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 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

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.

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.

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

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

Fourier transform spectrometry for fiber-optic sensor systems

NASA Technical Reports Server (NTRS)

Beheim, Glenn; Tuma, Margaret L.; Sotomayor, Jorge L.; Flatico, Joseph M.

1993-01-01

An integrated-optic Mach-Zehnder interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This type of spectrometer has an advantage over conventional grating spectrometers because it is better suited for use with time-division-multiplexed sensor networks. In addition, this spectrometer has the potential for low cost due to its use of a component that could be manufactured in large quantities for the optical communications industry.

Fizeau Fourier transform imaging spectroscopy: missing data reconstruction.

PubMed

Thurman, Samuel T; Fienup, James R

2008-04-28

Fizeau Fourier transform imaging spectroscopy yields both spatial and spectral information about an object. Spectral information, however, is not obtained for a finite area of low spatial frequencies. A nonlinear reconstruction algorithm based on a gray-world approximation is presented. Reconstruction results from simulated data agree well with ideal Michelson interferometer-based spectral imagery. This result implies that segmented-aperture telescopes and multiple telescope arrays designed for conventional imaging can be used to gather useful spectral data through Fizeau FTIS without the need for additional hardware.

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.

Cosine beamforming

NASA Astrophysics Data System (ADS)

Ruigrok, Elmer; Wapenaar, Kees

2014-05-01

In various application areas, e.g., seismology, astronomy and geodesy, arrays of sensors are used to characterize incoming wavefields due to distant sources. Beamforming is a general term for phased-adjusted summations over the different array elements, for untangling the directionality and elevation angle of the incoming waves. For characterizing noise sources, beamforming is conventionally applied with a temporal Fourier and a 2D spatial Fourier transform, possibly with additional weights. These transforms become aliased for higher frequencies and sparser array-element distributions. As a partial remedy, we derive a kernel for beamforming crosscorrelated data and call it cosine beamforming (CBF). By applying beamforming not directly to the data, but to crosscorrelated data, the sampling is effectively increased. We show that CBF, due to this better sampling, suffers less from aliasing and yields higher resolution than conventional beamforming. As a flip-side of the coin, the CBF output shows more smearing for spherical waves than conventional beamforming.

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.

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

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, I. S.; Shao, H. M.; Reed, I. S.; Shyu, H. C.

1986-01-01

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). A pipeline structure is used to implement this prime factor DFT over 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.

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.

Time efficient Gabor fused master slave optical coherence tomography

NASA Astrophysics Data System (ADS)

Cernat, Ramona; Bradu, Adrian; Rivet, Sylvain; Podoleanu, Adrian

2018-02-01

In this paper the benefits in terms of operation time that Master/Slave (MS) implementation of optical coherence tomography can bring in comparison to Gabor fused (GF) employing conventional fast Fourier transform based OCT are presented. The Gabor Fusion/Master Slave Optical Coherence Tomography architecture proposed here does not need any data stitching. Instead, a subset of en-face images is produced for each focus position inside the sample to be imaged, using a reduced number of theoretically inferred Master masks. These en-face images are then assembled into a final volume. When the channelled spectra are digitized into 1024 sampling points, and more than 4 focus positions are required to produce the final volume, the Master Slave implementation of the instrument is faster than the conventional fast Fourier transform based procedure.

Copy-move forgery detection utilizing Fourier-Mellin transform log-polar features

NASA Astrophysics Data System (ADS)

Dixit, Rahul; Naskar, Ruchira

2018-03-01

In this work, we address the problem of region duplication or copy-move forgery detection in digital images, along with detection of geometric transforms (rotation and rescale) and postprocessing-based attacks (noise, blur, and brightness adjustment). Detection of region duplication, following conventional techniques, becomes more challenging when an intelligent adversary brings about such additional transforms on the duplicated regions. In this work, we utilize Fourier-Mellin transform with log-polar mapping and a color-based segmentation technique using K-means clustering, which help us to achieve invariance to all the above forms of attacks in copy-move forgery detection of digital images. Our experimental results prove the efficiency of the proposed method and its superiority to the current state of the art.

A simple filter circuit for denoising biomechanical impact signals.

PubMed

Subramaniam, Suba R; Georgakis, Apostolos

2009-01-01

We present a simple scheme for denoising non-stationary biomechanical signals with the aim of accurately estimating their second derivative (acceleration). The method is based on filtering in fractional Fourier domains using well-known low-pass filters in a way that amounts to a time-varying cut-off threshold. The resulting algorithm is linear and its design is facilitated by the relationship between the fractional Fourier transform and joint time-frequency representations. The implemented filter circuit employs only three low-order filters while its efficiency is further supported by the low computational complexity of the fractional Fourier transform. The results demonstrate that the proposed method can denoise the signals effectively and is more robust against noise as compared to conventional low-pass filters.

A comparison of orthogonal transformations for digital speech processing.

NASA Technical Reports Server (NTRS)

Campanella, S. J.; Robinson, G. S.

1971-01-01

Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals. To rate their effectiveness in accomplishing this goal the quantizing error (or noise) resulting for each transformation method at various bit rates is computed and compared with that for conventional companded PCM processing. Based on this comparison, it is found that Karhunen-Loeve provides a reduction in bit rate of 13.5 kbits/s, Fourier 10 kbits/s, and Hadamard 7.5 kbits/s as compared with the bit rate required for companded PCM. These bit-rate reductions are shown to be somewhat independent of the transmission bit rate.

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).

Supercontinuum Fourier transform spectrometry with balanced detection on a single photodiode

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

Goncharov, Vasily V.; Hall, Gregory E., E-mail: gehall@bnl.gov

We demonstrate a method of combining a supercontinuum light source with a commercial Fourier transform spectrometer, using a novel approach to dual-beam balanced detection, implemented with phase-sensitive detection on a single light detector. A 40 dB reduction in the relative intensity noise is achieved for broadband light, analogous to conventional balanced detection methods using two matched photodetectors. Unlike conventional balanced detection, however, this method exploits the time structure of the broadband source to interleave signal and reference pulse trains in the time domain, recording the broadband differential signal at the fundamental pulse repetition frequency of the supercontinuum. The method ismore » capable of real-time correction for instability in the supercontinuum spectral structure over a broad range of wavelengths and is compatible with commercially designed spectrometers. A proof-of-principle experimental setup is demonstrated for weak absorption in the 1500-1600 nm region.« less

Security analysis of quadratic phase based cryptography

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.

2016-09-01

The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.

Choice of optical system is critical for the security of double random phase encryption systems

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Cassidy, Derek; Zhao, Liang; Ryle, James P.; Healy, John J.; Sheridan, John T.

2017-06-01

The linear canonical transform (LCT) is used in modeling a coherent light-field propagation through first-order optical systems. Recently, a generic optical system, known as the quadratic phase encoding system (QPES), for encrypting a two-dimensional image has been reported. In such systems, two random phase keys and the individual LCT parameters (α,β,γ) serve as secret keys of the cryptosystem. It is important that such encryption systems also satisfy some dynamic security properties. We, therefore, examine such systems using two cryptographic evaluation methods, the avalanche effect and bit independence criterion, which indicate the degree of security of the cryptographic algorithms using QPES. We compared our simulation results with the conventional Fourier and the Fresnel transform-based double random phase encryption (DRPE) systems. The results show that the LCT-based DRPE has an excellent avalanche and bit independence characteristics compared to the conventional Fourier and Fresnel-based encryption systems.

Radar cross-section reduction based on an iterative fast Fourier transform optimized metasurface

NASA Astrophysics Data System (ADS)

Song, Yi-Chuan; Ding, Jun; Guo, Chen-Jiang; Ren, Yu-Hui; Zhang, Jia-Kai

2016-07-01

A novel polarization insensitive metasurface with over 25 dB monostatic radar cross-section (RCS) reduction is introduced. The proposed metasurface is comprised of carefully arranged unit cells with spatially varied dimension, which enables approximate uniform diffusion of incoming electromagnetic (EM) energy and reduces the threat from bistatic radar system. An iterative fast Fourier transform (FFT) method for conventional antenna array pattern synthesis is innovatively applied to find the best unit cell geometry parameter arrangement. Finally, a metasurface sample is fabricated and tested to validate RCS reduction behavior predicted by full wave simulation software Ansys HFSSTM and marvelous agreement is observed.

Decision-feedback detection strategy for nonlinear frequency-division multiplexing

NASA Astrophysics Data System (ADS)

Civelli, Stella; Forestieri, Enrico; Secondini, Marco

2018-04-01

By exploiting a causality property of the nonlinear Fourier transform, a novel decision-feedback detection strategy for nonlinear frequency-division multiplexing (NFDM) systems is introduced. The performance of the proposed strategy is investigated both by simulations and by theoretical bounds and approximations, showing that it achieves a considerable performance improvement compared to previously adopted techniques in terms of Q-factor. The obtained improvement demonstrates that, by tailoring the detection strategy to the peculiar properties of the nonlinear Fourier transform, it is possible to boost the performance of NFDM systems and overcome current limitations imposed by the use of more conventional detection techniques suitable for the linear regime.

An improved scheme for Flip-OFDM based on Hartley transform in short-range IM/DD systems.

PubMed

Zhou, Ji; Qiao, Yaojun; Cai, Zhuo; Ji, Yuefeng

2014-08-25

In this paper, an improved Flip-OFDM scheme is proposed for IM/DD optical systems, where the modulation/demodulation processing takes advantage of the fast Hartley transform (FHT) algorithm. We realize the improved scheme in one symbol period while conventional Flip-OFDM scheme based on fast Fourier transform (FFT) in two consecutive symbol periods. So the complexity of many operations in improved scheme is half of that in conventional scheme, such as CP operation, polarity inversion and symbol delay. Compared to FFT with complex input constellation, the complexity of FHT with real input constellation is halved. The transmission experiment over 50-km SSMF has been realized to verify the feasibility of improved scheme. In conclusion, the improved scheme has the same BER performance with conventional scheme, but great superiority on complexity.

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

NASA Astrophysics Data System (ADS)

Viswanathan, V. K.

1980-11-01

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

Preliminary Method for Direct Quantification of Colistin Methanesulfonate by Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy

PubMed Central

Niece, Krista L.

2015-01-01

Colistin use has increased in response to the advent of infections caused by multidrug-resistant organisms. It is administered parenterally as an inactive prodrug, colistin methanesulfonate (CMS). Various formulations of CMS and labeling conventions can lead to confusion about colistin dosing, and questions remain about the pharmacokinetics of CMS. Since CMS does not have strong UV absorbance, current methods employ a laborious process of chemical conversion to colistin followed by precolumn derivatization to detect formed colistin by high-performance liquid chromatography. Here, we report a method for direct quantification of colistin methanesulfonate by attenuated total reflectance Fourier transform infrared spectroscopy (ATR FTIR). PMID:26124160

Real-time and high accuracy frequency measurements for intermediate frequency narrowband signals

NASA Astrophysics Data System (ADS)

Tian, Jing; Meng, Xiaofeng; Nie, Jing; Lin, Liwei

2018-01-01

Real-time and accurate measurements of intermediate frequency signals based on microprocessors are difficult due to the computational complexity and limited time constraints. In this paper, a fast and precise methodology based on the sigma-delta modulator is designed and implemented by first generating the twiddle factors using the designed recursive scheme. This scheme requires zero times of multiplications and only half amounts of addition operations by using the discrete Fourier transform (DFT) and the combination of the Rife algorithm and Fourier coefficient interpolation as compared with conventional methods such as DFT and Fast Fourier Transform. Experimentally, when the sampling frequency is 10 MHz, the real-time frequency measurements with intermediate frequency and narrowband signals have a measurement mean squared error of ±2.4 Hz. Furthermore, a single measurement of the whole system only requires approximately 0.3 s to achieve fast iteration, high precision, and less calculation time.

Tests of various colorants for application of a Fourier transform infrared imaging system to deciphering obliterated writings

NASA Astrophysics Data System (ADS)

Sugawara, Shigeru

2015-10-01

Obliterated writing is writing that has been obscured by different-colored materials. There are obliterated writings that cannot be detected by conventional methods. A method for deciphering such obliterated writings was developed in this study. Mid-infrared spectroscopic imaging in the wavelength range of 2.5-14 μm was used for deciphering because the infrared spectrum differs among different brands of colorants. Obliterated writings were made by pressing information protection stamps onto characters written by 4 kinds of colorants. The samples were tested for deciphering by the Fourier-transform infrared imaging system. Two peak areas of two specific wavenumber regions of each reflectance spectrum were calculated and the ratio of the two values is displayed as a unique gray scale in the spectroscopic image. As a result, the absorption peak at various wavenumbers could be used to decipher obliterated writings that could not be detected by the conventional methods. Ten different parameters for deciphering obliterated writing were found in this study.

Intracranial vascular stenosis and occlusion: Diagnostic accuracy of three-dimensional, fourier transform, time-of-flight MR angiography

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

Korogi, Yukunori; Takahashi, Mutsumasa; Mabuchi, Nobuhisa

1994-10-01

To assess the accuracy of three-dimensional, Fourier transform, time-of-flight magnetic resonance (MR) angiography in the detection of intracranial steno-occlusive diseases. One hundred thirty-one patients (62 male and 69 female patients, aged 6-77 years [mean, 53 years 8 months]) underwent MR and conventional angiography for evaluation of possible intracranial vascular disease. A total of 502 arteries were assessed. Eight projections and a collapsed image postprocessed by means of a maximum-intensity projection algorithm were reviewed by five observers in a blinded manner, with conventional angiography as the standard. A total of 32 steno-occlusive lesions were available for review. Receiver operating characteristic analysismore » from the pooled data revealed overall sensitivities of 85% and 88% and specificities of 96% and 97% for the internal carotid artery and the middle cerebral artery, respectively. MR angiography is useful as the primary diagnostic tool for evaluating suspected intracranial steno-occlusive disease. 22 refs., 7 figs., 5 tabs.« less

An optical Fourier transform coprocessor with direct phase determination.

PubMed

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

2017-10-20

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

Gas Measurement Using Static Fourier Transform Infrared Spectrometers.

PubMed

Köhler, Michael H; Schardt, Michael; Rauscher, Markus S; Koch, Alexander W

2017-11-13

Online monitoring of gases in industrial processes is an ambitious task due to adverse conditions such as mechanical vibrations and temperature fluctuations. Whereas conventional Fourier transform infrared (FTIR) spectrometers use rather complex optical and mechanical designs to ensure stable operation, static FTIR spectrometers do not require moving parts and thus offer inherent stability at comparatively low costs. Therefore, we present a novel, compact gas measurement system using a static single-mirror Fourier transform spectrometer (sSMFTS). The system works in the mid-infrared range from 650 cm - 1 to 1250 cm - 1 and can be operated with a customized White cell, yielding optical path lengths of up to 120 cm for highly sensitive quantification of gas concentrations. To validate the system, we measure different concentrations of 1,1,1,2-Tetrafluoroethane (R134a) and perform a PLS regression analysis of the acquired infrared spectra. Thereby, the measured absorption spectra show good agreement with reference data. Since the system additionally permits measurement rates of up to 200 Hz and high signal-to-noise ratios, an application in process analysis appears promising.

Gas Measurement Using Static Fourier Transform Infrared Spectrometers

PubMed Central

Schardt, Michael; Rauscher, Markus S.; Koch, Alexander W.

2017-01-01

Online monitoring of gases in industrial processes is an ambitious task due to adverse conditions such as mechanical vibrations and temperature fluctuations. Whereas conventional Fourier transform infrared (FTIR) spectrometers use rather complex optical and mechanical designs to ensure stable operation, static FTIR spectrometers do not require moving parts and thus offer inherent stability at comparatively low costs. Therefore, we present a novel, compact gas measurement system using a static single-mirror Fourier transform spectrometer (sSMFTS). The system works in the mid-infrared range from 650 cm−1 to 1250 cm−1 and can be operated with a customized White cell, yielding optical path lengths of up to 120 cm for highly sensitive quantification of gas concentrations. To validate the system, we measure different concentrations of 1,1,1,2-Tetrafluoroethane (R134a) and perform a PLS regression analysis of the acquired infrared spectra. Thereby, the measured absorption spectra show good agreement with reference data. Since the system additionally permits measurement rates of up to 200 Hz and high signal-to-noise ratios, an application in process analysis appears promising. PMID:29137193

Implementation of quantum and classical discrete fractional Fourier transforms.

PubMed

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Implementation of quantum and classical discrete fractional Fourier transforms

PubMed Central

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

Distributed ISAR Subimage Fusion of Nonuniform Rotating Target Based on Matching Fourier Transform.

