets show that the proposed AVW directional operator is more advantageous in terms of classification accuracy, particularly for low-dimensional spaces of spatial characteristics.

Fast precalculated triangular mesh algorithm for 3D binary computer-generated holograms.

PubMed

Yang, Fan; Kaczorowski, Andrzej; Wilkinson, Tim D

2014-12-10

A new method for constructing computer-generated holograms using a precalculated triangular mesh is presented. The speed of calculation can be increased dramatically by exploiting both the precalculated base triangle and GPU parallel computing. Unlike algorithms using point-based sources, this method can reconstruct a more vivid 3D object instead of a "hollow image." In addition, there is no need to do a fast Fourier transform for each 3D element every time. A ferroelectric liquid crystal spatial light modulator is used to display the binary hologram within our experiment and the hologram of a base right triangle is produced by utilizing just a one-step Fourier transform in the 2D case, which can be expanded to the 3D case by multiplying by a suitable Fresnel phase plane. All 3D holograms generated in this paper are based on Fresnel propagation; thus, the Fresnel plane is treated as a vital element in producing the hologram. A GeForce GTX 770 graphics card with 2 GB memory is used to achieve parallel computing.

Long-term changes in the chemical composition of soil organic matter, depending on fertilization and crop rotation

NASA Astrophysics Data System (ADS)

Tammik, Kerttu; Kauer, Karin; Astover, Alar

2017-04-01

The objective of this study was to determine whether it is possible to assess the impact of different management practices (crop rotation, fertilization (organic and mineral fertilizers) on the chemical composition of soil organic matter, using Fourier transform infrared spectroscopy (FTIR). The study is based IOSDV long-term (established in 1989) three field crop rotation (potato-wheat-barely) experiment located in Tartu, Estonia. Soil samples (Stagnic Albeluvisol) were collected from the 0-20 cm depth in the autumn of 2015, air dried, sieved to 2 mm and grinded to obtain homogeneous samples. The content of soil organic matter was measured by the dry combustion method in a varioMax CNS elemental analyser (ELEMENTAR, Germany). The samples were analysed using Thermo-Nicolet iS10 Fourier Transform Infrared Spectrophotometer (FT-IR) and OMNIC software. An intense and sharp peak was recorded in the region of Si-O vibrations of clay minerals and polysaccharides in all samples analysed. The volume of the peak correlated with the quantity of fertilizers administered

Evaluation of co-pyrolysis petrochemical wastewater sludge with lignite in a thermogravimetric analyzer and a packed-bed reactor: Pyrolysis characteristics, kinetics, and products analysis.

PubMed

Mu, Lin; Chen, Jianbiao; Yao, Pikai; Zhou, Dapeng; Zhao, Liang; Yin, Hongchao

2016-12-01

Co-pyrolysis characteristics of petrochemical wastewater sludge and Huolinhe lignite were investigated using thermogravimetric analyzer and packed-bed reactor coupled with Fourier transform infrared spectrometer and gas chromatography. The pyrolysis characteristics of the blends at various sludge blending ratios were compared with those of the individual materials. Thermogravimetric experiments showed that the interactions between the blends were beneficial to generate more residues. In packed-bed reactor, synergetic effects promoted the release of gas products and left less liquid and solid products than those calculated by additive manner. Fourier transform infrared spectrometer analysis showed that main functional groups in chars gradually disappeared with pyrolysis temperatures increasing, and H 2 O, CH 4 , CO, and CO 2 appeared in volatiles during pyrolysis. Gas compositions analysis indicated that, the yields of H 2 and CO clearly increased as the pyrolysis temperature and sludge blending ratio increasing, while the changes of CH 4 and CO 2 yields were relatively complex. Copyright © 2016 Elsevier Ltd. All rights reserved.

[On-line monitoring of biomass in 1,3-propanediol fermentation by Fourier-transformed near-infrared spectra analysis].

PubMed

Wang, Lu; Liu, Tao; Chen, Yang; Sun, Yaqin; Xiu, Zhilong

2017-01-25

Biomass is an important parameter reflecting the fermentation dynamics. Real-time monitoring of biomass can be used to control and optimize a fermentation process. To overcome the deficiencies of measurement delay and manual errors from offline measurement, we designed an experimental platform for online monitoring the biomass during a 1,3-propanediol fermentation process, based on using the fourier-transformed near-infrared (FT-NIR) spectra analysis. By pre-processing the real-time sampled spectra and analyzing the sensitive spectra bands, a partial least-squares algorithm was proposed to establish a dynamic prediction model for the biomass change during a 1,3-propanediol fermentation process. The fermentation processes with substrate glycerol concentrations of 60 g/L and 40 g/L were used as the external validation experiments. The root mean square error of prediction (RMSEP) obtained by analyzing experimental data was 0.341 6 and 0.274 3, respectively. These results showed that the established model gave good prediction and could be effectively used for on-line monitoring the biomass during a 1,3-propanediol fermentation process.

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.