PubMed

Li, Yuanyuan; Fu, Yaowen; Zhang, Wenpeng

2018-06-04

In real applications, the image quality of the conventional monostatic Inverse Synthetic Aperture Radar (ISAR) for the maneuvering target is subject to the strong fluctuation of Radar Cross Section (RCS), as the target aspect varies enormously. Meanwhile, the maneuvering target introduces nonuniform rotation after translation motion compensation which degrades the imaging performance of the conventional Fourier Transform (FT)-based method in the cross-range dimension. In this paper, a method which combines the distributed ISAR technique and the Matching Fourier Transform (MFT) is proposed to overcome these problems. Firstly, according to the characteristics of the distributed ISAR, the multiple channel echoes of the nonuniform rotation target from different observation angles can be acquired. Then, by applying the MFT to the echo of each channel, the defocused problem of nonuniform rotation target which is inevitable by using the FT-based imaging method can be avoided. Finally, after preprocessing, scaling and rotation of all subimages, the noncoherent fusion image containing all the RCS information in all channels can be obtained. The accumulation coefficients of all subimages are calculated adaptively according to the their image qualities. Simulation and experimental data are used to validate the effectiveness of the proposed approach, and fusion image with improved recognizability can be obtained. Therefore, by using the distributed ISAR technique and MFT, subimages of high-maneuvering target from different observation angles can be obtained. Meanwhile, by employing the adaptive subimage fusion method, the RCS fluctuation can be alleviated and more recognizable final image can be obtained.

THE PSTD ALGORITHM: A TIME-DOMAIN METHOD REQUIRING ONLY TWO CELLS PER WAVELENGTH. (R825225)

EPA Science Inventory

A pseudospectral time-domain (PSTD) method is developed for solutions of Maxwell's equations. It uses the fast Fourier transform (FFT), instead of finite differences on conventional finite-difference-time-domain (FDTD) methods, to represent spatial derivatives. Because the Fourie...

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

ERIC Educational Resources Information Center

Grimm, C. A.

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

Fourier transform infrared imaging of Cotton trash mixtures

USDA-ARS?s Scientific Manuscript database

There is much interest in the identification of trash types comingled with cotton lint. A good understanding of the specific trash types present can lead to the fabrication of new equipment which can identify and sort cotton trash found with cotton fiber. Conventional methods, including the High Vo...

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

USDA-ARS?s Scientific Manuscript database

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

Blind detection of isolated astrophysical pulses in the spatial Fourier transform domain

NASA Astrophysics Data System (ADS)

Schmid, Natalia A.; Prestage, Richard M.

2018-07-01

We present a novel approach for the detection of isolated transients in pulsar surveys and fast radio transient observations. Rather than the conventional approach of performing a computationally expensive blind dispersion measure search, we take the spatial Fourier transform (SFT) of short (˜ few seconds) sections of data. A transient will have a characteristic signature in the SFT domain, and we present a blind statistic which may be used to detect this signature at an empirical zero false alarm rate. The method has been evaluated using simulations, and also applied to two fast radio burst observations. In addition to its use for current observations, we expect this method will be extremely beneficial for future multibeam observations made by telescopes equipped with phased array feeds.

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.

Blind detection of isolated astrophysical pulses in the spatial Fourier transform domain

NASA Astrophysics Data System (ADS)

Schmid, Natalia A.; Prestage, Richard M.

2018-04-01

We present a novel approach for the detection of isolated transients in pulsar surveys and fast radio transient observations. Rather than the conventional approach of performing a computationally expensive blind DM search, we take the spatial Fourier transform (SFT) of short (˜ few seconds) sections of data. A transient will have a characteristic signature in the SFT domain, and we present a blind statistic which may be used to detect this signature at an empirical zero False Alarm Rate (FAR). The method has been evaluated using simulations, and also applied to two fast radio burst observations. In addition to its use for current observations, we expect this method will be extremely beneficial for future multi-beam observations made by telescopes equipped with phased array feeds.

Discrimination of organic coffee via Fourier transform infrared-photoacoustic spectroscopy.

PubMed

Gordillo-Delgado, Fernando; Marín, Ernesto; Cortés-Hernández, Diego Mauricio; Mejía-Morales, Claudia; García-Salcedo, Angela Janet

2012-08-30

Procedures for the evaluation of the origin and quality of ground and roasted coffee are constantly needed for the associated industry due to complexity of the related market. Conventional Fourier transform infrared (FTIR) spectroscopy can be used for detecting changes in functional groups of compounds, such as coffee. However, dispersion, reflection and non-homogeneity of the sample matrix can cause problems resulting in low spectral quality. On the other hand, sample preparation frequently takes place in a destructive way. To overcome these difficulties, in this work a photoacoustic cell has been adapted as a detector in a FTIR spectrophotometer to perform a study of roasted and ground coffee from three varieties of Coffea arabica grown by organic and conventional methods. Comparison between spectra of coffee recorded by FTIR-photoacoustic spectrometry (PAS) and by FTIR spectrophotometry showed a better resolution of the former method, which, aided by principal components analysis, allowed the identification of some absorption bands that allow the discrimination between organic and conventional coffee. The results obtained provide information about the spectral behavior of coffee powder which can be useful for establishing discrimination criteria. It has been demonstrated that FTIR-PAS can be a useful experimental tool for the characterization of coffee. Copyright © 2012 Society of Chemical Industry.

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…

Optical calculation of correlation filters for a robotic vision system

NASA Technical Reports Server (NTRS)

Knopp, Jerome

1989-01-01

A method is presented for designing optical correlation filters based on measuring three intensity patterns: the Fourier transform of a filter object, a reference wave and the interference pattern produced by the sum of the object transform and the reference. The method can produce a filter that is well matched to both the object, its transforming optical system and the spatial light modulator used in the correlator input plane. A computer simulation was presented to demonstrate the approach for the special case of a conventional binary phase-only filter. The simulation produced a workable filter with a sharp correlation peak.

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

Improved FFT-based numerical inversion of Laplace transforms via fast Hartley transform algorithm

NASA Technical Reports Server (NTRS)

Hwang, Chyi; Lu, Ming-Jeng; Shieh, Leang S.

1991-01-01

The disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them. The improved method is based on introducing a new integration step length Delta(omega) = pi/mT for trapezoidal-rule approximation of the Bromwich integral, in which a new parameter, m, is introduced for controlling the accuracy of the numerical integration. Naturally, this method leads to multiple sets of complex FFT computations. A new inversion formula is derived such that N equally spaced samples of the inverse Laplace transform function can be obtained by (m/2) + 1 sets of N-point complex FFT computations or by m sets of real fast Hartley transform (FHT) computations.

Fourier transform and particle swarm optimization based modified LQR algorithm for mitigation of vibrations using magnetorheological dampers

NASA Astrophysics Data System (ADS)

Kumar, Gaurav; Kumar, Ashok

2017-11-01

Structural control has gained significant attention in recent times. The standalone issue of power requirement during an earthquake has already been solved up to a large extent by designing semi-active control systems using conventional linear quadratic control theory, and many other intelligent control algorithms such as fuzzy controllers, artificial neural networks, etc. In conventional linear-quadratic regulator (LQR) theory, it is customary to note that the values of the design parameters are decided at the time of designing the controller and cannot be subsequently altered. During an earthquake event, the response of the structure may increase or decrease, depending the quasi-resonance occurring between the structure and the earthquake. In this case, it is essential to modify the value of the design parameters of the conventional LQR controller to obtain optimum control force to mitigate the vibrations due to the earthquake. A few studies have been done to sort out this issue but in all these studies it was necessary to maintain a database of the earthquake. To solve this problem and to find the optimized design parameters of the LQR controller in real time, a fast Fourier transform and particle swarm optimization based modified linear quadratic regulator method is presented here. This method comprises four different algorithms: particle swarm optimization (PSO), the fast Fourier transform (FFT), clipped control algorithm and the LQR. The FFT helps to obtain the dominant frequency for every time window. PSO finds the optimum gain matrix through the real-time update of the weighting matrix R, thereby, dispensing with the experimentation. The clipped control law is employed to match the magnetorheological (MR) damper force with the desired force given by the controller. The modified Bouc-Wen phenomenological model is taken to recognize the nonlinearities in the MR damper. The assessment of the advised method is done by simulation of a three-story structure having an MR damper at the ground floor level subjected to three different near-fault historical earthquake time histories, and the outcomes are equated with those of simple conventional LQR. The results establish that the advised methodology is more effective than conventional LQR controllers in reducing inter-storey drift, relative displacement, and acceleration response.

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…

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

PubMed

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

2014-03-01

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

A phase space model of Fourier ptychographic microscopy

PubMed Central

Horstmeyer, Roarke; Yang, Changhuei

2014-01-01

A new computational imaging technique, termed Fourier ptychographic microscopy (FPM), uses a sequence of low-resolution images captured under varied illumination to iteratively converge upon a high-resolution complex sample estimate. Here, we propose a mathematical model of FPM that explicitly connects its operation to conventional ptychography, a common procedure applied to electron and X-ray diffractive imaging. Our mathematical framework demonstrates that under ideal illumination conditions, conventional ptychography and FPM both produce datasets that are mathematically linked by a linear transformation. We hope this finding encourages the future cross-pollination of ideas between two otherwise unconnected experimental imaging procedures. In addition, the coherence state of the illumination source used by each imaging platform is critical to successful operation, yet currently not well understood. We apply our mathematical framework to demonstrate that partial coherence uniquely alters both conventional ptychography’s and FPM’s captured data, but up to a certain threshold can still lead to accurate resolution-enhanced imaging through appropriate computational post-processing. We verify this theoretical finding through simulation and experiment. PMID:24514995

Efficient convolutional sparse coding

DOEpatents

Wohlberg, Brendt

2017-06-20

Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.

Quantification of trans-1,4-polyisoprene in Eucommia ulmoides by fourier transform infrared spectroscopy and pyrolysis-gas chromatography/mass spectrometry.

PubMed

Takeno, Shinya; Bamba, Takeshi; Nakazawa, Yoshihisa; Fukusaki, Eiichiro; Okazawa, Atsushi; Kobayashi, Akio

2008-04-01

Commercial development of trans-1,4-polyisoprene from Eucommia ulmoides Oliver (EU-rubber) requires specific knowledge on selection of high-rubber-content lines and establishment of agronomic cultivation methods for achieving maximum EU-rubber yield. The development can be facilitated by high-throughput and highly sensitive analytical techniques for EU-rubber extraction and quantification. In this paper, we described an efficient EU-rubber extraction method, and validated that the accuracy was equivalent to that of the conventional Soxhlet extraction method. We also described a highly sensitive quantification method for EU-rubber by Fourier transform infrared spectroscopy (FT-IR) and pyrolysis-gas chromatography/mass spectrometry (PyGC/MS). We successfully applied the extraction/quantification method for study of seasonal changes in EU-rubber content and molecular weight distribution.

Supercontinuum Fourier transform spectrometry with balanced detection on a single photodiode

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

Goncharov, Vasily; Hall, Gregory

Here, we have developed phase-sensitive signal detection and processing algorithms for Fourier transform spectrometers fitted with supercontinuum sources for applications requiring ultimate sensitivity. Similar to well-established approach of source noise cancellation through balanced detection of monochromatic light, our method is capable of reducing the relative intensity noise of polychromatic light by 40 dB. Unlike conventional balanced detection, which relies on differential absorption measured with a well matched pair of photo-detectors, our algorithm utilizes phase-sensitive differential detection on a single photodiode and is capable of the real-time correction for instabilities in supercontinuum spectral structure over a broad range of wavelengths. Inmore » the resulting method is universal in terms of applicable wavelengths and compatible with commercial spectrometers. We present a proof-of-principle experimental« less

Supercontinuum Fourier transform spectrometry with balanced detection on a single photodiode

DOE PAGES

Goncharov, Vasily; Hall, Gregory

2016-08-25

Here, we have developed phase-sensitive signal detection and processing algorithms for Fourier transform spectrometers fitted with supercontinuum sources for applications requiring ultimate sensitivity. Similar to well-established approach of source noise cancellation through balanced detection of monochromatic light, our method is capable of reducing the relative intensity noise of polychromatic light by 40 dB. Unlike conventional balanced detection, which relies on differential absorption measured with a well matched pair of photo-detectors, our algorithm utilizes phase-sensitive differential detection on a single photodiode and is capable of the real-time correction for instabilities in supercontinuum spectral structure over a broad range of wavelengths. Inmore » the resulting method is universal in terms of applicable wavelengths and compatible with commercial spectrometers. We present a proof-of-principle experimental« less

A Preliminary Research on the Development of the Hard X-Ray Imaging Telescope

NASA Astrophysics Data System (ADS)

Zheng, C. X.; Cai, M. S.; Hu, Y. M.; Huang, Y. Y.; Gong, Y. Z.

2014-03-01

Since the 1860s, astronomers have explored a new field with the discovery of X-ray. Instead of the conventional imaging technique by using mirrors or lens, which can not work in the high-energy bands, direct imaging, coded aperture, and Fourier transform are used for the high-energy imaging. It can be implemented in various hardware configurations, among which the spatial modulation collimator are widely used. We adopt the grating collimator based on Fourier transform that is discussed in detail. This paper makes an investigation on the fabrication process of grating. The key components of the hard X-ray telescope based on the spatial modulation are developed, which contains 8 CsI-detector modules, 8-channel shaping amplifiers, and data acquisition system. The preliminary test results of readout electronics system are obtained.

Application of Fourier transform infrared spectroscopy to silica diagenesis: The opal-A to opal-CT transformation

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

Rice, S.B.; Freund, H.; Huang, W.L.

An important goal in silica diagenesis research is to understand the kinetics of opal transformation from noncrystalline opal-A to the disordered silica polymorph opal-CT. Because the conventional technique for monitoring the transformation, powder X-ray diffraction (XRD), is applicable only to phases with long-range order, the authors used Fourier transform infrared spectroscopy (FTIR) to monitor the transformation. They applied this technique, combined with XRD and TEM, to experimental run products and natural opals from the Monterey Formation and from siliceous deposits in the western Pacific Ocean. Using a ratio of two infrared absorption intensities ({omega} = I{sub 472 cm{sup {minus}1}}/I{sub 500more » cm{sup {minus}1}}), the relative proportions of opal-A and opal-CT can be determined. The progress of the transformation is marked by changes in slope of {omega} vs. depth or time when a sufficient stratigraphic profile is available. There are three stages in the opal-A to opal-CT reaction: (1) opal-A dissolution; (2) opal-CT precipitation, whose end point is marked by completion of opal-A dissolution; and (3) opal-CT ordering, during which tridymite stacking is eliminated in favor of crystobalite stacking.« less

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.

Random noise attenuation of non-uniformly sampled 3D seismic data along two spatial coordinates using non-equispaced curvelet transform

NASA Astrophysics Data System (ADS)

Zhang, Hua; Yang, Hui; Li, Hongxing; Huang, Guangnan; Ding, Zheyi

2018-04-01

The attenuation of random noise is important for improving the signal to noise ratio (SNR). However, the precondition for most conventional denoising methods is that the noisy data must be sampled on a uniform grid, making the conventional methods unsuitable for non-uniformly sampled data. In this paper, a denoising method capable of regularizing the noisy data from a non-uniform grid to a specified uniform grid is proposed. Firstly, the denoising method is performed for every time slice extracted from the 3D noisy data along the source and receiver directions, then the 2D non-equispaced fast Fourier transform (NFFT) is introduced in the conventional fast discrete curvelet transform (FDCT). The non-equispaced fast discrete curvelet transform (NFDCT) can be achieved based on the regularized inversion of an operator that links the uniformly sampled curvelet coefficients to the non-uniformly sampled noisy data. The uniform curvelet coefficients can be calculated by using the inversion algorithm of the spectral projected-gradient for ℓ1-norm problems. Then local threshold factors are chosen for the uniform curvelet coefficients for each decomposition scale, and effective curvelet coefficients are obtained respectively for each scale. Finally, the conventional inverse FDCT is applied to the effective curvelet coefficients. This completes the proposed 3D denoising method using the non-equispaced curvelet transform in the source-receiver domain. The examples for synthetic data and real data reveal the effectiveness of the proposed approach in applications to noise attenuation for non-uniformly sampled data compared with the conventional FDCT method and wavelet transformation.

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

PubMed

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

2015-10-20

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

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.

[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.

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…

Computationally efficient algorithm for high sampling-frequency operation of active noise control

NASA Astrophysics Data System (ADS)

Rout, Nirmal Kumar; Das, Debi Prasad; Panda, Ganapati

2015-05-01

In high sampling-frequency operation of active noise control (ANC) system the length of the secondary path estimate and the ANC filter are very long. This increases the computational complexity of the conventional filtered-x least mean square (FXLMS) algorithm. To reduce the computational complexity of long order ANC system using FXLMS algorithm, frequency domain block ANC algorithms have been proposed in past. These full block frequency domain ANC algorithms are associated with some disadvantages such as large block delay, quantization error due to computation of large size transforms and implementation difficulties in existing low-end DSP hardware. To overcome these shortcomings, the partitioned block ANC algorithm is newly proposed where the long length filters in ANC are divided into a number of equal partitions and suitably assembled to perform the FXLMS algorithm in the frequency domain. The complexity of this proposed frequency domain partitioned block FXLMS (FPBFXLMS) algorithm is quite reduced compared to the conventional FXLMS algorithm. It is further reduced by merging one fast Fourier transform (FFT)-inverse fast Fourier transform (IFFT) combination to derive the reduced structure FPBFXLMS (RFPBFXLMS) algorithm. Computational complexity analysis for different orders of filter and partition size are presented. Systematic computer simulations are carried out for both the proposed partitioned block ANC algorithms to show its accuracy compared to the time domain FXLMS algorithm.

Iterative image reconstruction for PROPELLER-MRI using the nonuniform fast fourier transform.

PubMed

Tamhane, Ashish A; Anastasio, Mark A; Gui, Minzhi; Arfanakis, Konstantinos

2010-07-01

To investigate an iterative image reconstruction algorithm using the nonuniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) MRI. Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it with that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased signal to noise ratio, reduced artifacts, for similar spatial resolution, compared with gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter, the new reconstruction technique may provide PROPELLER images with improved image quality compared with conventional gridding. (c) 2010 Wiley-Liss, Inc.

Iterative Image Reconstruction for PROPELLER-MRI using the NonUniform Fast Fourier Transform

PubMed Central

Tamhane, Ashish A.; Anastasio, Mark A.; Gui, Minzhi; Arfanakis, Konstantinos

2013-01-01

Purpose To investigate an iterative image reconstruction algorithm using the non-uniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping parallEL Lines with Enhanced Reconstruction) MRI. Materials and Methods Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it to that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. Results It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased SNR, reduced artifacts, for similar spatial resolution, compared to gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. Conclusion An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter the new reconstruction technique may provide PROPELLER images with improved image quality compared to conventional gridding. PMID:20578028

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.

Structural correlation of the chalcogenide Ge40Se60 glass

NASA Astrophysics Data System (ADS)

Moharram, A. H.

2017-01-01

Binary Ge40Se60 glass was prepared using the melt-quench technique. The total structure factors, S( K), are obtained using the X-ray diffraction in the wave vector interval 0.28 ≤ K ≤ 6.5 Å-1. The appearance of the first sharp diffraction peak (FSDP) in the structure factor indicates the presence of the intermediate range order. Radial distribution functions, RDF( r), have been obtained using either the conventional (Fourier) transformation or the Monte Carlo simulation of the experimental X-ray data. The short range order parameters deduced from the Monte Carlo total correlation, T( r), functions are better than those obtained from the conventional (Fourier) T( r) data. Gaussian analyses of the total correlation function show that Ge2(Se1/2)6 molecular units are the basic structural units for the investigated Ge40Se60 glass.

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

PubMed

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

2009-04-01

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

Baseline correction combined partial least squares algorithm and its application in on-line Fourier transform infrared quantitative analysis.

PubMed

Peng, Jiangtao; Peng, Silong; Xie, Qiong; Wei, Jiping

2011-04-01

In order to eliminate the lower order polynomial interferences, a new quantitative calibration algorithm "Baseline Correction Combined Partial Least Squares (BCC-PLS)", which combines baseline correction and conventional PLS, is proposed. By embedding baseline correction constraints into PLS weights selection, the proposed calibration algorithm overcomes the uncertainty in baseline correction and can meet the requirement of on-line attenuated total reflectance Fourier transform infrared (ATR-FTIR) quantitative analysis. The effectiveness of the algorithm is evaluated by the analysis of glucose and marzipan ATR-FTIR spectra. BCC-PLS algorithm shows improved prediction performance over PLS. The root mean square error of cross-validation (RMSECV) on marzipan spectra for the prediction of the moisture is found to be 0.53%, w/w (range 7-19%). The sugar content is predicted with a RMSECV of 2.04%, w/w (range 33-68%). Copyright © 2011 Elsevier B.V. All rights reserved.

Artefacts in geometric phase analysis of compound materials.

PubMed

Peters, Jonathan J P; Beanland, Richard; Alexe, Marin; Cockburn, John W; Revin, Dmitry G; Zhang, Shiyong Y; Sanchez, Ana M

2015-10-01

The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

General optical discrete z transform: design and application.

PubMed

Ngo, Nam Quoc

2016-12-20

This paper presents a generalization of the discrete z transform algorithm. It is shown that the GOD-ZT algorithm is a generalization of several important conventional discrete transforms. Based on the GOD-ZT algorithm, a tunable general optical discrete z transform (GOD-ZT) processor is synthesized using the silica-based finite impulse response transversal filter. To demonstrate the effectiveness of the method, the design and simulation of a tunable optical discrete Fourier transform (ODFT) processor as a special case of the synthesized GOD-ZT processor is presented. It is also shown that the ODFT processor can function as a real-time optical spectrum analyzer. The tunable ODFT has an important potential application as a tunable optical demultiplexer at the receiver end of an optical orthogonal frequency-division multiplexing transmission system.

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

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

NASA Astrophysics Data System (ADS)

Zhang, Rui; Xin, Binjie

2016-08-01

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

Spectral estimation—What is new? What is next?

NASA Astrophysics Data System (ADS)

Tary, Jean Baptiste; Herrera, Roberto Henry; Han, Jiajun; van der Baan, Mirko

2014-12-01

Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.

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.

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

Linear prediction data extrapolation superresolution radar imaging

NASA Astrophysics Data System (ADS)

Zhu, Zhaoda; Ye, Zhenru; Wu, Xiaoqing

1993-05-01

Range resolution and cross-range resolution of range-doppler imaging radars are related to the effective bandwidth of transmitted signal and the angle through which the object rotates relatively to the radar line of sight (RLOS) during the coherent processing time, respectively. In this paper, linear prediction data extrapolation discrete Fourier transform (LPDEDFT) superresolution imaging method is investigated for the purpose of surpassing the limitation imposed by the conventional FFT range-doppler processing and improving the resolution capability of range-doppler imaging radar. The LPDEDFT superresolution imaging method, which is conceptually simple, consists of extrapolating observed data beyond the observation windows by means of linear prediction, and then performing the conventional IDFT of the extrapolated data. The live data of a metalized scale model B-52 aircraft mounted on a rotating platform in a microwave anechoic chamber and a flying Boeing-727 aircraft were processed. It is concluded that, compared to the conventional Fourier method, either higher resolution for the same effective bandwidth of transmitted signals and total rotation angle of the object or equal-quality images from smaller bandwidth and total angle may be obtained by LPDEDFT.

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product.

PubMed

Oktem, Figen S; Ozaktas, Haldun M

2010-08-01

Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

Fourier-based linear systems description of free-breathing pulmonary magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Capaldi, D. P. I.; Svenningsen, S.; Cunningham, I. A.; Parraga, G.

2015-03-01

Fourier-decomposition of free-breathing pulmonary magnetic resonance imaging (FDMRI) was recently piloted as a way to provide rapid quantitative pulmonary maps of ventilation and perfusion without the use of exogenous contrast agents. This method exploits fast pulmonary MRI acquisition of free-breathing proton (1H) pulmonary images and non-rigid registration to compensate for changes in position and shape of the thorax associated with breathing. In this way, ventilation imaging using conventional MRI systems can be undertaken but there has been no systematic evaluation of fundamental image quality measurements based on linear systems theory. We investigated the performance of free-breathing pulmonary ventilation imaging using a Fourier-based linear system description of each operation required to generate FDMRI ventilation maps. Twelve subjects with chronic obstructive pulmonary disease (COPD) or bronchiectasis underwent pulmonary function tests and MRI. Non-rigid registration was used to co-register the temporal series of pulmonary images. Pulmonary voxel intensities were aligned along a time axis and discrete Fourier transforms were performed on the periodic signal intensity pattern to generate frequency spectra. We determined the signal-to-noise ratio (SNR) of the FDMRI ventilation maps using a conventional approach (SNRC) and using the Fourier-based description (SNRF). Mean SNR was 4.7 ± 1.3 for subjects with bronchiectasis and 3.4 ± 1.8, for COPD subjects (p>.05). SNRF was significantly different than SNRC (p<.01). SNRF was approximately 50% of SNRC suggesting that the linear system model well-estimates the current approach.

Pursuing optimal electric machines transient diagnosis: The adaptive slope transform

NASA Astrophysics Data System (ADS)

Pons-Llinares, Joan; Riera-Guasp, Martín; Antonino-Daviu, Jose A.; Habetler, Thomas G.

2016-12-01

The aim of this paper is to introduce a new linear time-frequency transform to improve the detection of fault components in electric machines transient currents. Linear transforms are analysed from the perspective of the atoms used. A criterion to select the atoms at every point of the time-frequency plane is proposed, taking into account the characteristics of the searched component at each point. This criterion leads to the definition of the Adaptive Slope Transform, which enables a complete and optimal capture of the different components evolutions in a transient current. A comparison with conventional linear transforms (Short-Time Fourier Transform and Wavelet Transform) is carried out, showing their inherent limitations. The approach is tested with laboratory and field motors, and the Lower Sideband Harmonic is captured for the first time during an induction motor startup and subsequent load oscillations, accurately tracking its evolution.

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.

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.

On the application of a fast polynomial transform and the Chinese remainder theorem to compute a two-dimensional convolution

NASA Technical Reports Server (NTRS)

Truong, T. K.; Lipes, R.; Reed, I. S.; Wu, C.

1980-01-01

A fast algorithm is developed to compute two dimensional convolutions of an array of d sub 1 X d sub 2 complex number points, where d sub 2 = 2(M) and d sub 1 = 2(m-r+) for some 1 or = r or = m. This algorithm requires fewer multiplications and about the same number of additions as the conventional fast fourier transform method for computing the two dimensional convolution. It also has the advantage that the operation of transposing the matrix of data can be avoided.

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

NASA Astrophysics Data System (ADS)

Cai, Jianhua

2017-05-01

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

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.

Wavelet transform: fundamentals, applications, and implementation using acousto-optic correlators

NASA Astrophysics Data System (ADS)

DeCusatis, Casimer M.; Koay, J.; Litynski, Daniel M.; Das, Pankaj K.

1995-10-01

In recent years there has been a great deal of interest in the use of wavelets to supplement or replace conventional Fourier transform signal processing. This paper provides a review of wavelet transforms for signal processing applications, and discusses several emerging applications which benefit from the advantages of wavelets. The wavelet transform can be implemented as an acousto-optic correlator; perfect reconstruction of digital signals may also be achieved using acousto-optic finite impulse response filter banks. Acousto-optic image correlators are discussed as a potential implementation of the wavelet transform, since a 1D wavelet filter bank may be encoded as a 2D image. We discuss applications of the wavelet transform including nondestructive testing of materials, biomedical applications in the analysis of EEG signals, and interference excision in spread spectrum communication systems. Computer simulations and experimental results for these applications are also provided.

[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.

Incipient fault diagnosis of power transformers using optical spectro-photometric technique

NASA Astrophysics Data System (ADS)

Hussain, K.; Karmakar, Subrata

2015-06-01

Power transformers are the vital equipment in the network of power generation, transmission and distribution. Mineral oil in oil-filled transformers plays very important role as far as electrical insulation for the winding and cooling of the transformer is concerned. As transformers are always under the influence of electrical and thermal stresses, incipient faults like partial discharge, sparking and arcing take place. As a result, mineral oil deteriorates there by premature failure of the transformer occurs causing huge losses in terms of revenue and assets. Therefore, the transformer health condition has to be monitored continuously. The Dissolved Gas Analysis (DGA) is being extensively used for this purpose, but it has some drawbacks like it needs carrier gas, regular instrument calibration, etc. To overcome these drawbacks, Ultraviolet (UV) -Visible and Fourier Transform Infrared (FTIR) Spectro-photometric techniques are used as diagnostic tools for investigating the degraded transformer oil affected by electrical, mechanical and thermal stresses. The technique has several advantages over the conventional DGA technique.

Analysis of bacteria on steel surfaces using reflectance micro-Fourier transform infrared spectroscopy.

PubMed

Ojeda, Jesús J; Romero-González, María E; Banwart, Steven A

2009-08-01

Reflectance micro-Fourier transform infrared (FT-IR) analysis has been applied to characterize biofilm formation of Aquabacterium commune, a common microorganism present on drinking water distribution systems, onto the increasingly popular pipe material stainless steel EN1.4307. The applicability of the reflectance micro-FT-IR technique for analyzing the bacterial functional groups is discussed, and the results are compared to spectra obtained using more conventional FT-IR techniques: transmission micro-FT-IR, attenuated transmitted reflectance (ATR), and KBr pellets. The differences between the infrared spectra of wet and dried bacteria, as well as free versus attached bacteria, are also discussed. The spectra obtained using reflectance micro-FT-IR spectroscopy were comparable to those obtained using other FT-IR techniques. The absence of sample preparation, the potential to analyze intact samples, and the ability to characterize opaque and thick samples without the need to transfer the bacterial samples to an infrared transparent medium or produce a pure culture were the main advantages of reflectance micro-FT-IR spectroscopy.

Electron capture dissociation of polypeptides using a 3 Tesla Fourier transform ion cyclotron resonance mass spectrometer.

PubMed

Polfer, Nicolas C; Haselmann, Kim F; Zubarev, Roman A; Langridge-Smith, Pat R R

2002-01-01

Electron capture dissociation (ECD) of polypeptides has been demonstrated using a commercially available 3 Tesla Fourier transform ion cyclotron resonance (FTICR) instrument. A conventional rhenium filament, designed for high-energy electron impact ionisation, was used to effect ECD of substance P, bee venom melittin and bovine insulin, oxidised B chain. A retarding field analysis of the effective electron kinetic energy distribution entering the ICR cell suggests that one of the most important parameters governing ECD for this particular instrument is the need to employ low trapping plate voltages. This is shown to maximise the abundance of low-energy electrons. The demonstration of ECD at this relatively low magnetic field strength could offer the prospect of more routine ECD analysis for the wider research community, given the reduced cost of such magnets and (at least theoretically) the greater ease of electron/ion cloud overlap at lower field. Copyright 2002 John Wiley & Sons, Ltd.

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.

Evaluation of biodegradable plastics for rubber seedling applications

NASA Astrophysics Data System (ADS)

Mansor, Mohd Khairulniza; Dayang Habibah A. I., H.; Kamal, Mazlina Mustafa

2015-08-01

The main negative consequence of conventional plastics in agriculture is related to handling the wastes plasticand the associated environmental impact. Hence, a study of different types of potentially biodegradable plastics used for nursery applications have been evaluated on its mechanical,water absorption propertiesand Fourier transform infra-red (FTIR) spectroscopy. Supplied samples from different companies were designated as SF, CF and CO. Most of the polybags exhibited mechanical properties quite similar to the conventional plastics (polybag LDPE). CO polybag which is based on PVA however had extensively higher tensile strength and water absorption properties. FTIR study revealed a characteristics absorbance of conventional plastic, SF, CF and CO biodegradable polybag are associated with polyethylene, poly(butylene adipate-co-terephthalate) (PBAT), polyethylene and polyvinyl alcohol (PVA) structures respectively.

Molecular evidence of heavy-oil weathering following the M/V Cosco Busan spill: insights from Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Lemkau, Karin L; McKenna, Amy M; Podgorski, David C; Rodgers, Ryan P; Reddy, Christopher M

2014-04-01

Recent studies have highlighted a critical need to investigate oil weathering beyond the analytical window afforded by conventional gas chromatography (GC). In particular, techniques capable of detecting polar and higher molecular weight (HMW; > 400 Da) components abundant in crude and heavy fuel oils (HFOs) as well as transformation products. Here, we used atmospheric pressure photoionization Fourier transform ion cyclotron resonance mass spectrometry (APPI FT-ICR MS) to identify molecular transformations in oil-residue samples from the 2007 M/V Cosco Busan HFO spill (San Francisco, CA). Over 617 days, the abundance and diversity of oxygen-containing compounds increased relative to the parent HFO, likely from bio- and photodegradation. HMW, highly aromatic, alkylated compounds decreased in relative abundance concurrent with increased relative abundance of less alkylated stable aromatic structures. Combining these results with GC-based data yielded a more comprehensive understanding of oil spill weathering. For example, dealkylation trends and the overall loss of HMW species observed by FT-ICR MS has not previously been documented and is counterintuitive given losses of lower molecular weight species observed by GC. These results suggest a region of relative stability at the interface of these techniques, which provides new indicators for studying long-term weathering and identifying sources.

Radar Measurements of Ocean Surface Waves using Proper Orthogonal Decomposition

DTIC Science & Technology

2017-03-30

rely on use of Fourier transforms (FFT) and filtering spectra on the linear dispersion relationship for ocean surface waves. This report discusses...the measured signal (e.g., Young et al., 1985). In addition, the methods often rely on filtering the FFT of radar backscatter or Doppler velocities...to those obtained with conventional FFT and dispersion curve filtering techniques (iv) Compare both results of(iii) to ground truth sensors (i .e

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.

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

ERIC Educational Resources Information Center

Eastman, M. P.; And Others

1986-01-01

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

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)

The application and improvement of Fourier transform spectrometer experiment

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

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.