Artifacts in Radar Imaging of Moving Targets

DTIC Science & Technology

2012-09-01

CA, USA, 2007. [11] B. Borden, Radar imaging of airborne targets: A primer for Applied mathematicians and Physicists . New York, NY: Taylor and... Project (0704–0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 21 September 2012 3. REPORT TYPE AND DATES COVERED...CW Continuous Wave DAC Digital to Analog Convertor DFT Discrete Fourier Transform FBP Filtered Back Projection FFT Fast Fourier Transform GPS

Determination of grain size distribution function using two-dimensional Fourier transforms of tone pulse encoded images

NASA Technical Reports Server (NTRS)

Generazio, E. R.

1986-01-01

Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain size distribution function from which the mean grain shape, size, and orientation can be obtained.

Physical Modeling for Processing Geosynchronous Imaging Fourier Transform Spectrometer-Indian Ocean METOC Imager (GIFTS-IOMI) Hyperspectral Data

DTIC Science & Technology

2002-09-30

Physical Modeling for Processing Geosynchronous Imaging Fourier Transform Spectrometer-Indian Ocean METOC Imager ( GIFTS -IOMI) Hyperspectral Data...water quality assessment. OBJECTIVES The objective of this DoD research effort is to develop and demonstrate a fully functional GIFTS - IOMI...environment once GIFTS -IOMI is stationed over the Indian Ocean. The system will provide specialized methods for the characterization of the atmospheric

Passive Standoff Detection of Chemical Vapors by Differential FTIR Radiometry

DTIC Science & Technology

2001-01-01

8217 utilisation d’un interferometre infrarouge a transformation de Fourier (FTIR) a double entree optimise pour la soustraction optique. En vue de sa mise...Valcartier (DREV) is currently developing a passive Fourier Transform InfraRed (FTIR) technique for the standoff detection and identification of...chemical vapors. A well-known difficulty associated with this technique is that the recorded signal also contains a large amount of unwanted background

Industrial realization of a direct Fourier transform in automated experimental data processing systems

NASA Technical Reports Server (NTRS)

Lyubashevskiy, G. S.

1973-01-01

Fourier processing of automatic signals transforms direct current voltage into a numerical form through bandpass filtration in time-pulse multiplying devices. It is shown that the ratio of the interference energy to the useful signal energy is inversely proportional to the square of the product of the depth of the width modulation and the ratio of the time constant averaging to the cross-multiplied signals.

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).

An algorithm for the basis of the finite Fourier transform

NASA Technical Reports Server (NTRS)

Santhanam, Thalanayar S.

1995-01-01

The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.

Calculation of the equilibrium distribution for a deleterious gene by the finite Fourier transform.

PubMed

Lange, K

1982-03-01

In a population of constant size every deleterious gene eventually attains a stochastic equilibrium between mutation and selection. The individual probabilities of this equilibrium distribution can be computed by an application of the finite Fourier transform to an appropriate branching process formula. Specific numerical examples are discussed for the autosomal dominants, Huntington's chorea and chondrodystrophy, and for the X-linked recessive, Becker's muscular dystrophy.

Parameter Estimation for the Blind Restoration of Blurred Imagery.

DTIC Science & Technology

1986-09-01

17 Noise Process .... ............. 23 Restoration Methods .... .......... 26 Inverse Filter .... ........... 26 Wiener Filter...of Eq. (155) ....... .................... ... 64 Table 2 Restored Pictures and Noise Variances ........ . 69 v 5𔃼 5- viq °,. r -’ .’S’ .N’% N...restoration system. g(x,y) Degraded image. G(u,v) Discrete Fourier Transform of the degraded image. n(x,y) Noise . N(u,v) Discrete Fourier transform of n

Fourier spectroscopy with a one-million-point transformation

NASA Technical Reports Server (NTRS)

Connes, J.; Delouis, H.; Connes, P.; Guelachvili, G.; Maillard, J.; Michel, G.

1972-01-01

A new type of interferometer for use in Fourier spectroscopy has been devised at the Aime Cotton Laboratory of the National Center for Scientific Research (CNRS), Orsay, France. With this interferometer and newly developed computational techniques, interferograms comprising as many as one million samples can now be transformed. The techniques are described, and examples of spectra of thorium and holmium, derived from one million-point interferograms, are presented.

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.

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.

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

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.

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.

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.

An efficient and accurate molecular alignment and docking technique using ab initio quality scoring

PubMed Central

Füsti-Molnár, László; Merz, Kenneth M.

2008-01-01

An accurate and efficient molecular alignment technique is presented based on first principle electronic structure calculations. This new scheme maximizes quantum similarity matrices in the relative orientation of the molecules and uses Fourier transform techniques for two purposes. First, building up the numerical representation of true ab initio electronic densities and their Coulomb potentials is accelerated by the previously described Fourier transform Coulomb method. Second, the Fourier convolution technique is applied for accelerating optimizations in the translational coordinates. In order to avoid any interpolation error, the necessary analytical formulas are derived for the transformation of the ab initio wavefunctions in rotational coordinates. The results of our first implementation for a small test set are analyzed in detail and compared with published results of the literature. A new way of refinement of existing shape based alignments is also proposed by using Fourier convolutions of ab initio or other approximate electron densities. This new alignment technique is generally applicable for overlap, Coulomb, kinetic energy, etc., quantum similarity measures and can be extended to a genuine docking solution with ab initio scoring. PMID:18624561

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

PubMed

Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C

2017-08-01

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

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.