Pattern-Recognition Processor Using Holographic Photopolymer

NASA Technical Reports Server (NTRS)

Chao, Tien-Hsin; Cammack, Kevin

2006-01-01

proposed joint-transform optical correlator (JTOC) would be capable of operating as a real-time pattern-recognition processor. The key correlation-filter reading/writing medium of this JTOC would be an updateable holographic photopolymer. The high-resolution, high-speed characteristics of this photopolymer would enable pattern-recognition processing to occur at a speed three orders of magnitude greater than that of state-of-the-art digital pattern-recognition processors. There are many potential applications in biometric personal identification (e.g., using images of fingerprints and faces) and nondestructive industrial inspection. In order to appreciate the advantages of the proposed JTOC, it is necessary to understand the principle of operation of a conventional JTOC. In a conventional JTOC (shown in the upper part of the figure), a collimated laser beam passes through two side-by-side spatial light modulators (SLMs). One SLM displays a real-time input image to be recognized. The other SLM displays a reference image from a digital memory. A Fourier-transform lens is placed at its focal distance from the SLM plane, and a charge-coupled device (CCD) image detector is placed at the back focal plane of the lens for use as a square-law recorder. Processing takes place in two stages. In the first stage, the CCD records the interference pattern between the Fourier transforms of the input and reference images, and the pattern is then digitized and saved in a buffer memory. In the second stage, the reference SLM is turned off and the interference pattern is fed back to the input SLM. The interference pattern thus becomes Fourier-transformed, yielding at the CCD an image representing the joint-transform correlation between the input and reference images. This image contains a sharp correlation peak when the input and reference images are matched. The drawbacks of a conventional JTOC are the following: The CCD has low spatial resolution and is not an ideal square-law detector for the purpose of holographic recording of interference fringes. A typical state-of-the-art CCD has a pixel-pitch limited resolution of about 100 lines/mm. In contrast, the holographic photopolymer to be used in the proposed JTOC offers a resolution > 2,000 lines/mm. In addition to being disadvantageous in itself, the low resolution of the CCD causes overlap of a DC term and the desired correlation term in the output image. This overlap severely limits the correlation signal-to-noise ratio. The two-stage nature of the process limits the achievable throughput rate. A further limit is imposed by the low frame rate (typical video rates) of low- and medium-cost commercial CCDs.

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

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

[Optical-fiber Fourier transform spectrometer].

PubMed

Liu, Yong; Li, Bao-sheng; Liu, Yan; Zhai, Yu-feng; Wang, An

2006-10-01

A novel Fourier transform spectrum analyzer based on a single mode fiber Mach-Zehnder interferometer is reported. An optical fiber Fourier transform spectrometer, with bulk optics components replaced by fiber optical components and with the moving mirror replaced by a piezoelectric element fiber stretcher was constructed. The output spectrum of a LD below threshold was measured. Experiment result agrees with that by using grating spectrum analyzer, showing the feasibility of the optic fiber Fourier transform spectrometer for practical spectrum measurement. Spectrum resolution -7 cm(-1) was obtained in our experiment. The resolution can be further improved by increasing the maximum optical path difference.

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

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)

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

PubMed

Guo, Ya; Tan, Jinglu

2014-12-21

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

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.

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.

Extraction of microseismic waveforms characteristics prior to rock burst using Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Li, Xuelong; Li, Zhonghui; Wang, Enyuan; Feng, Junjun; Chen, Liang; Li, Nan; Kong, Xiangguo

2016-09-01

This study provides a new research idea concerning rock burst prediction. The characteristics of microseismic (MS) waveforms prior to and during the rock burst were studied through the Hilbert-Huang transform (HHT). In order to demonstrate the advantage of the MS features extraction based on HHT, the conventional analysis method (Fourier transform) was also used to make a comparison. The results show that HHT is simple and reliable, and could extract in-depth information about the characteristics of MS waveforms. About 10 days prior to the rock burst, the main frequency of MS waveforms transforms from the high-frequency to low-frequency. What's more, the waveforms energy also presents accumulation characteristic. Based on our study results, it can be concluded that the MS signals analysis through HHT could provide valuable information about the coal or rock deformation and fracture.

Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform.

PubMed

Larkin, Kieran G; Fletcher, Peter A

2014-03-01

X-ray Talbot moiré interferometers can now simultaneously generate two differential phase images of a specimen. The conventional approach to integrating differential phase is unstable and often leads to images with loss of visible detail. We propose a new reconstruction method based on the inverse Riesz transform. The Riesz approach is stable and the final image retains visibility of high resolution detail without directional bias. The outline Riesz theory is developed and an experimentally acquired X-ray differential phase data set is presented for qualitative visual appraisal. The inverse Riesz phase image is compared with two alternatives: the integrated (quantitative) phase and the modulus of the gradient of the phase. The inverse Riesz transform has the computational advantages of a unitary linear operator, and is implemented directly as a complex multiplication in the Fourier domain also known as the spiral phase transform.

Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform

PubMed Central

Larkin, Kieran G.; Fletcher, Peter A.

2014-01-01

X-ray Talbot moiré interferometers can now simultaneously generate two differential phase images of a specimen. The conventional approach to integrating differential phase is unstable and often leads to images with loss of visible detail. We propose a new reconstruction method based on the inverse Riesz transform. The Riesz approach is stable and the final image retains visibility of high resolution detail without directional bias. The outline Riesz theory is developed and an experimentally acquired X-ray differential phase data set is presented for qualitative visual appraisal. The inverse Riesz phase image is compared with two alternatives: the integrated (quantitative) phase and the modulus of the gradient of the phase. The inverse Riesz transform has the computational advantages of a unitary linear operator, and is implemented directly as a complex multiplication in the Fourier domain also known as the spiral phase transform. PMID:24688823

Applications of wavelets in interferometry and artificial vision

NASA Astrophysics Data System (ADS)

Escalona Z., Rafael A.

2001-08-01

In this paper we present a different point of view of phase measurements performed in interferometry, image processing and intelligent vision using Wavelet Transform. In standard and white-light interferometry, the phase function is retrieved by using phase-shifting, Fourier-Transform, cosinus-inversion and other known algorithms. Our novel technique presented here is faster, robust and shows excellent accuracy in phase determinations. Finally, in our second application, fringes are no more generate by some light interaction but result from the observation of adapted strip set patterns directly printed on the target of interest. The moving target is simply observed by a conventional vision system and usual phase computation algorithms are adapted to an image processing by wavelet transform, in order to sense target position and displacements with a high accuracy. In general, we have determined that wavelet transform presents properties of robustness, relative speed of calculus and very high accuracy in phase computations.

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.

MR Image Reconstruction Using Block Matching and Adaptive Kernel Methods.

PubMed

Schmidt, Johannes F M; Santelli, Claudio; Kozerke, Sebastian

2016-01-01

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ1-regularized parallel imaging methods.

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.

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.

Collision cross section (CCS) measurement by ion cyclotron resonance mass spectrometry with short-time Fourier transform.

PubMed

Hu, Miao; Zhang, Linzhou; He, Shan; Xu, Chunming; Shi, Quan

2018-05-15

The collision cross section (CCS) is an important shape parameter which is often used in molecular structure investigation. In Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), the CCS affects the ion signal damping shape due to the effect of ion-neutral collisions. It is potential to obtain ion CCS values from FTICR-MS with the help of a proper ion-collision model. We have developed a rapid method to obtain the ion damping profile and CCS for mixtures by only one FTICR-MS measurement. The method utilizes short-time Fourier transform (STFT) to process FTICR-MS time domain signals. The STFT-processed result is a three-dimensional (3D) spectrum which has an additional time axis in addition to the conventional mass-to-charge ratio and intensity domains. The damping profile of each ion can be recognized from the 3D spectrum. After extracting the decay profile of a specified ion, all the three ion-neutral collision models were tested in curve fitting. The hard-sphere model was proven to be suitable for our experimental setup. A linear relationship was observed between the CCS value and hard-sphere model parameters. Therefore, the CCS values of all the peaks were obtained through the addition of internal model compounds and linear calibration. The proposed method was successfully applied to determine the CCSs of fatty acids and polyalanines in a petroleum gas oil matrix. This technique can be used for simultaneous measurement of cross sections for many ions in congested spectra. Copyright © 2018 John Wiley & Sons, Ltd.

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

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.

Double peak-induced distance error in short-time-Fourier-transform-Brillouin optical time domain reflectometers event detection and the recovery method.

PubMed

Yu, Yifei; Luo, Linqing; Li, Bo; Guo, Linfeng; Yan, Jize; Soga, Kenichi

2015-10-01

The measured distance error caused by double peaks in the BOTDRs (Brillouin optical time domain reflectometers) system is a kind of Brillouin scattering spectrum (BSS) deformation, discussed and simulated for the first time in the paper, to the best of the authors' knowledge. Double peak, as a kind of Brillouin spectrum deformation, is important in the enhancement of spatial resolution, measurement accuracy, and crack detection. Due to the variances of the peak powers of the BSS along the fiber, the measured starting point of a step-shape frequency transition region is shifted and results in distance errors. Zero-padded short-time-Fourier-transform (STFT) can restore the transition-induced double peaks in the asymmetric and deformed BSS, thus offering more accurate and quicker measurements than the conventional Lorentz-fitting method. The recovering method based on the double-peak detection and corresponding BSS deformation can be applied to calculate the real starting point, which can improve the distance accuracy of the STFT-based BOTDR system.

Effect of ingested tungsten oxide (WOx) nanofibers on digestive gland tissue of Porcellio scaber (Isopoda, Crustacea): fourier transform infrared (FTIR) imaging.

PubMed

Novak, Sara; Drobne, Damjana; Vaccari, Lisa; Kiskinova, Maya; Ferraris, Paolo; Birarda, Giovanni; Remškar, Maja; Hočevar, Matej

2013-10-01

Tungsten nanofibers are recognized as biologically potent. We study deviations in molecular composition between normal and digestive gland tissue of WOx nanofibers (nano-WOx) fed invertebrate Porcellio scaber (Iosopda, Crustacea) and revealed mechanisms of nano-WOx effect in vivo. Fourier Transform Infrared (FTIR) imaging performed on digestive gland epithelium was supplemented by toxicity and cytotoxicity analyses as well as scanning electron microscopy (SEM) of the surface of the epithelium. The difference in the spectra of the Nano-WOx treated and control cells showed up in the central region of the cells and were related to lipid peroxidation, and structural changes of nucleic acids. The conventional toxicity parameters failed to show toxic effects of nano-WOx, whereas the cytotoxicity biomarkers and SEM investigation of digestive gland epithelium indicated sporadic effects of nanofibers. Since toxicological and cytological measurements did not highlight severe effects, the biochemical alterations evidenced by FTIR imaging have been explained as the result of cell protection (acclimation) mechanisms to unfavorable conditions and indication of a nonhomeostatic state, which can lead to toxic effects.

Hyperspectral imager for components identification in the atmosphere

NASA Astrophysics Data System (ADS)

Dewandel, Jean-Luc; Beghuin, Didier; Dubois, Xavier; Antoine, Philippe

2017-11-01

Several applications require the identification of chemical elements during re-entry of material in the atmosphere. The materials can be from human origin or meteorites. The Automated Transfer Vehicle (ATV) re-entry has been filmed with conventional camera from airborne manual operation. In order to permit the identification of the separate elements from their glow, spectral analysis needs to be added to the video data. In a LET-SME contract with ESA, Lambda-X has built a Fourier Transform Imaging Spectrometer to permit, in a future work, to bring the technology to the readiness level required for the application. In this paper, the principles of the Fourier Transform Imaging spectroscopy are recalled, the different interferometers suitable for supporting the technique are reviewed and the selection process is explained. The final selection of the interferometer corresponds to a birefringent prism based common path shear interferometer. The design of the breadboard and its performances are presented in terms of spatial resolution, aperture, and spectral resolution. A discussion is open regarding perspective of the technique for other remote sensing applications compared to more usual push broom configurations.

Cloud cover typing from environmental satellite imagery. Discriminating cloud structure with Fast Fourier Transforms (FFT)

NASA Technical Reports Server (NTRS)

Logan, T. L.; Huning, J. R.; Glackin, D. L.

1983-01-01

The use of two dimensional Fast Fourier Transforms (FFTs) subjected to pattern recognition technology for the identification and classification of low altitude stratus cloud structure from Geostationary Operational Environmental Satellite (GOES) imagery was examined. The development of a scene independent pattern recognition methodology, unconstrained by conventional cloud morphological classifications was emphasized. A technique for extracting cloud shape, direction, and size attributes from GOES visual imagery was developed. These attributes were combined with two statistical attributes (cloud mean brightness, cloud standard deviation), and interrogated using unsupervised clustering amd maximum likelihood classification techniques. Results indicate that: (1) the key cloud discrimination attributes are mean brightness, direction, shape, and minimum size; (2) cloud structure can be differentiated at given pixel scales; (3) cloud type may be identifiable at coarser scales; (4) there are positive indications of scene independence which would permit development of a cloud signature bank; (5) edge enhancement of GOES imagery does not appreciably improve cloud classification over the use of raw data; and (6) the GOES imagery must be apodized before generation of FFTs.

Quantification of microplastic mass and removal rates at wastewater treatment plants applying Focal Plane Array (FPA)-based Fourier Transform Infrared (FT-IR) imaging.

PubMed

Simon, Márta; van Alst, Nikki; Vollertsen, Jes

2018-05-17

This paper presents a method for microplastic (MP) mass quantification using a Focal Plane Array-based Fourier Transform Infrared imaging technique. It discusses the issue that particle number is not a conserved base quantity and hence less suited than mass to compare independent studies on MP in the environment. It concludes that MP mass should be included when quantifying MP pollution in the environment, supplementing the conventional approach of reporting particle numbers. Applying mass as the unit of MP measurement, the paper presents data showing that Danish wastewater treatment plants discharge around 3 t/year of MP in the size range 10-500 μm. This value corresponds to an annual per capita emission from these plants of 0.56 g MP/(capita year). The distribution of polymer types by mass and particle number differed because the size of MP particles of the different material types varied. Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.

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.

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

PubMed

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

Secure Hashing of Dynamic Hand Signatures Using Wavelet-Fourier Compression with BioPhasor Mixing and [InlineEquation not available: see fulltext.] Discretization

NASA Astrophysics Data System (ADS)

Wai Kuan, Yip; Teoh, Andrew B. J.; Ngo, David C. L.

2006-12-01

We introduce a novel method for secure computation of biometric hash on dynamic hand signatures using BioPhasor mixing and[InlineEquation not available: see fulltext.] discretization. The use of BioPhasor as the mixing process provides a one-way transformation that precludes exact recovery of the biometric vector from compromised hashes and stolen tokens. In addition, our user-specific[InlineEquation not available: see fulltext.] discretization acts both as an error correction step as well as a real-to-binary space converter. We also propose a new method of extracting compressed representation of dynamic hand signatures using discrete wavelet transform (DWT) and discrete fourier transform (DFT). Without the conventional use of dynamic time warping, the proposed method avoids storage of user's hand signature template. This is an important consideration for protecting the privacy of the biometric owner. Our results show that the proposed method could produce stable and distinguishable bit strings with equal error rates (EERs) of[InlineEquation not available: see fulltext.] and[InlineEquation not available: see fulltext.] for random and skilled forgeries for stolen token (worst case) scenario, and[InlineEquation not available: see fulltext.] for both forgeries in the genuine token (optimal) scenario.

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.

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.

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.

Direct and simultaneous quantification of tannin mean degree of polymerization and percentage of galloylation in grape seeds using diffuse reflectance fourier transform-infrared spectroscopy.

PubMed

Pappas, Christos; Kyraleou, Maria; Voskidi, Eleni; Kotseridis, Yorgos; Taranilis, Petros A; Kallithraka, Stamatina

2015-02-01

The direct and simultaneous quantitative determination of the mean degree of polymerization (mDP) and the degree of galloylation (%G) in grape seeds were quantified using diffuse reflectance infrared Fourier transform spectroscopy and partial least squares (PLS). The results were compared with those obtained using the conventional analysis employing phloroglucinolysis as pretreatment followed by high performance liquid chromatography-UV and mass spectrometry detection. Infrared spectra were recorded in solid state samples after freeze drying. The 2nd derivative of the 1832 to 1416 and 918 to 739 cm(-1) spectral regions for the quantification of mDP, the 2nd derivative of the 1813 to 607 cm(-1) spectral region for the degree of %G determination and PLS regression were used. The determination coefficients (R(2) ) of mDP and %G were 0.99 and 0.98, respectively. The corresponding values of the root-mean-square error of calibration were found 0.506 and 0.692, the root-mean-square error of cross validation 0.811 and 0.921, and the root-mean-square error of prediction 0.612 and 0.801. The proposed method in comparison with the conventional method is simpler, less time consuming, more economical, and requires reduced quantities of chemical reagents and fewer sample pretreatment steps. It could be a starting point for the design of more specific models according to the requirements of the wineries. © 2015 Institute of Food Technologists®

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

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...

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.

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.

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.

A new method to estimate local pitch angles in spiral galaxies: Application to spiral arms and feathers in M81 and M51

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

Puerari, Ivânio; Elmegreen, Bruce G.; Block, David L., E-mail: puerari@inaoep.mx

2014-12-01

We examine 8 μm IRAC images of the grand design two-arm spiral galaxies M81 and M51 using a new method whereby pitch angles are locally determined as a function of scale and position, in contrast to traditional Fourier transform spectral analyses which fit to average pitch angles for whole galaxies. The new analysis is based on a correlation between pieces of a galaxy in circular windows of (lnR,θ) space and logarithmic spirals with various pitch angles. The diameter of the windows is varied to study different scales. The result is a best-fit pitch angle to the spiral structure as amore » function of position and scale, or a distribution function of pitch angles as a function of scale for a given galactic region or area. We apply the method to determine the distribution of pitch angles in the arm and interarm regions of these two galaxies. In the arms, the method reproduces the known pitch angles for the main spirals on a large scale, but also shows higher pitch angles on smaller scales resulting from dust feathers. For the interarms, there is a broad distribution of pitch angles representing the continuation and evolution of the spiral arm feathers as the flow moves into the interarm regions. Our method shows a multiplicity of spiral structures on different scales, as expected from gas flow processes in a gravitating, turbulent and shearing interstellar medium. We also present results for M81 using classical 1D and 2D Fourier transforms, together with a new correlation method, which shows good agreement with conventional 2D Fourier transforms.« less

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.

Microwave and Infrared Absorption Properties of Atmospheric Species with Special Emphasis on Line Widths and Shifts.

DTIC Science & Technology

1985-07-01

studied pressure-broadening of the 110.8 GHz line of ozone (6 1 5 6 0 6) for the foreign gases N2 and 02. Considering a temper- ature range from 200...nitrogen and oxygen as tje perturbing gases . Calculations using * conventional Anderson theory or quantum Fourier transform theory2 are shown to be...one gases in the region from 0 to 10,000 cm-’. Emphasis on this edition has been on the addition of numerous millimeter and submillimeter transitions

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.

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.

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...

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.

3-D surface profilometry based on modulation measurement by applying wavelet transform method

NASA Astrophysics Data System (ADS)

Zhong, Min; Chen, Feng; Xiao, Chao; Wei, Yongchao

2017-01-01

A new analysis of 3-D surface profilometry based on modulation measurement technique by the application of Wavelet Transform method is proposed. As a tool excelling for its multi-resolution and localization in the time and frequency domains, Wavelet Transform method with good localized time-frequency analysis ability and effective de-noizing capacity can extract the modulation distribution more accurately than Fourier Transform method. Especially for the analysis of complex object, more details of the measured object can be well remained. In this paper, the theoretical derivation of Wavelet Transform method that obtains the modulation values from a captured fringe pattern is given. Both computer simulation and elementary experiment are used to show the validity of the proposed method by making a comparison with the results of Fourier Transform method. The results show that the Wavelet Transform method has a better performance than the Fourier Transform method in modulation values retrieval.

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...

Complete fourier direct magnetic resonance imaging (CFD-MRI) for diffusion MRI

PubMed Central

Özcan, Alpay

2013-01-01

The foundation for an accurate and unifying Fourier-based theory of diffusion weighted magnetic resonance imaging (DW–MRI) is constructed by carefully re-examining the first principles of DW–MRI signal formation and deriving its mathematical model from scratch. The derivations are specifically obtained for DW–MRI signal by including all of its elements (e.g., imaging gradients) using complex values. Particle methods are utilized in contrast to conventional partial differential equations approach. The signal is shown to be the Fourier transform of the joint distribution of number of the magnetic moments (at a given location at the initial time) and magnetic moment displacement integrals. In effect, the k-space is augmented by three more dimensions, corresponding to the frequency variables dual to displacement integral vectors. The joint distribution function is recovered by applying the Fourier transform to the complete high-dimensional data set. In the process, to obtain a physically meaningful real valued distribution function, phase corrections are applied for the re-establishment of Hermitian symmetry in the signal. Consequently, the method is fully unconstrained and directly presents the distribution of displacement integrals without any assumptions such as symmetry or Markovian property. The joint distribution function is visualized with isosurfaces, which describe the displacement integrals, overlaid on the distribution map of the number of magnetic moments with low mobility. The model provides an accurate description of the molecular motion measurements via DW–MRI. The improvement of the characterization of tissue microstructure leads to a better localization, detection and assessment of biological properties such as white matter integrity. The results are demonstrated on the experimental data obtained from an ex vivo baboon brain. PMID:23596401

Application of multibounce attenuated total reflectance fourier transform infrared spectroscopy and chemometrics for determination of aspartame in soft drinks.

PubMed

Khurana, Harpreet Kaur; Cho, Il Kyu; Shim, Jae Yong; Li, Qing X; Jun, Soojin

2008-02-13

Aspartame is a low-calorie sweetener commonly used in soft drinks; however, the maximum usage dose is limited by the U.S. Food and Drug Administration. Fourier transform infrared (FTIR) spectroscopy with attenuated total reflectance sampling accessory and partial least-squares regression (PLS) was used for rapid determination of aspartame in soft drinks. On the basis of spectral characterization, the highest R2 value, and lowest PRESS value, the spectral region between 1600 and 1900 cm(-1) was selected for quantitative estimation of aspartame. The potential of FTIR spectroscopy for aspartame quantification was examined and validated by the conventional HPLC method. Using the FTIR method, aspartame contents in four selected carbonated diet soft drinks were found to average from 0.43 to 0.50 mg/mL with prediction errors ranging from 2.4 to 5.7% when compared with HPLC measurements. The developed method also showed a high degree of accuracy because real samples were used for calibration, thus minimizing potential interference errors. The FTIR method developed can be suitably used for routine quality control analysis of aspartame in the beverage-manufacturing sector.

Liquid chromatography/Fourier transform IR spectrometry interface flow cell

DOEpatents

Johnson, Charles C.; Taylor, Larry T.

1986-01-01

A zero dead volume (ZDV) microbore high performance liquid chromatography (.mu.HPLC)/Fourier transform infrared (FTIR) interface flow cell includes an IR transparent crystal having a small diameter bore therein through which a sample liquid is passed. The interface flow cell further includes a metal holder in combination with a pair of inner, compressible seals for directly coupling the thus configured spectrometric flow cell to the outlet of a .mu.HPLC column end fitting to minimize the transfer volume of the effluents exiting the .mu.HPLC column which exhibit excellent flow characteristics due to the essentially unencumbered, open-flow design. The IR beam passes transverse to the sample flow through the circular bore within the IR transparent crystal, which is preferably comprised of potassium bromide (KBr) or calcium fluoride (CaF.sub.2), so as to minimize interference patterns and vignetting encountered in conventional parallel-plate IR cells. The long IR beam pathlength and lensing effect of the circular cross-section of the sample volume in combination with the refractive index differences between the solvent and the transparent crystal serve to focus the IR beam in enhancing sample detection sensitivity by an order of magnitude.

Liquid chromatography/Fourier transform IR spectrometry interface flow cell

DOEpatents

Johnson, C.C.; Taylor, L.T.

1985-01-04

A zero dead volume (ZDV) microbore high performance liquid chromatography (..mu.. HPLC)/Fourier transform infrared (FTIR) interface flow cell includes an IR transparent crystal having a small diameter bore therein through which a sample liquid is passed. The interface flow cell further includes a metal holder in combination with a pair of inner, compressible seals for directly coupling the thus configured spectrometric flow cell to the outlet of a ..mu.. HPLC column end fitting to minimize the transfer volume of the effluents exiting the ..mu.. HPLC column which exhibit excellent flow characteristics due to the essentially unencumbered, open-flow design. The IR beam passes transverse to the sample flow through the circular bore within the IR transparent crystal, which is preferably comprised of potassium bromide (KBr) or calcium fluoride (CaF/sub 2/), so as to minimize interference patterns and vignetting encountered in conventional parallel-plate IR cells. The long IR beam pathlength and lensing effect of the circular cross-section of the sample volume in combination with the refractive index differences between the solvent and the transparent crystal serve to focus the IR beam in enhancing sample detection sensitivity by an order of magnitude.

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

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.

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)

Data Reduction and Image Reconstruction Techniques for Non-redundant Masking

NASA Astrophysics Data System (ADS)

Sallum, S.; Eisner, J.

2017-11-01

The technique of non-redundant masking (NRM) transforms a conventional telescope into an interferometric array. In practice, this provides a much better constrained point-spread function than a filled aperture and thus higher resolution than traditional imaging methods. Here, we describe an NRM data reduction pipeline. We discuss strategies for NRM observations regarding dithering patterns and calibrator selection. We describe relevant image calibrations and use example Large Binocular Telescope data sets to show their effects on the scatter in the Fourier measurements. We also describe the various ways to calculate Fourier quantities, and discuss different calibration strategies. We present the results of image reconstructions from simulated observations where we adjust prior images, weighting schemes, and error bar estimation. We compare two imaging algorithms and discuss implications for reconstructing images from real observations. Finally, we explore how the current state of the art compares to next-generation Extremely Large Telescopes.

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.

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 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.

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.

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

PubMed

Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

2012-04-20

It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

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.

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)

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.

[Differentiation and characterization of yeasts pathogenic for humans (Candida albicans, Exophiala dermatitidis) and algae pathogenic for animals (Prototheca spp.) using Fourier transform infrared spectroscopy (FTIR) in comparison with conventional methods].

PubMed

Schmalreck, A F; Tränkle, P; Vanca, E; Blaschke-Hellmessen, R

1998-01-01

Due to the Fourier-Transform Infrared Spectroscopy (FT-IR) of strain specific traits demonstrated to be a suitable and efficient method for diagnostic and epidemiological determinations for the yeasts Candida albicans, Exophiala dermatitidis and the chlorophylless algae of the genus Prototheca. FT-IR leads in a rapid and economical way to reproducible results according to the spectral differences of intact cells (IR-fingerprints). Different genera, species and sub-species respectively, different strains can be recognized and grouped into different clusters and subclusters. The FT-IR analysis of Candida albicans isolates (n = 150) of 22 newborns-at-risk of an intensive care unit showed, that 86% of the children were colonised with several (2-4) different strains in the oral cavities and faeces. Stationary cross-infections could definitely be determined. Exophiala dermatitidis isolates (n = 31), mostly isolated repetitively within a period of 3 years from sputa of patients suffering from cystic fibrosis could be characterized and grouped patient-specifically over the total sampling period. Of 6 from 8 patients (75%) their individual strains remain the same and could be tracked over the three years. Cross-infections during the stationary treatment could be clearly identified by FT-IR. The Prototheca isolate (n = 43) from live-stock and farm environment showed clear distinguishable clusters differentiating the species P. wickerhamii, P. zopfii and P. stagnora. In addition, the biotypes of P. zopfii could be distinguished, especially the subclusters of variants II and III. It could be demonstrated, that FT-IR is suitable for the routine identification and differentiation of yeasts and algae. However, in spite of the gain of knowledge by using FT-IR for the characterization of microorganisms, the conventional phenotyping and/or genetic analysis of yeast or algae strains cannot be replaced completely. For a final taxonomic classification a combination of conventional methods on FT-IR together with more sophisticated molecular genetic procedures is necessary.

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.

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

PubMed

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

2011-06-24

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

Automated Bayesian model development for frequency detection in biological time series

PubMed Central

2011-01-01

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

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.

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...

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

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.

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 High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions

NASA Technical Reports Server (NTRS)

Sun, Xian-He; Zhuang, Yu

1997-01-01

In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.

Mid-infrared, long wave infrared (4-12 μm) molecular emission signatures from pharmaceuticals using laser-induced breakdown spectroscopy (LIBS).

PubMed

Yang, Clayton S-C; Brown, Ei E; Kumi-Barimah, Eric; Hommerich, Uwe H; Jin, Feng; Trivedi, Sudhir B; Samuels, Alan C; Snyder, A Peter

2014-01-01

In an effort to augment the atomic emission spectra of conventional laser-induced breakdown spectroscopy (LIBS) and to provide an increase in selectivity, mid-wave to long-wave infrared (IR), LIBS studies were performed on several organic pharmaceuticals. Laser-induced breakdown spectroscopy signature molecular emissions of target organic compounds are observed for the first time in the IR fingerprint spectral region between 4-12 μm. The IR emission spectra of select organic pharmaceuticals closely correlate with their respective standard Fourier transform infrared spectra. Intact and/or fragment sample molecular species evidently survive the LIBS event. The combination of atomic emission signatures derived from conventional ultraviolet-visible-near-infrared LIBS with fingerprints of intact molecular entities determined from IR LIBS promises to be a powerful tool for chemical detection.

Dynamics of modulated beams in spectral domain

DOE PAGES

Yampolsky, Nikolai A.

2017-07-16

General formalism for describing dynamics of modulated beams along linear beamlines is developed. We describe modulated beams with spectral distribution function which represents Fourier transform of the conventional beam distribution function in the 6-dimensional phase space. The introduced spectral distribution function is localized in some region of the spectral domain for nearly monochromatic modulations. It can be characterized with a small number of typical parameters such as the lowest order moments of the spectral distribution. We study evolution of the modulated beams in linear beamlines and find that characteristic spectral parameters transform linearly. The developed approach significantly simplifies analysis ofmore » various schemes proposed for seeding X-ray free electron lasers. We use this approach to study several recently proposed schemes and find the bandwidth of the output bunching in each case.« less

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.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

PubMed

Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun

2009-05-01

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

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.

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

Investigation of hidden periodic structures on SEM images of opal-like materials using FFT and IFFT.

PubMed

Stephant, Nicolas; Rondeau, Benjamin; Gauthier, Jean-Pierre; Cody, Jason A; Fritsch, Emmanuel

2014-01-01

We have developed a method to use fast Fourier transformation (FFT) and inverse fast Fourier transformation (IFFT) to investigate hidden periodic structures on SEM images. We focused on samples of natural, play-of-color opals that diffract visible light and hence are periodically structured. Conventional sample preparation by hydrofluoric acid etch was not used; untreated, freshly broken surfaces were examined at low magnification relative to the expected period of the structural features, and, the SEM was adjusted to get a very high number of pixels in the images. These SEM images were treated by software to calculate autocorrelation, FFT, and IFFT. We present how we adjusted SEM acquisition parameters for best results. We first applied our procedure on an SEM image on which the structure was obvious. Then, we applied the same procedure on a sample that must contain a periodic structure because it diffracts visible light, but on which no structure was visible on the SEM image. In both cases, we obtained clearly periodic patterns that allowed measurements of structural parameters. We also investigated how the irregularly broken surface interfered with the periodic structure to produce additional periodicity. We tested the limits of our methodology with the help of simulated images. © 2014 Wiley Periodicals, Inc.

A Direction Finding Method with A 3-D Array Based on Aperture Synthesis

NASA Astrophysics Data System (ADS)

Li, Shiwen; Chen, Liangbing; Gao, Zhaozhao; Ma, Wenfeng

2018-01-01

Direction finding for electronic warfare application should provide a wider field of view as possible. But the maximum unambiguous field of view for conventional direction finding methods is a hemisphere. It cannot distinguish the direction of arrival of the signals from the back lobe of the array. In this paper, a full 3-D direction finding method based on aperture synthesis radiometry is proposed. The model of the direction finding system is illustrated, and the fundamentals are presented. The relationship between the outputs of the measurements of a 3-D array and the 3-D power distribution of the point sources can be represented by a 3-D Fourier transform, and then the 3-D power distribution of the point sources can be reconstructed by an inverse 3-D Fourier transform. And in order to display the 3-D power distribution of the point sources conveniently, the whole spherical distribution is represented by two 2-D circular distribution images, one of which is for the upper hemisphere, and the other is for the lower hemisphere. Then a numeric simulation is designed and conducted to demonstrate the feasibility of the method. The results show that the method can estimate the arbitrary direction of arrival of the signals in the 3-D space correctly.

First Signal on the Cryogenic Fourier-Transform Ion Cyclotron Resonance Mass Spectrometer

PubMed Central

Lin, Cheng; Mathur, Raman; Aizikov, Kostantin; O'Connor, Peter B.

2009-01-01

The construction and achievement of the first signal on a cryogenic Fourier-transform ion cyclotron resonance mass spectrometer (FT-ICR-MS) are reported here, demonstrating proof-of-concept of this new instrument design. Building the FTICR cell into the cold bore of a superconducting magnet provided advantages over conventional warm bore design. At 4.2 K, the vacuum system cryopumps itself, thus removing the requirement for a large bore to achieve the desired pumping speed for maintaining base pressure. Furthermore, because the bore diameter has been reduced, the amount of magnet wire needed to achieve high field and homogeneity was also reduced, greatly decreasing the cost/Tesla of the magnet. The current instrument implements an actively shielded 14-Tesla magnet of vertical design with an external matrix assisted laser desorption/ionization (MALDI) source. The first signal was obtained by detecting the laser desorbed/ionized (LDI) C60+• ions, with the magnet at 7 Tesla, unshimmed, and the preamplifier mounted outside of the vacuum chamber at room temperature. A subsequent experiment done with the magnet at 14 Tesla and properly shimmed produced a C60 spectrum showing ∼350,000 resolving power at m/z ∼720. Increased magnetic field strength improves many FTMS performance parameters simultaneously, particularly mass resolving power and accuracy. PMID:17931882

Advanced Mass Spectrometric Methods for the Rapid and Quantitative Characterization of Proteomes

DOE PAGES

Smith, Richard D.