A FOURIER-TRANSFORMED BREMSSTRAHLUNG FLASH MODEL FOR THE PRODUCTION OF X-RAY TIME LAGS IN ACCRETING BLACK HOLE SOURCES

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

Kroon, John J.; Becker, Peter A., E-mail: jkroon@gmu.edu, E-mail: pbecker@gmu.edu

Accreting black hole sources show a wide variety of rapid time variability, including the manifestation of time lags during X-ray transients, in which a delay (phase shift) is observed between the Fourier components of the hard and soft spectra. Despite a large body of observational evidence for time lags, no fundamental physical explanation for the origin of this phenomenon has been presented. We develop a new theoretical model for the production of X-ray time lags based on an exact analytical solution for the Fourier transform describing the diffusion and Comptonization of seed photons propagating through a spherical corona. The resultingmore » Green's function can be convolved with any source distribution to compute the associated Fourier transform and time lags, hence allowing us to explore a wide variety of injection scenarios. We show that thermal Comptonization is able to self-consistently explain both the X-ray time lags and the steady-state (quiescent) X-ray spectrum observed in the low-hard state of Cyg X-1. The reprocessing of bremsstrahlung seed photons produces X-ray time lags that diminish with increasing Fourier frequency, in agreement with the observations for a wide range of sources.« less

Biomolecular surface construction by PDE transform

PubMed Central

Zheng, Qiong; Yang, Siyang; Wei, Guo-Wei

2011-01-01

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high order PDE transforms. The fast Fourier transform is utilized to accomplish the PDE transform so as to avoid stringent stability constraints in solving high order PDEs. As a consequence, the time integration of high order PDEs can be done efficiently with the fast Fourier transform. The present approach is validated with a variety of test examples in two and three-dimensional settings. We explore the impact of the PDE transform parameters, such as the PDE order and propagation time, on the quality of resulting surfaces. Additionally, we utilize a set of 10 proteins to compare the computational efficiency of the present surface generation method and the MSMS approach in Cartesian meshes. Moreover, we analyze the present method by examining some benchmark indicators of biomolecular surface, i.e., surface area, surface enclosed volume, solvation free energy and surface electrostatic potential. A test set of 13 protein molecules is used in the present investigation. The electrostatic analysis is carried out via the Poisson-Boltzmann equation model. To further demonstrate the utility of the present PDE transform based surface method, we solve the Poisson-Nernst-Planck (PNP) equations with a PDE transform surface of a protein. Second order convergence is observed for the electrostatic potential and concentrations. Finally, to test the capability and efficiency of the present PDE transform based surface generation method, we apply it to the construction of an excessively large biomolecule, a virus surface capsid. Virus surface morphologies of different resolutions are attained by adjusting the propagation time. Therefore, the present PDE transform provides a multiresolution analysis in the surface visualization. Extensive numerical experiment and comparison with an established surface model indicate that the present PDE transform is a robust, stable and efficient approach for biomolecular surface generation in Cartesian meshes. PMID:22582140

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

NASA Astrophysics Data System (ADS)

Zhao, Liang; Muniraj, Inbarasan; Healy, John J.; Malallah, Ra'ed; Cui, Xiao-Guang; Ryle, James P.; Sheridan, John T.

2017-05-01

The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random- Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.

Fourier transform of the multicenter product of 1s hydrogenic orbitals and Coulomb or Yukawa potentials and the analytically reduced form for subsequent integrals that include plane waves

NASA Technical Reports Server (NTRS)

Straton, Jack C.

1989-01-01

The Fourier transform of the multicenter product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials is given as an (M+N-1)-dimensional Feynman integral with external momenta and shifted coordinates. This is accomplished through the introduction of an integral transformation, in addition to the standard Feynman transformation for the denominators of the momentum representation of the terms in the product, which moves the resulting denominator into an exponential. This allows the angular dependence of the denominator to be combined with the angular dependence in the plane waves.

A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis

NASA Technical Reports Server (NTRS)

Ioup, G. E.

1980-01-01

Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.

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.

Light diffusion in N-layered turbid media: steady-state domain.

PubMed

Liemert, André; Kienle, Alwin

2010-01-01

We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.

Wavelength modulation spectroscopy--digital detection of gas absorption harmonics based on Fourier analysis.

PubMed

Mei, Liang; Svanberg, Sune

2015-03-20

This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.

A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers

NASA Technical Reports Server (NTRS)

Campbell, Joel

2008-01-01

A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.

Generalization and modularization of two-dimensional adaptive coordinate transformations for the Fourier modal method.

PubMed

Küchenmeister, Jens

2014-04-21

The Fourier modal method (FMM) has advanced greatly by using adaptive coordinates and adaptive spatial resolution. The convergence characteristics were shown to be improved significantly, a construction principle for suitable meshes was demonstrated and a guideline for the optimal choice of the coordinate transformation parameters was found. However, the construction guidelines published so far rely on a certain restriction that is overcome with the formulation presented in this paper. Moreover, a modularization principle is formulated that significantly eases the construction of coordinate transformations in unit cells with reappearing shapes and complex sub-structures.

Swept sine testing of rotor-bearing system for damping estimation

NASA Astrophysics Data System (ADS)

Chandra, N. Harish; Sekhar, A. S.

2014-01-01

Many types of rotating components commonly operate above the first or second critical speed and they are subjected to run-ups and shutdowns frequently. The present study focuses on developing FRF of rotor bearing systems for damping estimation from swept-sine excitation. The principle of active vibration control states that with increase in angular acceleration, the amplitude of vibration due to unbalance will reduce and the FRF envelope will shift towards the right (or higher frequency). The frequency response function (FRF) estimated by tracking filters or Co-Quad analyzers was proved to induce an error into the FRF estimate. Using Fast Fourier Transform (FFT) algorithm and stationary wavelet transform (SWT) decomposition FRF distortion can be reduced. To obtain a theoretical clarity, the shifting of FRF envelope phenomenon is incorporated into conventional FRF expressions and validation is performed with the FRF estimated using the Fourier Transform approach. The half-power bandwidth method is employed to extract damping ratios from the FRF estimates. While deriving half-power points for both types of responses (acceleration and displacement), damping ratio (ζ) is estimated with different approximations like classical definition (neglecting damping ratio of order higher than 2), third order (neglecting damping ratios with order higher than 4) and exact (no assumptions on damping ratio). The use of stationary wavelet transform to denoise the noise corrupted FRF data is explained. Finally, experiments are performed on a test rotor excited with different sweep rates to estimate the damping ratio.

Application of the one-dimensional Fourier transform for tracking moving objects in noisy environments

NASA Technical Reports Server (NTRS)

Rajala, S. A.; Riddle, A. N.; Snyder, W. E.

1983-01-01

In Riddle and Rajala (1981), an algorithm was presented which operates on an image sequence to identify all sets of pixels having the same velocity. The algorithm operates by performing a transformation in which all pixels with the same two-dimensional velocity map to a peak in a transform space. The transform can be decomposed into applications of the one-dimensional Fourier transform and therefore can gain from the computational advantages of the FFT. The aim of this paper is the concern with the fundamental limitations of that algorithm, particularly as relates to its sensitivity to image-disturbing parameters as noise, jitter, and clutter. A modification to the algorithm is then proposed which increases its robustness in the presence of these disturbances.

a Signal-Tuned Gabor Transform with Application to Eeg Analysis

NASA Astrophysics Data System (ADS)

Torreão, José R. A.; Victer, Silvia M. C.; Fernandes, João L.

2013-04-01

We introduce a time-frequency transform based on Gabor functions whose parameters are given by the Fourier transform of the analyzed signal. At any given frequency, the width and the phase of the Gabor function are obtained, respectively, from the magnitude and the phase of the signal's corresponding Fourier component, yielding an analyzing kernel which is a representation of the signal's content at that particular frequency. The resulting Gabor transform tunes itself to the input signal, allowing the accurate detection of time and frequency events, even in situations where the traditional Gabor and S-transform approaches tend to fail. This is the case, for instance, when considering the time-frequency representation of electroencephalogram traces (EEG) of epileptic subjects, as illustrated by the experimental study presented here.

Real-Time Fourier Transformed Holographic Associative Memory With Photorefractive Material

NASA Astrophysics Data System (ADS)

Changsuk, Oh; Hankyu, Park

1989-02-01

We describe a volume holographic associative memory using photorefractive material and conventional planar mirror. Multiple hologram is generated with two angular multiplexed writing beams and Fourier transformed object beam in BaTiO3 crystal at 0.6328 μm. Complete image can be recalled successfully by partial input of original stored image. It is proved that our system is useful for optical implementation of real-time associative memory and location addressable memory.

A hybrid silicon membrane spatial light modulator for optical information processing

NASA Technical Reports Server (NTRS)

Pape, D. R.; Hornbeck, L. J.

1984-01-01

A new two dimensional, fast, analog, electrically addressable, silicon based membrane spatial light modulator (SLM) was developed for optical information processing applications. Coherent light reflected from the mirror elements is phase modulated producing an optical Fourier transform of an analog signal input to the device. The DMD architecture and operating parameters related to this application are presented. A model is developed that describes the optical Fourier transform properties of the DMD.

Metabolic fingerprinting of lichen Usnea baileyi by Fourier transform infrared spectroscopy

NASA Astrophysics Data System (ADS)

Bakar, Siti Zaharah Abu; Latip, Jalifah; bin Din, Laily; Samsuddin, Mohd Wahid

2014-09-01

The lichen Usnea baileyi collected from different environments was characterised using Fourier transform infrared spectroscopy. This preliminary study was done to determine the effects of different environment populations on U. baileyi chemical composition. Results showed that the absorbance peaks of Golf Course 2 (GCU2) are more intense compared to Taman Awana (TA), Jalan Awana (JA) and Jalan Gohtong (JG). U. baileyi contains of dibenzofurans, depsides, depsidones, xanthones and terpenoids.

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.

Physical Modeling for Processing Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Hyperspectral Data

DTIC Science & Technology

2003-09-30

Physical Modeling for Processing Geosynchronous Imaging Fourier Transform Spectrometer ( GIFTS ) Hyperspectral Data Dr. Allen H.-L. Huang...ssec.wisc.edu Award Number: N000140110850 Grant Number: 144KE70 http://www.ssec.wisc.edu/ gifts /navy/ LONG-TERM GOALS This Office of Naval...objective of this DoD research effort is to develop and demonstrate a fully functional GIFTS hyperspectral data processing system with the potential for a

Quantum-classical analogies in waveguide arrays: From Fourier transforms to ion-laser interactions

NASA Astrophysics Data System (ADS)

Moya-Cessa, Héctor M.