2002-01-01

Progress is reviewedmore » towards the development of a global strategy that aims to extend the sensitivity, dynamic range, comprehensiveness and throughput of proteomic measurements based upon the use of high performance separations and mass spectrometry. The approach uses high accuracy mass measurements from Fourier transform ion cyclotron resonance mass spectrometry (FTICR) to validate peptide ‘accurate mass tags’ (AMTs) produced by global protein enzymatic digestions for a specific organism, tissue or cell type from ‘potential mass tags’ tentatively identified using conventional tandem mass spectrometry (MS/MS). This provides the basis for subsequent measurements without the need for MS/ MS. High resolution capillary liquid chromatography separations combined with high sensitivity, and high resolution accurate FTICR measurements are shown to be capable of characterizing peptide mixtures of more than 10 5 components. The strategy has been initially demonstrated using the microorganisms Saccharomyces cerevisiae and Deinococcus radiodurans. Advantages of the approach include the high confidence of protein identification, its broad proteome coverage, high sensitivity, and the capability for stableisotope labeling methods for precise relative protein abundance measurements. Abbreviations : LC, liquid chromatography; FTICR, Fourier transform ion cyclotron resonance; AMT, accurate mass tag; PMT, potential mass tag; MMA, mass measurement accuracy; MS, mass spectrometry; MS/MS, tandem mass spectrometry; ppm, parts per million.« less

Production of Starch Based Bioplastic from Cassava Peel Reinforced with Microcrystalline Celllulose Avicel PH101 Using Sorbitol as Plasticizer

NASA Astrophysics Data System (ADS)

Maulida; Siagian, M.; Tarigan, P.

2016-04-01

The production of starch based bioplastics from cassava peel reeinforced with microcrystalline cellulose using sorbitol as plasticizer were investigated. Physical properties of bioplastics were determined by density, water uptake, tensile strength and Fourier Transform Infrared Spectroscopy. Bioplastics were prepared from cassava peel starch plasticized using sorbitol with variation of 20; 25; 30% (wt/v of sorbitol to starch) reinforced with microcrystalline celllulose (MCC) Avicel PH101 fillers with range of 0 to 6% (wt/wt of MCC to starch). The results showed improvement in tensile strength with higher MCC content up to 9, 12 mpa compared to non-reinforced bioplastics. This could be mainly attributed to the strong hydrogen bonds between MCC and starch. On the contrary, the addition of MCC decreased the elongation at break, density and water uptake. Fourier Transform Infrared Spectroscopy showed the functional groups of bioplastics, which the majority of O-H groups were found at the bioplastics with reinforcing filler MCC that represented substantial hydrogen bonds. The highest tensile strength value was obtained for bioplastic with MCC content 6% and sorbitol content 20%. With good adhesion between MCC and starch the production of bioplastics could be widely used as a substitute for conventional plastics with more benefits to the environment.

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.

The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.

ERIC Educational Resources Information Center

Suslick, Kenneth S.; And Others

1987-01-01

Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)

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 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

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.

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.

Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods

NASA Astrophysics Data System (ADS)

Liu, Zhangjun; Liu, Zenghui; Peng, Yongbo

2018-03-01

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods.

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.

Synchrotron FTIR Imaging For The Identification Of Cell Types Within Human Tissues

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

Walsh, Michael J.; Pounder, F. Nell; Nasse, Michael J.

2010-02-03

The use of synchrotron Fourier Transform Infrared spectroscopy (S-FTIR) has been shown to be a very promising tool for biomedical research. S-FTIR spectroscopy allows for the fast acquisition of infrared (IR) spectra at a spatial resolution approaching the IR diffraction limit. The development of the Infrared Environmental Imaging (IRENI) beamline at the Synchrotron Radiation Center (SRC) at the University of Wisconsin-Madison has allowed for diffraction limited imaging measurements of cells in human prostate and breast tissues. This has allowed for the identification of cell types within tissues that would otherwise not have been resolvable using conventional FTIR sources.

Design of Phosphonated Imidazolium-Based Ionic Liquids Grafted on γ-Alumina: Potential Model for Hybrid Membranes

PubMed Central

Pizzoccaro, Marie-Alix; Drobek, Martin; Petit, Eddy; Guerrero, Gilles; Hesemann, Peter; Julbe, Anne

2016-01-01

Imidazolium bromide-based ionic liquids bearing phosphonyl groups on the cationic part were synthesized and grafted on γ-alumina (γ-Al2O3) powders. These powders were prepared as companion samples of conventional mesoporous γ-alumina membranes, in order to favor a possible transfer of the results to supported membrane materials, which could be used for CO2 separation applications. Effective grafting was demonstrated using energy dispersive X-ray spectrometry (EDX), N2 adsorption measurements, fourier transform infrared spectroscopy (FTIR), and special attention was paid to 31P and 13C solid state nuclear magnetic resonance spectroscopy (NMR). PMID:27472321

Neurotransmitters in the Gas Phase: La-Mb Studies

NASA Astrophysics Data System (ADS)

Cabezas, C.; Mata, S.; López, J. C.; Alonso, J. L.

2011-06-01

LA-MB-FTMW spectroscopy combines laser ablation with Fourier transform microwave spectroscopy in supersonic jets overcoming the problems of thermal decomposition associated with conventional heating methods. We present here the results on LA-MB-FTMW studies of some neurotransmitters. Six conformers of dopamine, four of adrenaline, five of noradrenaline and three conformers of serotonin have been characterized in the gas phase. The rotational and nuclear quadrupole coupling constants extracted from the analysis of the rotational spectrum are directly compared with those predicted by ab initio methods to achieve the conclusive identification of different conformers and the experimental characterization of the intramolecular forces at play which control conformational preferences.

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

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.

Synthesis and characterization of polylactide/doxorubicin/magnetic nanoparticles composites for drug delivery

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

Mhlanga, Nikiwe; Ray, Suprakas Sinha; DST/CSIR National Centre for Nanostructured Materials, Council for Scientific and Industrial Research, Pretoria, 0001

Magnetic iron oxide nanoparticles have potential to transform conventional therapeutics, through targeted delivery by external magnetic field modulation. Conventional drug delivery lacks specificity; both normal and infected cells are exposed to toxic drugs. Consequently, the toxicity towards healthy cells leads to detrimental side effects which are formidable. However, iron oxide research in biomedicine has been hindered by their lack of stability. This study reports on the stabilization of iron oxide by polylactide (PLA). Besides affording stable iron oxide, PLA is also good for sustained delivery of the drug. PLA/doxorubicin/magnetic nanoparticles (PLA/DOX/MNPs) spheres were synthesized by solvent evaporation method and DOXmore » anticancer drug was encapsulated. The spheres were characterized using scanning electron microscope, Fourier transform infrared microscope, thermogravimetric analyzer and UV-visible spectroscopy, which ascertained formation of the anticipated spheres and incorporation of DOX. In vitro drug release studies were carried out in both phosphate buffer (pH 7.4) and acetate buffer (pH 4.6) and they showed the same trend in both mediums. Drug release kinetics followed Higuchi model, which proved drug release by diffusion via a diffusion gradient.« less

Ultrasonic backscatter imaging by shear-wave-induced echo phase encoding of target locations.

PubMed

McAleavey, Stephen

2011-01-01

We present a novel method for ultrasound backscatter image formation wherein lateral resolution of the target is obtained by using traveling shear waves to encode the lateral position of targets in the phase of the received echo. We demonstrate that the phase modulation as a function of shear wavenumber can be expressed in terms of a Fourier transform of the lateral component of the target echogenicity. The inverse transform, obtained by measurements of the phase modulation over a range of shear wave spatial frequencies, yields the lateral scatterer distribution. Range data are recovered from time of flight as in conventional ultrasound, yielding a B-mode-like image. In contrast to conventional ultrasound imaging, where mechanical or electronic focusing is used and lateral resolution is determined by aperture size and wavelength, we demonstrate that lateral resolution using the proposed method is independent of the properties of the aperture. Lateral resolution of the target is achieved using a stationary, unfocused, single-element transducer. We present simulated images of targets of uniform and non-uniform shear modulus. Compounding for speckle reduction is demonstrated. Finally, we demonstrate image formation with an unfocused transducer in gelatin phantoms of uniform shear modulus.

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.

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.

Synthesis of PZT powder by conventional method at various conditions

NASA Astrophysics Data System (ADS)

Necira, Z.; Boutarfaia, A.; Abba, M.; Abdessalem, N.

2012-06-01

In this work, the formation of Pb(Zr1-xTix)O3 solid solutions with composition near the morphotropic phase boundary (MPB) using the conventional ceramic method have been studied by changing the thermal conditions such as temperature ramp rate and isothermal times during the calcination treatment performed between 700 and 900 °C. The perovskite phase formation and morphology of undoped Pb(Zr0.52Ti0.48)O3 (abbreviated PZT) and doped new material Pb0.98Gd0.02[(Zr0.52Ti0.48)0.98 (Mg1/3Nb2/3)0.01 (Ni1/3Sb2/3)0.01]O3 (abbreviated PZT-PGMNNS) specimens have been examined by powder X-ray diffraction (XRD), scanning electron microscopy (SEM) and Fourier Transform Infrared (FTIR) while the thermal evolution of the initial precursor was followed by TG-DTA. So the results of these studies have been discussed.

Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam

NASA Astrophysics Data System (ADS)

Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa

2017-08-01

In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.

Model-based spectral estimation of Doppler signals using parallel genetic algorithms.

PubMed

Solano González, J; Rodríguez Vázquez, K; García Nocetti, D F

2000-05-01

Conventional spectral analysis methods use a fast Fourier transform (FFT) on consecutive or overlapping windowed data segments. For Doppler ultrasound signals, this approach suffers from an inadequate frequency resolution due to the time segment duration and the non-stationarity characteristics of the signals. Parametric or model-based estimators can give significant improvements in the time-frequency resolution at the expense of a higher computational complexity. This work describes an approach which implements in real-time a parametric spectral estimator method using genetic algorithms (GAs) in order to find the optimum set of parameters for the adaptive filter that minimises the error function. The aim is to reduce the computational complexity of the conventional algorithm by using the simplicity associated to GAs and exploiting its parallel characteristics. This will allow the implementation of higher order filters, increasing the spectrum resolution, and opening a greater scope for using more complex methods.

Accelerated computer generated holography using sparse bases in the STFT domain.

PubMed

Blinder, David; Schelkens, Peter

2018-01-22

Computer-generated holography at high resolutions is a computationally intensive task. Efficient algorithms are needed to generate holograms at acceptable speeds, especially for real-time and interactive applications such as holographic displays. We propose a novel technique to generate holograms using a sparse basis representation in the short-time Fourier space combined with a wavefront-recording plane placed in the middle of the 3D object. By computing the point spread functions in the transform domain, we update only a small subset of the precomputed largest-magnitude coefficients to significantly accelerate the algorithm over conventional look-up table methods. We implement the algorithm on a GPU, and report a speedup factor of over 30. We show that this transform is superior over wavelet-based approaches, and show quantitative and qualitative improvements over the state-of-the-art WASABI method; we report accuracy gains of 2dB PSNR, as well improved view preservation.

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.

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

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...

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

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.

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.

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.

Sound Source Localization Using Non-Conformal Surface Sound Field Transformation Based on Spherical Harmonic Wave Decomposition

PubMed Central

Zhang, Lanyue; Ding, Dandan; Yang, Desen; Wang, Jia; Shi, Jie

2017-01-01

Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on generalized Fourier transform. When the sound source is on the cylindrical surface, it is difficult to locate by using spherical surface conformal transform. The non-conformal sound field transformation by making a transfer matrix based on spherical harmonic wave decomposition is proposed in this paper, which can achieve the transformation of a spherical surface into a cylindrical surface by using spherical array data. The theoretical expressions of the proposed method are deduced, and the performance of the method is simulated. Moreover, the experiment of sound source localization by using a spherical array with randomly and uniformly distributed elements is carried out. Results show that the non-conformal surface sound field transformation from a spherical surface to a cylindrical surface is realized by using the proposed method. The localization deviation is around 0.01 m, and the resolution is around 0.3 m. The application of the spherical array is extended, and the localization ability of the spherical array is improved. PMID:28489065

Methods for investigating the local spatial anisotropy and the preferred orientation of cones in adaptive optics retinal images

PubMed Central

Cooper, Robert F.; Lombardo, Marco; Carroll, Joseph; Sloan, Kenneth R.; Lombardo, Giuseppe

2016-01-01

The ability to non-invasively image the cone photoreceptor mosaic holds significant potential as a diagnostic for retinal disease. Central to the realization of this potential is the development of sensitive metrics for characterizing the organization of the mosaic. Here we evaluated previously-described (Pum et al., 1990) and newly-developed (Fourier- and Radon-based) methods of measuring cone orientation in both simulated and real images of the parafoveal cone mosaic. The proposed algorithms correlated well across both simulated and real mosaics, suggesting that each algorithm would provide an accurate description of individual photoreceptor orientation. Despite the high agreement between algorithms, each performed differently in response to image intensity variation and cone coordinate jitter. The integration property of the Fourier transform allowed the Fourier-based method to be resistant to cone coordinate jitter and perform the most robustly of all three algorithms. Conversely, when there is good image quality but unreliable cone identification, the Radon algorithm performed best. Finally, in cases where both the image and cone coordinate reliability was excellent, the method of Pum et al. (1990) performed best. These descriptors are complementary to conventional descriptive metrics of the cone mosaic, such as cell density and spacing, and have the potential to aid in the detection of photoreceptor pathology. PMID:27484961

Nanosize Fe x O y @SBA-3: A Comparative Study Between Conventional and Microwave Assisted Synthesis.

PubMed

Barik, Sunita; Badamali, Sushanta K; Sahoo, Sagarika; Behera, Nandakishor; Dapurkar, Sudhir E

2018-01-01

The present study is focussed on development of highly dispersed nanosize iron oxide (FexOy) particles within the uniform mesopore channels of SBA-3. Herein we report a comparative study between conventional incipient wetness and microwave assisted synthesis routes adopted to devise nanoparticles. The developed materials are characterised by following X-ray diffraction, high resolution transmission electron microscopy, proton induced X-ray emission, diffuse reflectance UV-visible spectroscopy, thermogravimetry and Fourier transform infrared spectroscopy. Mesoporous siliceous SBA-3 was prepared at room temperature to obtain samples with good crystallinity and ordered pore structure. Pore channels of SBA-3 were used as nanoreactor for developing iron oxide nanoparticles. Iron oxide nanoparticles developed under microwave activation showed uniform distribution within the SBA-3 structure along with retaining the orderness of the pore architecture. On the contrary, iron oxides developed under incipient wetness method followed by conventional heating resulted in agglomeration of nanoparticles along with significant loss in SBA-3 pore structure. Proton induced X-ray emission studies revealed the extremely high purity of the samples and almost thrice higher amount of iron oxide particles are encapsulated within the host by microwave assisted preparation as compared to incipient/conventional heating method.

Near-Infrared Spectroscopic Method for Monitoring Water Content in Epoxy Resins and Fiber-Reinforced Composites

PubMed Central

Gagani, Abedin I.; Echtermeyer, Andreas T.

2018-01-01

Monitoring water content and predicting the water-induced drop in strength of fiber-reinforced composites are of great importance for the oil and gas and marine industries. Fourier transform infrared (FTIR) spectroscopic methods are broadly available and often used for process and quality control in industrial applications. A benefit of using such spectroscopic methods over the conventional gravimetric analysis is the possibility to deduce the mass of an absolutely dry material and subsequently the true water content, which is an important indicator of water content-dependent properties. The objective of this study is to develop an efficient and detailed method for estimating the water content in epoxy resins and fiber-reinforced composites. In this study, Fourier transform near-infrared (FT-NIR) spectroscopy was applied to measure the water content of amine-epoxy neat resin. The method was developed and successfully extended to glass fiber-reinforced composite materials. Based on extensive measurements of neat resin and composite samples of varying water content and thickness, regression was performed, and the quantitative absorbance dependence on water content in the material was established. The mass of an absolutely dry resin was identified, and the true water content was obtained. The method was related to the Beer–Lambert law and explained in such terms. A detailed spectroscopic method for measuring water content in resins and fiber-reinforced composites was developed and described. PMID:29641451

Automated acid and base number determination of mineral-based lubricants by fourier transform infrared spectroscopy: commercial laboratory evaluation.

PubMed

Winterfield, Craig; van de Voort, F R

2014-12-01

The Fluid Life Corporation assessed and implemented Fourier transform infrared spectroscopy (FTIR)-based methods using American Society for Testing and Materials (ASTM)-like stoichiometric reactions for determination of acid and base number for in-service mineral-based oils. The basic protocols, quality control procedures, calibration, validation, and performance of these new quantitative methods are assessed. ASTM correspondence is attained using a mixed-mode calibration, using primary reference standards to anchor the calibration, supplemented by representative sample lubricants analyzed by ASTM procedures. A partial least squares calibration is devised by combining primary acid/base reference standards and representative samples, focusing on the main spectral stoichiometric response with chemometrics assisting in accounting for matrix variability. FTIR(AN/BN) methodology is precise, accurate, and free of most interference that affects ASTM D664 and D4739 results. Extensive side-by-side operational runs produced normally distributed differences with mean differences close to zero and standard deviations of 0.18 and 0.26 mg KOH/g, respectively. Statistically, the FTIR methods are a direct match to the ASTM methods, with superior performance in terms of analytical throughput, preparation time, and solvent use. FTIR(AN/BN) analysis is a viable, significant advance for in-service lubricant analysis, providing an economic means of trending samples instead of tedious and expensive conventional ASTM(AN/BN) procedures. © 2014 Society for Laboratory Automation and Screening.