2018-04-01

By using the fact that infinite and semi-infinite systems of differential equations may be casted as Schrödinger-like equations we show how quantum-classical analogies may be achieved. In particular we show how the analogies of ion-laser, functions of a phase operator and quantised-field-two-level-atom interactions may be emulated. We also show a realization of the fractional discrete Fourier transform.

Apparatus and methods for continuous beam fourier transform mass spectrometry

DOEpatents

McLuckey, Scott A.; Goeringer, Douglas E.

2002-01-01

A continuous beam Fourier transform mass spectrometer in which a sample of ions to be analyzed is trapped in a trapping field, and the ions in the range of the mass-to-charge ratios to be analyzed are excited at their characteristic frequencies of motion by a continuous excitation signal. The excited ions in resonant motions generate real or image currents continuously which can be detected and processed to provide a mass spectrum.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

PubMed

Chen, Xin; Wu, Yinghua; Batista, Victor S

2005-02-08

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

Using single buffers and data reorganization to implement a multi-megasample fast Fourier transform

NASA Technical Reports Server (NTRS)

Brown, R. D.

1992-01-01

Data ordering in large fast Fourier transforms (FFT's) is both conceptually and implementationally difficult. Discribed here is a method of visualizing data orderings as vectors of address bits, which enables the engineer to use more efficient data orderings and reduce double-buffer memory designs. Also detailed are the difficulties and algorithmic solutions involved in FFT lengths up to 4 megasamples (Msamples) and sample rates up to 80 MHz.

Using vertical Fourier transforms to invert potential-field data to magnetization or density models in the presence of topography

USGS Publications Warehouse

Phillips, Jeffrey

2014-01-01

A physical property inversion approach based on the use of 3D (or 2D) Fourier transforms to calculate the potential-field within a 3D (or 2D) volume from a known physical property distribution within the volume is described. Topographic surfaces and observations at arbitrary locations are easily accommodated. The limitations of the approach and applications to real data are considered.

Beyond MOS and Fibers: Wide-FoV Imaging Fourier Transform Spectroscopy - an Instrumentation Proposal for the Present and Future Mexican Telescopes

NASA Astrophysics Data System (ADS)

Rosales-Ortega, F. F.; Castillo, E.; Sánchez, S. F.; Iglesias-Páramo, J.; Mollá, J. I. M.; Chávez, M.

2016-10-01

In order to extend the current suite of instruments offered in the Observatorio Astrofísico Guillermo Haro (OAGH) in Cananea, Mexico (INAOE), and to explore a second-generation instrument for the future 6.5 m Telescopio San Pedro Martir (TSPM), we propose a prototype instrument that will provide un-biased wide-field (few arcmin) spectroscopic information, with the flexibility of operating at different spectral resolutions (R˜1-104), with a spatial resolution limited by seeing, and therefore to be used in a wide range of astronomical problems. This instrument will make use of the Fourier Transform Spectroscopy technique, which has been proved to be feasible in the optical wavelength range. Here we give the basic technical description of a Fourier transform spectrograph, as well as the technical advantages and weaknesses, and the science cases in which this instrument can be implemented.

Fast data reconstructed method of Fourier transform imaging spectrometer based on multi-core CPU

NASA Astrophysics Data System (ADS)

Yu, Chunchao; Du, Debiao; Xia, Zongze; Song, Li; Zheng, Weijian; Yan, Min; Lei, Zhenggang

2017-10-01

Imaging spectrometer can gain two-dimensional space image and one-dimensional spectrum at the same time, which shows high utility in color and spectral measurements, the true color image synthesis, military reconnaissance and so on. In order to realize the fast reconstructed processing of the Fourier transform imaging spectrometer data, the paper designed the optimization reconstructed algorithm with OpenMP parallel calculating technology, which was further used for the optimization process for the HyperSpectral Imager of `HJ-1' Chinese satellite. The results show that the method based on multi-core parallel computing technology can control the multi-core CPU hardware resources competently and significantly enhance the calculation of the spectrum reconstruction processing efficiency. If the technology is applied to more cores workstation in parallel computing, it will be possible to complete Fourier transform imaging spectrometer real-time data processing with a single computer.

Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1989-01-01

This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the cross-correlation function (CCF) of time series which are not evenly sampled. The series may consist of quantized point data (e.g., yes/no processes such as photon arrival). The DFT, which can be inverted to recover the original data and the sampling, is used to compute correlation functions by means of a procedure which is effectively, but not explicitly, an interpolation. The CCF can be computed for two time series not even sampled at the same set of times. Techniques for removing the distortion of the correlation functions caused by the sampling, determining the value of a constant component to the data, and treating unequally weighted data are also discussed. FORTRAN code for the Fourier transform algorithm and numerical examples of the techniques are given.

Ultrafast and versatile spectroscopy by temporal Fourier transform

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

2014-06-01

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.

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.

Particle beam experiments for the analysis of reactive sputtering processes in metals and polymer surfaces

NASA Astrophysics Data System (ADS)

Corbella, Carles; Grosse-Kreul, Simon; Kreiter, Oliver; de los Arcos, Teresa; Benedikt, Jan; von Keudell, Achim

2013-10-01

A beam experiment is presented to study heterogeneous reactions relevant to plasma-surface interactions in reactive sputtering applications. Atom and ion sources are focused onto the sample to expose it to quantified beams of oxygen, nitrogen, hydrogen, noble gas ions, and metal vapor. The heterogeneous surface processes are monitored in situ by means of a quartz crystal microbalance and Fourier transform infrared spectroscopy. Two examples illustrate the capabilities of the particle beam setup: oxidation and nitriding of aluminum as a model of target poisoning during reactive magnetron sputtering, and plasma pre-treatment of polymers (PET, PP).

The ISPM unified radio and plasma wave experiment

NASA Technical Reports Server (NTRS)

Stone, R. G.; Caldwell, J.; Deconchy, Y.; Deschanciaux, C.; Ebbett, R.; Epstein, G.; Groetz, K.; Harvey, C. C.; Hoang, S.; Howard, R.

1983-01-01

Hardware for the International Solar Polar Mission (ISPM) Unified Radio and Plasma (URAP) wave experiment is presented. The URAP determines direction and polarization of distant radio sources for remote sensing of the heliosphere, and studies local wave phenomena which determine the transport coefficients of the ambient plasma. Electric and magnetic field antennas and preamplifiers; the electromagnetic compatibility plan and grounding; radio astronomy and plasma frequency receivers; a fast Fourier transformation data processing unit waveform analyzer; dc voltage measurements; a fast envelope sampler for the solar wind, and plasmas near Jupiter; a sounder; and a power converter are described.

Estimating tropical-forest density profiles from multibaseline interferometric SAR

NASA Technical Reports Server (NTRS)

Treuhaft, Robert; Chapman, Bruce; dos Santos, Joao Roberto; Dutra, Luciano; Goncalves, Fabio; da Costa Freitas, Corina; Mura, Jose Claudio; de Alencastro Graca, Paulo Mauricio

2006-01-01

Vertical profiles of forest density are potentially robust indicators of forest biomass, fire susceptibility and ecosystem function. Tropical forests, which are among the most dense and complicated targets for remote sensing, contain about 45% of the world's biomass. Remote sensing of tropical forest structure is therefore an important component to global biomass and carbon monitoring. This paper shows preliminary results of a multibasline interfereomtric SAR (InSAR) experiment over primary, secondary, and selectively logged forests at La Selva Biological Station in Costa Rica. The profile shown results from inverse Fourier transforming 8 of the 18 baselines acquired. A profile is shown compared to lidar and field measurements. Results are highly preliminary and for qualitative assessment only. Parameter estimation will eventually replace Fourier inversion as the means to producing profiles.

Detecting the spatial chirp signals by fractional Fourier lens with transformation materials

NASA Astrophysics Data System (ADS)

Chen, J.; Hu, J.

2018-02-01

Fractional Fourier transform (FrFT) is the general form of the Fourier transform and is an important tool in signal processing. As one typical application of FrFT, detecting the chirp rate (CR, or known as the rate of frequency change) of a chirp signal is important in many optical measurements. The optical FrFT that based on graded index lens fails to detect the high CR chirp because the short wave propagation distance of the impulse in the lens will weaken the paraxial approximation condition. With the help of transformation optics, the improved FrFT lens is proposed to adjust the high CR as well as the impulse location of the given input chirp signal. The designed transformation materials can implement the effect of space compression, making the input chirp signal is equivalent to have lower CR, therefore the system can satisfy the paraxial approximation better. As a result, this lens can improve the detection precision for the high CR. The numerical simulations verified the design. The proposed device may have both theoretical and practical values, and the design demonstrates the ability and flexibility of TO in spatial signal processing.

Application of the windowed-Fourier-transform-based fringe analysis technique for investigating temperature and concentration fields in fluids.

PubMed

Mohanan, Sharika; Srivastava, Atul

2014-04-10

The present work is concerned with the development and application of a novel fringe analysis technique based on the principles of the windowed-Fourier-transform (WFT) for the determination of temperature and concentration fields from interferometric images for a range of heat and mass transfer applications. Based on the extent of the noise level associated with the experimental data, the technique has been coupled with two different phase unwrapping methods: the Itoh algorithm and the quality guided phase unwrapping technique for phase extraction. In order to generate the experimental data, a range of experiments have been carried out which include cooling of a vertical flat plate in free convection conditions, combustion of mono-propellant flames, and growth of organic as well as inorganic crystals from their aqueous solutions. The flat plate and combustion experiments are modeled as heat transfer applications wherein the interest is to determine the whole-field temperature distribution. Aqueous-solution-based crystal growth experiments are performed to simulate the mass transfer phenomena and the interest is to determine the two-dimensional solute concentration field around the growing crystal. A Mach-Zehnder interferometer has been employed to record the path-integrated quantity of interest (temperature and/or concentration) in the form of interferometric images in the experiments. The potential of the WFT method has also been demonstrated on numerically simulated phase data for varying noise levels, and the accuracy in phase extraction have been quantified in terms of the root mean square errors. Three levels of noise, i.e., 0%, 10%, and 20% have been considered. Results of the present study show that the WFT technique allows an accurate extraction of phase values that can subsequently be converted into two-dimensional temperature and/or concentration distribution fields. Moreover, since WFT is a local processing technique, speckle patterns and the inherent noise in the interferometric data do not affect the resultant phase values. Brief comparisons of the accuracy of the WFT with other standard techniques such as conventional Fourier-filtering methods are also presented.

Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs

NASA Astrophysics Data System (ADS)

Roychoudhuri, Chandrasekhar

2007-09-01

We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.

Spectral correlations in Anderson insulating wires

NASA Astrophysics Data System (ADS)

Marinho, M.; Micklitz, T.

2018-01-01

We calculate the spectral level-level correlation function of Anderson insulating wires for all three Wigner-Dyson classes. A measurement of its Fourier transform, the spectral form factor, is within reach of state-of-the-art cold atom quantum quench experiments, and we find good agreement with recent numerical simulations of the latter. Our derivation builds on a representation of the level-level correlation function in terms of a local generating function which may prove useful in other contexts.

Laser and Fourier Transform Emission Spectroscopy of the G4Φ-X4Φ System of TiF

NASA Astrophysics Data System (ADS)

Ram, R. S.; Peers, J. R. D.; Teng, Ying; Adam, A. G.; Muntianu, A.; Bernath, P. F.; Davis, S. P.

1997-07-01

The emission spectrum of theG4Φ-X4Φ transition of TiF has been observed in the region 13 500-16 000 cm-1using a Fourier transform spectrometer (FTS), as well as by laser excitation spectroscopy. In the FTS experiments the bands were excited in a carbon tube furnace by the reaction of titanium metal vapor with CF4at a temperature of about 2300°C. In the laser experiments the TiF molecules were produced by laser vaporization of a Ti rod followed by reaction with SF6using a pulsed supersonic jet source. Three groups of bands with high-wavenumber subband heads at 14 388, 15 033, and 15 576 cm-1have been assigned as 0-1, 0-0, and 1-0 vibrational bands of theG4Φ-X4Φ transition, respectively. Each vibrational band consists of four subbands assigned as4Φ3/2-4Φ3/2,4Φ5/2-4Φ5/2,4Φ7/2-4Φ7/2, and4Φ9/2-4Φ9/2. A rotational analysis has been performed and molecular constants for the ground and excited states have been extracted using the combined FTS and laser excitation measurements. The correspondence between the electronic states of TiF, TiH, and Ti+has also been discussed.

Color image encryption using random transforms, phase retrieval, chaotic maps, and diffusion

NASA Astrophysics Data System (ADS)

Annaby, M. H.; Rushdi, M. A.; Nehary, E. A.

2018-04-01

The recent tremendous proliferation of color imaging applications has been accompanied by growing research in data encryption to secure color images against adversary attacks. While recent color image encryption techniques perform reasonably well, they still exhibit vulnerabilities and deficiencies in terms of statistical security measures due to image data redundancy and inherent weaknesses. This paper proposes two encryption algorithms that largely treat these deficiencies and boost the security strength through novel integration of the random fractional Fourier transforms, phase retrieval algorithms, as well as chaotic scrambling and diffusion. We show through detailed experiments and statistical analysis that the proposed enhancements significantly improve security measures and immunity to attacks.

Mineralogical transformations controlling acid mine drainage chemistry

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

Peretyazhko, Tetyana; Zachara, John M.; Boily, Jean F.

2009-05-30

The role of Fe(III) minerals in controlling acid mine drainage (AMD) chemistry was studied using samples from two AMD sites [Gum Boot (GB) and Fridays-2 (FR)] located in northern Pennsylvania. Chemical extractions, X-ray diffraction (XRD), scanning electron microscopy (SEM), and Fourier transform infrared spectroscopy (FTIR) were used to identify and characterize Fe(III) phases. The mineralogical analysis revealed that schwertmannite and goethite were the principal Fe(III) phases in the sediments. Schwertmannite transformation occurred at the GB site where poorly-crystallized goethite rich in surface-bound sulfate was initially formed. In contrast, no schwertmannite transformation occurred at the FR site. The goethite in GBmore » sediments had spherical morphology due to preservation of schwertmannite structure by adsorbed sulfate. Results of chemical extractions showed that poorly-crystallized goethite was subject to further crystallization accompanied by sulfate desorption. Changes in sulfate speciation preceded its desorption, with a conversion of bidentate- to monodentate-bound sulfate surface complexes. Laboratory sediment incubation experiments were conducted to evaluate the effect of mineral transformation on water chemistry. Incubation experiments were carried out with schwertmannite-containing sediments and AMD waters with different pH and chemical composition. The pH decreased to 1.9-2.2 in all suspensions and the concentrations of dissolved Fe and S increased significantly. Regardless of differences in the initial water composition, pH, Fe and S were similar in suspensions of the same sediment. XRD measurements revealed that schwertmannite transformed into goethite in GB and FR sediments during laboratory incubation. The incubation experiment demonstrated that schwertmannite transformation controlled AMD water chemistry during “closed system” laboratory contact.« less

Four Fourier transform spectrometers and the Arctic polar vortex: instrument intercomparison and ACE-FTS validation at Eureka during the IPY springs of 2007 and 2008

NASA Astrophysics Data System (ADS)

Batchelor, R. L.; Kolonjari, F.; Lindenmaier, R.; Mittermeier, R. L.; Daffer, W.; Fast, H.; Manney, G.; Strong, K.; Walker, K. A.