Ultrafast electrical spectrum analyzer based on all-optical Fourier transform and temporal magnification.

PubMed

Duan, Yuhua; Chen, Liao; Zhou, Haidong; Zhou, Xi; Zhang, Chi; Zhang, Xinliang

2017-04-03

Real-time electrical spectrum analysis is of great significance for applications involving radio astronomy and electronic warfare, e.g. the dynamic spectrum monitoring of outer space signal, and the instantaneous capture of frequency from other electronic systems. However, conventional electrical spectrum analyzer (ESA) has limited operation speed and observation bandwidth due to the electronic bottleneck. Therefore, a variety of photonics-assisted methods have been extensively explored due to the bandwidth advantage of the optical domain. Alternatively, we proposed and experimentally demonstrated an ultrafast ESA based on all-optical Fourier transform and temporal magnification in this paper. The radio-frequency (RF) signal under test is temporally multiplexed to the spectrum of an ultrashort pulse, thus the frequency information is converted to the time axis. Moreover, since the bandwidth of this ultrashort pulse is far beyond that of the state-of-the-art photo-detector, a temporal magnification system is applied to stretch the time axis, and capture the RF spectrum with 1-GHz resolution. The observation bandwidth of this ultrafast ESA is over 20 GHz, limited by that of the electro-optic modulator. Since all the signal processing is in the optical domain, the acquisition frame rate can be as high as 50 MHz. This ultrafast ESA scheme can be further improved with better dispersive engineering, and is promising for some ultrafast spectral information acquisition applications.

Micro Fourier Transform Profilometry (μFTP): 3D shape measurement at 10,000 frames per second

NASA Astrophysics Data System (ADS)

Zuo, Chao; Tao, Tianyang; Feng, Shijie; Huang, Lei; Asundi, Anand; Chen, Qian

2018-03-01

Fringe projection profilometry is a well-established technique for optical 3D shape measurement. However, in many applications, it is desirable to make 3D measurements at very high speed, especially with fast moving or shape changing objects. In this work, we demonstrate a new 3D dynamic imaging technique, Micro Fourier Transform Profilometry (μFTP), which can realize an acquisition rate up to 10,000 3D frame per second (fps). The high measurement speed is achieved by the number of patterns reduction as well as high-speed fringe projection hardware. In order to capture 3D information in such a short period of time, we focus on the improvement of the phase recovery, phase unwrapping, and error compensation algorithms, allowing to reconstruct an accurate, unambiguous, and distortion-free 3D point cloud with every two projected patterns. We also develop a high-frame-rate fringe projection hardware by pairing a high-speed camera and a DLP projector, enabling binary pattern switching and precisely synchronized image capture at a frame rate up to 20,000 fps. Based on this system, we demonstrate high-quality textured 3D imaging of 4 transient scenes: vibrating cantilevers, rotating fan blades, flying bullet, and bursting balloon, which were previously difficult or even unable to be captured with conventional approaches.

Measurement of fugitive volatile organic compound emissions from a petrochemical tank farm using open-path Fourier transform infrared spectrometry

NASA Astrophysics Data System (ADS)

Wu, Chang-Fu; Wu, Tzong-gang; Hashmonay, Ram A.; Chang, Shih-Ying; Wu, Yu-Syuan; Chao, Chun-Ping; Hsu, Cheng-Ping; Chase, Michael J.; Kagann, Robert H.

2014-01-01

Fugitive emission of air pollutants is conventionally estimated based on standard emission factors. The Vertical Radial Plume Mapping (VRPM) technique, as described in the US EPA OTM-10, is designed to measure emission flux by directly monitoring the concentration of the plume crossing a vertical plane downwind of the site of interest. This paper describes the evaluation results of implementing VRPM in a complex industrial setting (a petrochemical tank farm). The vertical plane was constructed from five retroreflectors and an open-path Fourier transform infrared spectrometer. The VRPM configuration was approximately 189.2 m in width × 30.7 m in height. In the accompanying tracer gas experiment, the bias of the VRPM estimate was less than 2% and its 95% confidence interval contained the true release rate. Emission estimates of the target VOCs (benzene, m-xylene, o-xylene, p-xylene, and toluene) ranged from 0.86 to 2.18 g s-1 during the 14-day field campaign, while estimates based on the standard emission factors were one order of magnitude lower, possibly leading to an underestimation of the impact of these fugitive emissions on air quality and human health. It was also demonstrated that a simplified 3-beam geometry (i.e., without one dimensional scanning lines) resulted in higher uncertainties in the emission estimates.

Micro Fourier Transform Profilometry (μFTP): 3D shape measurement at 10,000 frames per second

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

Zuo, Chao; Tao, Tianyang; Feng, Shijie

We report that fringe projection profilometry is a well-established technique for optical 3D shape measurement. However, in many applications, it is desirable to make 3D measurements at very high speed, especially with fast moving or shape changing objects. In this work, we demonstrate a new 3D dynamic imaging technique, Micro Fourier Transform Profilometry (μFTP), which can realize an acquisition rate up to 10,000 3D frame per second (fps). The high measurement speed is achieved by the number of patterns reduction as well as high-speed fringe projection hardware. In order to capture 3D information in such a short period of time,more » we focus on the improvement of the phase recovery, phase unwrapping, and error compensation algorithms, allowing to reconstruct an accurate, unambiguous, and distortion-free 3D point cloud with every two projected patterns. We also develop a high-frame-rate fringe projection hardware by pairing a high-speed camera and a DLP projector, enabling binary pattern switching and precisely synchronized image capture at a frame rate up to 20,000 fps. Lastly, based on this system, we demonstrate high-quality textured 3D imaging of 4 transient scenes: vibrating cantilevers, rotating fan blades, flying bullet, and bursting balloon, which were previously difficult or even unable to be captured with conventional approaches.« less

Application of Fourier-transform infrared (FT-IR) spectroscopy for simple and easy determination of chylomicron-triglyceride and very low density lipoprotein-triglyceride.

PubMed

Sato, Kenichi; Seimiya, Masanori; Kodera, Yoshio; Kitamura, Akihide; Nomura, Fumio

2010-02-01

Fourier-transform infrared (FT-IR) spectroscopy is a simple and reagent-free physicochemical analysis method, and is a potential alternative to more time-consuming and labor-intensive procedures. In this study, we aimed to use FT-IR spectroscopy to determine serum concentrations of chylomicron-triglyceride (TG) and very low density lipoprotein (VLDL)-TG. We analyzed a chylomicron fraction and VLDL fraction, which had been obtained by ultracentrifugation, to search for wavelengths to designate to each fraction. Then, partial least square (PLS) calibrations were developed using a training set of samples, for which TG concentrations had been determined by conventional procedures. Validation was conducted with another set of samples using the PLS model to predict serum TG concentrations on the basis of the samples' IR spectra. We analyzed a total of 150 samples. Serum concentrations of chylomicron-TG and VLDL-TG estimated by FT-IR spectroscopy agreed well with those obtained by the reference method (r=0.97 for both lipoprotein fractions). FT-IR spectrometric analysis required 15mul of serum and was completed within 1min. Serum chylomicron-TG and VLDL-TG concentrations can be determined with FT-IR spectroscopy. This rapid and simple test may have a great impact on the management of patients with dyslipidemia. Copyright 2009. Published by Elsevier B.V.

Micro Fourier Transform Profilometry (μFTP): 3D shape measurement at 10,000 frames per second

DOE PAGES

Zuo, Chao; Tao, Tianyang; Feng, Shijie; ...

2017-11-06

We report that fringe projection profilometry is a well-established technique for optical 3D shape measurement. However, in many applications, it is desirable to make 3D measurements at very high speed, especially with fast moving or shape changing objects. In this work, we demonstrate a new 3D dynamic imaging technique, Micro Fourier Transform Profilometry (μFTP), which can realize an acquisition rate up to 10,000 3D frame per second (fps). The high measurement speed is achieved by the number of patterns reduction as well as high-speed fringe projection hardware. In order to capture 3D information in such a short period of time,more » we focus on the improvement of the phase recovery, phase unwrapping, and error compensation algorithms, allowing to reconstruct an accurate, unambiguous, and distortion-free 3D point cloud with every two projected patterns. We also develop a high-frame-rate fringe projection hardware by pairing a high-speed camera and a DLP projector, enabling binary pattern switching and precisely synchronized image capture at a frame rate up to 20,000 fps. Lastly, based on this system, we demonstrate high-quality textured 3D imaging of 4 transient scenes: vibrating cantilevers, rotating fan blades, flying bullet, and bursting balloon, which were previously difficult or even unable to be captured with conventional approaches.« less

Probing Vitamine C, Aspirin and Paracetamol in the Gas Phase: High Resolution Rotational Studies

NASA Astrophysics Data System (ADS)

Mata, S.; Cabezas, C.; Varela, M.; Pena, I.; Nino, A.; López, J. C.; Alonso, J. L.; Grabow, J.-U.

2011-06-01

A solid sample of Vitamin C (m.p. 190°C) vaporized by laser ablation has been investigated in gas phase and characterized through their rotational spectra. Two spectroscopy techniques has been used to obtain the spectra: a new design of broadband chirped pulse Fourier transform microwave spectroscopy with in-phase/quadrature-phase-modulation passage-acquired-coherence technique (IMPACT) and conventional laser ablation molecular beam Fourier transform microwave spectroscopy (LA-MB-FTMW). Up to now, two low-energy conformer have been observed and their rotational constants determined. Ab initio calculations at the MP2/6-311++G (d,p) level of theory predicted rotational constants which helped us to identify these conformers unequivocally. Among the molecules to benefit from the LA-MB-FTMW technique there are common important drugs never observed in the gas phase through rotational spectroscopy. We present here the results on acetyl salicylic acid and acetaminophen (m.p. 136°C), commonly known as aspirin and paracetamol respectively. We have observed two stable conformers of aspirin and two for paracetamol. The internal rotation barrier of the methyl group in aspirin has been determined for both conformers from the analysis of the A-E splittings due to the coupling of internal and overall rotation. J. L. Alonso, C. Pérez, M. E. Sanz, J. C. López, S. Blanco, Phys. Chem. Chem. Phys. 11,617-627 (2009)and references therein

Near-Infrared Spectroscopic Method for Monitoring Water Content in Epoxy Resins and Fiber-Reinforced Composites.

PubMed

Krauklis, Andrey E; Gagani, Abedin I; Echtermeyer, Andreas T

2018-04-11

Monitoring water content and predicting the water-induced drop in strength of fiber-reinforced composites are of great importance for the oil and gas and marine industries. Fourier transform infrared (FTIR) spectroscopic methods are broadly available and often used for process and quality control in industrial applications. A benefit of using such spectroscopic methods over the conventional gravimetric analysis is the possibility to deduce the mass of an absolutely dry material and subsequently the true water content, which is an important indicator of water content-dependent properties. The objective of this study is to develop an efficient and detailed method for estimating the water content in epoxy resins and fiber-reinforced composites. In this study, Fourier transform near-infrared (FT-NIR) spectroscopy was applied to measure the water content of amine-epoxy neat resin. The method was developed and successfully extended to glass fiber-reinforced composite materials. Based on extensive measurements of neat resin and composite samples of varying water content and thickness, regression was performed, and the quantitative absorbance dependence on water content in the material was established. The mass of an absolutely dry resin was identified, and the true water content was obtained. The method was related to the Beer-Lambert law and explained in such terms. A detailed spectroscopic method for measuring water content in resins and fiber-reinforced composites was developed and described.

Discrimination of cultivation ages and cultivars of ginseng leaves using Fourier transform infrared spectroscopy combined with multivariate analysis

PubMed Central

Kwon, Yong-Kook; Ahn, Myung Suk; Park, Jong Suk; Liu, Jang Ryol; In, Dong Su; Min, Byung Whan; Kim, Suk Weon

2013-01-01

To determine whether Fourier transform (FT)-IR spectral analysis combined with multivariate analysis of whole-cell extracts from ginseng leaves can be applied as a high-throughput discrimination system of cultivation ages and cultivars, a total of total 480 leaf samples belonging to 12 categories corresponding to four different cultivars (Yunpung, Kumpung, Chunpung, and an open-pollinated variety) and three different cultivation ages (1 yr, 2 yr, and 3 yr) were subjected to FT-IR. The spectral data were analyzed by principal component analysis and partial least squares-discriminant analysis. A dendrogram based on hierarchical clustering analysis of the FT-IR spectral data on ginseng leaves showed that leaf samples were initially segregated into three groups in a cultivation age-dependent manner. Then, within the same cultivation age group, leaf samples were clustered into four subgroups in a cultivar-dependent manner. The overall prediction accuracy for discrimination of cultivars and cultivation ages was 94.8% in a cross-validation test. These results clearly show that the FT-IR spectra combined with multivariate analysis from ginseng leaves can be applied as an alternative tool for discriminating of ginseng cultivars and cultivation ages. Therefore, we suggest that this result could be used as a rapid and reliable F1 hybrid seed-screening tool for accelerating the conventional breeding of ginseng. PMID:24558311

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.

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.

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,...

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.

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.

Insights into Comparative Antimicrobial Efficacies of Synthetic and Organic Agents: The Case of ZnS Nanoparticles and Zingiber officinale Rosc.

NASA Astrophysics Data System (ADS)

Obidi, O. F.; Nejo, A. O.; Ayeni, R. A.; Revaprasadu, N.

2018-03-01

The differences among the antimicrobial activities of synthetic nanoparticles (NPs), organic agents and conventional antibiotics against human pathogens are little known. We compared the antimicrobial activities of aqueous, ethanol and ethyl acetate extracts of Zingiber officinale rhizomes with ZnS NPs and tetracycline/nystatin using agar-diffusion techniques. Transmission electron microscopy (TEM), Fourier transform infrared (FTIR) and ultraviolet spectroscopy were used to characterize ZnS NPs. At 100 mg/ml, ethanol and ethyl acetate extract inhibited Acinetobacter baumannii, Salmonella typhimurium, Enterococcus faecium, Shigella flexneri, Klebsiella pneumoniae, Staphylococcus epidermidis and Candida albicans with zones of inhibition (ZOI) ranging between 0-42 mm and 0-39 mm, respectively. Candida albicans had a remarkable ZOI of 42 mm and 22 mm from ethanol and ZnS NPs compared with 20 mm from conventional nystatin. TEM and FTIR revealed spherically shaped polydispersed NPs with particle size of 12.5 nm and the role of banana peel extracts in ZnS NPs synthesis. Organic and synthetic NPs proved potential alternatives to conventional antimicrobial agents.

Insights into Comparative Antimicrobial Efficacies of Synthetic and Organic Agents: The Case of ZnS Nanoparticles and Zingiber officinale Rosc.

NASA Astrophysics Data System (ADS)

Obidi, O. F.; Nejo, A. O.; Ayeni, R. A.; Revaprasadu, N.

2018-06-01

The differences among the antimicrobial activities of synthetic nanoparticles (NPs), organic agents and conventional antibiotics against human pathogens are little known. We compared the antimicrobial activities of aqueous, ethanol and ethyl acetate extracts of Zingiber officinale rhizomes with ZnS NPs and tetracycline/nystatin using agar-diffusion techniques. Transmission electron microscopy (TEM), Fourier transform infrared (FTIR) and ultraviolet spectroscopy were used to characterize ZnS NPs. At 100 mg/ml, ethanol and ethyl acetate extract inhibited Acinetobacter baumannii, Salmonella typhimurium, Enterococcus faecium, Shigella flexneri, Klebsiella pneumoniae, Staphylococcus epidermidis and Candida albicans with zones of inhibition (ZOI) ranging between 0-42 mm and 0-39 mm, respectively. Candida albicans had a remarkable ZOI of 42 mm and 22 mm from ethanol and ZnS NPs compared with 20 mm from conventional nystatin. TEM and FTIR revealed spherically shaped polydispersed NPs with particle size of 12.5 nm and the role of banana peel extracts in ZnS NPs synthesis. Organic and synthetic NPs proved potential alternatives to conventional antimicrobial agents.

Thermal effusivity measurement of conventional and organic coffee oils via photopyroelectric technique.

PubMed

Bedoya, A; Gordillo-Delgado, F; Cruz-Santillana, Y E; Plazas, J; Marin, E

2017-12-01

In this work, oil samples extracted from organic and conventional coffee beans were studied. A fatty acids profile analysis was done using gas chromatography and physicochemical analysis of density and acidity index to verify the oil purity. Additionally, Mid-Infrared Fourier Transform Photoacoustic Spectroscopy (FTIR-PAS) aided by Principal Component Analysis (PCA) was used to identify differences between the intensities of the absorption bands related to functional groups. Thermal effusivity values between 592±3 and 610±4Ws 1/2 m -2 K -1 were measured using the photopyroelectric technique in a front detection configuration. The acidity index was between 1.11 and 1.27% and the density changed between 0.921 and 0.94g/mL. These variables, as well as the extraction yield between 12,6 and 14,4%, showed a similar behavior than that observed for the thermal effusivity, demonstrating that this parameter can be used as a criterion for discrimination between oil samples extracted from organic and conventional coffee beans. Copyright © 2017 Elsevier Ltd. All rights reserved.

A novel poly(acrylic acid-co-acrylamide)/diatomite composite flocculant with outstanding flocculation performance.