2010-01-01

The Canadian Arctic Atmospheric Chemistry Experiment Validation Campaigns have been carried out at Eureka, Nunavut (80.05° N, 86.42° W) during the polar sunrise period since 2004. During the International Polar Year (IPY) springs of 2007 and 2008, three ground-based Fourier transform infrared (FTIR) spectrometers were operated simultaneously. This paper presents a comparison of trace gas measurements of stratospherically important species involved in ozone depletion, namely O3, HCl, ClONO2, HNO3 and HF, recorded with these three spectrometers. Total column densities of the gases measured with the new Canadian Network for the Detection of Atmospheric Change (CANDAC) Bruker 125HR are shown to agree to within 3.5% with the existing Environment Canada Bomem DA8 measurements. After smoothing both of these sets of measurements to account for the lower spectral resolution of the University of Waterloo Portable Atmospheric Research Interferometric Spectrometer for the Infrared (PARIS-IR), the measurements were likewise shown to agree with PARIS-IR to within 7%. Concurrent measurements of these gases were also made with the satellite-based Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) during overpasses of Eureka during these time periods. While one of the mandates of the ACE satellite mission is to study ozone depletion in the polar spring, previous validation exercises have identified the highly variable polar vortex conditions of the spring period to be a challenge for validation efforts. In this work, comparisons between the CANDAC Bruker 125HR and ACE-FTS have been used to develop strict criteria that allow the ground- and satellite-based instruments to be confidently compared. When these criteria are taken into consideration, the observed biases between the ACE-FTS and ground-based FTIR spectrometer are not persistent for both years and are generally insignificant, though small positive biases of ~5%, comparable in magnitude to those seen in previous validation exercises, are observed for HCl and HF in 2007, and negative biases of -15.3%, -4.8% and -1.5% are seen for ClONO2, HNO3 and O3 in 2008.

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.

Classification and identification of Rhodobryum roseum Limpr. and its adulterants based on fourier-transform infrared spectroscopy (FTIR) and chemometrics.

PubMed

Cao, Zhen; Wang, Zhenjie; Shang, Zhonglin; Zhao, Jiancheng

2017-01-01

Fourier-transform infrared spectroscopy (FTIR) with the attenuated total reflectance technique was used to identify Rhodobryum roseum from its four adulterants. The FTIR spectra of six samples in the range from 4000 cm-1 to 600 cm-1 were obtained. The second-derivative transformation test was used to identify the small and nearby absorption peaks. A cluster analysis was performed to classify the spectra in a dendrogram based on the spectral similarity. Principal component analysis (PCA) was used to classify the species of six moss samples. A cluster analysis with PCA was used to identify different genera. However, some species of the same genus exhibited highly similar chemical components and FTIR spectra. Fourier self-deconvolution and discrete wavelet transform (DWT) were used to enhance the differences among the species with similar chemical components and FTIR spectra. Three scales were selected as the feature-extracting space in the DWT domain. The results show that FTIR spectroscopy with chemometrics is suitable for identifying Rhodobryum roseum and its adulterants.

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.

Behavioral Context of Call Production by Eastern North Pacific Blue Whales

DTIC Science & Technology

2007-01-25

pairs occurring in a repeated song sequence; B calls from a different blue whale are also evident; spectrogram parameters: fast Fourier transform (FFT...Acoustic data were viewed in spectrogram form ( fast Fourier transform [FFT] length 1 s, 80% overlap, Hanning window) to de- termine the presence of calls...dura- tion to song A and B units (Table 2), but the intermit - tent timing clearly distinguishes them from song. Whales producing singular calls were

Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array

NASA Astrophysics Data System (ADS)

Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin

2011-03-01

The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.

Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array

NASA Astrophysics Data System (ADS)

Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin

2010-07-01

The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.

Fast Fourier transformation results from gamma-ray burst profiles

NASA Technical Reports Server (NTRS)

Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.

1992-01-01

Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.

Bilayer free-standing beam splitter for Fourier transform infrared spectrometry.

PubMed

Rowell, N L; Wang, E A

1996-06-01

We describe the design, fabrication, testing, and performance of a two-layer free-standing beam splitter for use in far-infrared Fourier transform infrared spectrometers. This bilayer beam splitter, consisting of a low-index polymer layer in combination with a high-index semiconductor layer, has an efficiency that is higher than that of the best combination of four single-layer Mylar beam splitters currently in use for spectrometry from 50 to 550 cm(-1).

A Study of the Applicability of Atomic Emission Spectroscopy (AES), Fourier Transform Infrared (FT-IR) Spectroscopy, Direct Reading and Analytical Ferrography on High Performance Aircraft Engine Lubricating Oils

DTIC Science & Technology

1998-01-01

Ferrography on High Performance Aircraft Engine Lubricating Oils Allison M. Toms, Sharon 0. Hem, Tim Yarborough Joint Oil Analysis Program Technical...turbine engines by spectroscopy (AES and FT-IR) and direct reading and analytical ferrography . A statistical analysis of the data collected is...presented. Key Words: Analytical ferrography ; atomic emission spectroscopy; condition monitoring; direct reading ferrography ; Fourier transform infrared