PubMed

Xu, Kun; Liu, Yao; Wang, Yang; Tan, Ying; Liang, Xuecheng; Lu, Cuige; Wang, Haiwei; Liu, Xiusheng; Wang, Pixin

2015-01-01

Series of anionic flocculants with outstanding flocculation performance, poly(acrylic acid-co-acrylamide)/diatomite composite flocculants (PAAD) were successfully prepared through aqueous solution copolymerization and applied to flocculate from oil-field fracturing waste-water. The structure of PAAD was characterized by Fourier transform infra-red spectroscopy, (13)C nuclear magnetic resonance and X-ray diffraction tests, and its properties were systematically evaluated by viscometer, thermogravimetry analysis and flocculation measurements. Furthermore, the influences of various reaction parameters on the apparent viscosity of flocculant solution were studied, and the optimum synthesis condition was determined. The novel composite flocculants exhibited outstanding flocculation properties. Specifically, the dosage of composite flocculants that could make the transmittance of treated wastewater exceed 90% was only approximately 12-35 ppm, which was far lower than that of conventional flocculants. Meanwhile, the settling time was lower than 5 s, which was similar to that of conventional flocculants. This was because PAAD flocculants had a higher absorption capacity, and larger chain extending space than conventional linear flocculants, which could refrain from the entanglement of linear polymer chains and significantly improve flocculation capacity.

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.

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)

Fast focus estimation using frequency analysis in digital holography.

PubMed

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

2014-11-17

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

Demodulation of micro fiber-optic Fabry-Perot interferometer using subcarrier and dual-wavelength method

NASA Astrophysics Data System (ADS)

Lu, En; Ran, Zengling; Peng, Fei; Liu, Zhiwei; Xu, Fuguo

2012-03-01

Subcarrier technology and dual-wavelength demodulation method are combined for tracking the cavity length variation of a micro fiber-optic Fabry-Perot (F-P). Compared with conventional dual-wavelength demodulation method, two operation wavelengths for demodulation are modulated with two different carrier frequencies, respectively, and then injected into optical link connected with the F-P cavity. Light power reflected for the two wavelengths is obtained by interrogating the powers of Fast Fourier Transform (FFT) spectrum at their carrier frequencies. Because the light at the two wavelengths experiences the same optical and electrical routes, measurement deviation resulting from the drift of optical and electrical links can be entirely eliminated.

Demodulation of micro fiber-optic Fabry-Perot interferometer using subcarrier and dual-wavelength method

NASA Astrophysics Data System (ADS)

Ran, Zengling; Rao, Yunjiang; Liu, Zhiwei; Xu, Fuguo

2011-05-01

Subcarrier technology and dual-wavelength demodulation method are combined for tracking the cavity length variation of a micro fiber-optic fabry-periot (F-P). Compared with conventional dual-wavelength demodulation method, two operation wavelengths for demodulation are modulated with two different carrier frequencies, respectively, and then injected into optical link connected with the F-P cavity. Light power reflected for the two wavelengths is obtained by interrogating the powers of Fast Fourier Transform (FFT) spectrum at their carrier frequencies. Because the light at the two wavelengths experiences the same optical and electrical routes, measurement deviation resulting from the drift of optical and electrical links can be entirely eliminated.

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...

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.

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.

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.

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.

Devil's vortex Fresnel lens phase masks on an asymmetric cryptosystem based on phase-truncation in gyrator wavelet transform domain

NASA Astrophysics Data System (ADS)

Singh, Hukum

2016-06-01

An asymmetric scheme has been proposed for optical double images encryption in the gyrator wavelet transform (GWT) domain. Grayscale and binary images are encrypted separately using double random phase encoding (DRPE) in the GWT domain. Phase masks based on devil's vortex Fresnel Lens (DVFLs) and random phase masks (RPMs) are jointly used in spatial as well as in the Fourier plane. The images to be encrypted are first gyrator transformed and then single-level discrete wavelet transformed (DWT) to decompose LL , HL , LH and HH matrices of approximation, horizontal, vertical and diagonal coefficients. The resulting coefficients from the DWT are multiplied by other RPMs and the results are applied to inverse discrete wavelet transform (IDWT) for obtaining the encrypted images. The images are recovered from their corresponding encrypted images by using the correct parameters of the GWT, DVFL and its digital implementation has been performed using MATLAB 7.6.0 (R2008a). The mother wavelet family, DVFL and gyrator transform orders associated with the GWT are extra keys that cause difficulty to an attacker. Thus, the scheme is more secure as compared to conventional techniques. The efficacy of the proposed scheme is verified by computing mean-squared-error (MSE) between recovered and the original images. The sensitivity of the proposed scheme is verified with encryption parameters and noise attacks.

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.

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.

Accelerated Compressed Sensing Based CT Image Reconstruction.

PubMed

Hashemi, SayedMasoud; Beheshti, Soosan; Gill, Patrick R; Paul, Narinder S; Cobbold, Richard S C

2015-01-01

In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

Accelerated Compressed Sensing Based CT Image Reconstruction

PubMed Central

Hashemi, SayedMasoud; Beheshti, Soosan; Gill, Patrick R.; Paul, Narinder S.; Cobbold, Richard S. C.

2015-01-01

In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization. PMID:26167200

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.

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.

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.

The Filtered Abel Transform and Its Application in Combustion Diagnostics

NASA Technical Reports Server (NTRS)

Simons, Stephen N. (Technical Monitor); Yuan, Zeng-Guang

2003-01-01

Many non-intrusive combustion diagnosis methods generate line-of-sight projections of a flame field. To reconstruct the spatial field of the measured properties, these projections need to be deconvoluted. When the spatial field is axisymmetric, commonly used deconvolution method include the Abel transforms, the onion peeling method and the two-dimensional Fourier transform method and its derivatives such as the filtered back projection methods. This paper proposes a new approach for performing the Abel transform method is developed, which possesses the exactness of the Abel transform and the flexibility of incorporating various filters in the reconstruction process. The Abel transform is an exact method and the simplest among these commonly used methods. It is evinced in this paper that all the exact reconstruction methods for axisymmetric distributions must be equivalent to the Abel transform because of its uniqueness and exactness. Detailed proof is presented to show that the two dimensional Fourier methods when applied to axisymmetric cases is identical to the Abel transform. Discrepancies among various reconstruction method stem from the different approximations made to perform numerical calculations. An equation relating the spectrum of a set of projection date to that of the corresponding spatial distribution is obtained, which shows that the spectrum of the projection is equal to the Abel transform of the spectrum of the corresponding spatial distribution. From the equation, if either the projection or the distribution is bandwidth limited, the other is also bandwidth limited, and both have the same bandwidth. If the two are not bandwidth limited, the Abel transform has a bias against low wave number components in most practical cases. This explains why the Abel transform and all exact deconvolution methods are sensitive to high wave number noises. The filtered Abel transform is based on the fact that the Abel transform of filtered projection data is equal to an integral transform of the original projection data with the kernel function being the Abel transform of the filtering function. The kernel function is independent of the projection data and can be obtained separately when the filtering function is selected. Users can select the best filtering function for a particular set of experimental data. When the kernal function is obtained, it can be used repeatedly to a number of projection data sets (rovs) from the same experiment. When an entire flame image that contains a large number of projection lines needs to be processed, the new approach significantly reduces computational effort in comparison with the conventional approach in which each projection data set is deconvoluted separately. Computer codes have been developed to perform the filter Abel transform for an entire flame field. Measured soot volume fraction data of a jet diffusion flame are processed as an example.

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.

Beyond Fourier

NASA Astrophysics Data System (ADS)

Hoch, Jeffrey C.

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.

Local Guided Wavefield Analysis for Characterization of Delaminations in Composites

NASA Technical Reports Server (NTRS)

Rogge, Matthew D.; Campbell Leckey, Cara A.

2012-01-01

Delaminations in composite laminates resulting from impact events may be accompanied by minimal indication of damage at the surface. As such, inspection techniques are required to ensure defects are within allowable limits. Conventional ultrasonic scanning techniques have been shown to effectively characterize the size and depth of delaminations but require physical contact with the structure. Alternatively, a noncontact scanning laser vibrometer may be used to measure guided wave propagation in the laminate structure. A local Fourier domain analysis method is presented for processing guided wavefield data to estimate spatially-dependent wavenumber values, which can be used to determine delamination depth. The technique is applied to simulated wavefields and results are analyzed to determine limitations of the technique with regards to determining defect size and depth. Finally, experimental wavefield data obtained in quasi-isotropic carbon fiber reinforced polymer (CFRP) laminates with impact damage is analyzed and wavenumber is measured to an accuracy of 8.5% in the region of shallow delaminations. Keywords: Ultrasonic wavefield imaging, Windowed Fourier transforms, Guided waves, Structural health monitoring, Nondestructive evaluation

Regridding reconstruction algorithm for real-time tomographic imaging

PubMed Central

Marone, F.; Stampanoni, M.

2012-01-01

Sub-second temporal-resolution tomographic microscopy is becoming a reality at third-generation synchrotron sources. Efficient data handling and post-processing is, however, difficult when the data rates are close to 10 GB s−1. This bottleneck still hinders exploitation of the full potential inherent in the ultrafast acquisition speed. In this paper the fast reconstruction algorithm gridrec, highly optimized for conventional CPU technology, is presented. It is shown that gridrec is a valuable alternative to standard filtered back-projection routines, despite being based on the Fourier transform method. In fact, the regridding procedure used for resampling the Fourier space from polar to Cartesian coordinates couples excellent performance with negligible accuracy degradation. The stronger dependence of the observed signal-to-noise ratio for gridrec reconstructions on the number of angular views makes the presented algorithm even superior to filtered back-projection when the tomographic problem is well sampled. Gridrec not only guarantees high-quality results but it provides up to 20-fold performance increase, making real-time monitoring of the sub-second acquisition process a reality. PMID:23093766

Super-resolution Doppler beam sharpening method using fast iterative adaptive approach-based spectral estimation

NASA Astrophysics Data System (ADS)

Mao, Deqing; Zhang, Yin; Zhang, Yongchao; Huang, Yulin; Yang, Jianyu

2018-01-01

Doppler beam sharpening (DBS) is a critical technology for airborne radar ground mapping in forward-squint region. In conventional DBS technology, the narrow-band Doppler filter groups formed by fast Fourier transform (FFT) method suffer from low spectral resolution and high side lobe levels. The iterative adaptive approach (IAA), based on the weighted least squares (WLS), is applied to the DBS imaging applications, forming narrower Doppler filter groups than the FFT with lower side lobe levels. Regrettably, the IAA is iterative, and requires matrix multiplication and inverse operation when forming the covariance matrix, its inverse and traversing the WLS estimate for each sampling point, resulting in a notably high computational complexity for cubic time. We propose a fast IAA (FIAA)-based super-resolution DBS imaging method, taking advantage of the rich matrix structures of the classical narrow-band filtering. First, we formulate the covariance matrix via the FFT instead of the conventional matrix multiplication operation, based on the typical Fourier structure of the steering matrix. Then, by exploiting the Gohberg-Semencul representation, the inverse of the Toeplitz covariance matrix is computed by the celebrated Levinson-Durbin (LD) and Toeplitz-vector algorithm. Finally, the FFT and fast Toeplitz-vector algorithm are further used to traverse the WLS estimates based on the data-dependent trigonometric polynomials. The method uses the Hermitian feature of the echo autocorrelation matrix R to achieve its fast solution and uses the Toeplitz structure of R to realize its fast inversion. The proposed method enjoys a lower computational complexity without performance loss compared with the conventional IAA-based super-resolution DBS imaging method. The results based on simulations and measured data verify the imaging performance and the operational efficiency.

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

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.

Transform- and multi-domain deep learning for single-frame rapid autofocusing in whole slide imaging.

PubMed

Jiang, Shaowei; Liao, Jun; Bian, Zichao; Guo, Kaikai; Zhang, Yongbing; Zheng, Guoan

2018-04-01

A whole slide imaging (WSI) system has recently been approved for primary diagnostic use in the US. The image quality and system throughput of WSI is largely determined by the autofocusing process. Traditional approaches acquire multiple images along the optical axis and maximize a figure of merit for autofocusing. Here we explore the use of deep convolution neural networks (CNNs) to predict the focal position of the acquired image without axial scanning. We investigate the autofocusing performance with three illumination settings: incoherent Kohler illumination, partially coherent illumination with two plane waves, and one-plane-wave illumination. We acquire ~130,000 images with different defocus distances as the training data set. Different defocus distances lead to different spatial features of the captured images. However, solely relying on the spatial information leads to a relatively bad performance of the autofocusing process. It is better to extract defocus features from transform domains of the acquired image. For incoherent illumination, the Fourier cutoff frequency is directly related to the defocus distance. Similarly, autocorrelation peaks are directly related to the defocus distance for two-plane-wave illumination. In our implementation, we use the spatial image, the Fourier spectrum, the autocorrelation of the spatial image, and combinations thereof as the inputs for the CNNs. We show that the information from the transform domains can improve the performance and robustness of the autofocusing process. The resulting focusing error is ~0.5 µm, which is within the 0.8-µm depth-of-field range. The reported approach requires little hardware modification for conventional WSI systems and the images can be captured on the fly without focus map surveying. It may find applications in WSI and time-lapse microscopy. The transform- and multi-domain approaches may also provide new insights for developing microscopy-related deep-learning networks. We have made our training and testing data set (~12 GB) open-source for the broad research community.

Resolution enhancement of robust Bayesian pre-stack inversion in the frequency domain

NASA Astrophysics Data System (ADS)

Yin, Xingyao; Li, Kun; Zong, Zhaoyun

2016-10-01

AVO/AVA (amplitude variation with an offset or angle) inversion is one of the most practical and useful approaches to estimating model parameters. So far, publications on AVO inversion in the Fourier domain have been quite limited in view of its poor stability and sensitivity to noise compared with time-domain inversion. For the resolution and stability of AVO inversion in the Fourier domain, a novel robust Bayesian pre-stack AVO inversion based on the mixed domain formulation of stationary convolution is proposed which could solve the instability and achieve superior resolution. The Fourier operator will be integrated into the objective equation and it avoids the Fourier inverse transform in our inversion process. Furthermore, the background constraints of model parameters are taken into consideration to improve the stability and reliability of inversion which could compensate for the low-frequency components of seismic signals. Besides, the different frequency components of seismic signals can realize decoupling automatically. This will help us to solve the inverse problem by means of multi-component successive iterations and the convergence precision of the inverse problem could be improved. So, superior resolution compared with the conventional time-domain pre-stack inversion could be achieved easily. Synthetic tests illustrate that the proposed method could achieve high-resolution results with a high degree of agreement with the theoretical model and verify the quality of anti-noise. Finally, applications on a field data case demonstrate that the proposed method could obtain stable inversion results of elastic parameters from pre-stack seismic data in conformity with the real logging data.

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.

Recent Advances in Techniques for Starch Esters and the Applications: A Review

PubMed Central

Hong, Jing; Zeng, Xin-An; Brennan, Charles S.; Brennan, Margaret; Han, Zhong

2016-01-01

Esterification is one of the most important methods to alter the structure of starch granules and improve its applications. Conventionally, starch esters are prepared by conventional or dual modification techniques, which have the disadvantages of being expensive, have regent overdoses, and are time-consuming. In addition, the degree of substitution (DS) is often considered as the primary factor in view of its contribution to estimate substituted groups of starch esters. In order to improve the detection accuracy and production efficiency, different detection techniques, including titration, nuclear magnetic resonance (NMR), Fourier transform infrared spectroscopy (FT-IR), thermal gravimetric analysis/infrared spectroscopy (TGA/IR) and headspace gas chromatography (HS-GC), have been developed for DS. This paper gives a comprehensive overview on the recent advances in DS analysis and starch esterification techniques. Additionally, the advantages, limitations, some perspectives on future trends of these techniques and the applications of their derivatives in the food industry are also presented. PMID:28231145

Development of panel loudspeaker system: design, evaluation and enhancement.

PubMed

Bai, M R; Huang, T

2001-06-01

Panel speakers are investigated in terms of structural vibration and acoustic radiation. A panel speaker primarily consists of a panel and an inertia exciter. Contrary to conventional speakers, flexural resonance is encouraged such that the panel vibrates as randomly as possible. Simulation tools are developed to facilitate system integration of panel speakers. In particular, electro-mechanical analogy, finite element analysis, and fast Fourier transform are employed to predict panel vibration and the acoustic radiation. Design procedures are also summarized. In order to compare the panel speakers with the conventional speakers, experimental investigations were undertaken to evaluate frequency response, directional response, sensitivity, efficiency, and harmonic distortion of both speakers. The results revealed that the panel speakers suffered from a problem of sensitivity and efficiency. To alleviate the problem, a woofer using electronic compensation based on H2 model matching principle is utilized to supplement the bass response. As indicated in the result, significant improvement over the panel speaker alone was achieved by using the combined panel-woofer system.

Preparation and characterization of nanoparticles of carboxymethyl cellulose acetate butyrate containing acyclovir

NASA Astrophysics Data System (ADS)

Vedula, Venkata Bharadwaz; Chopra, Maulick; Joseph, Emil; Mazumder, Sonal

2016-02-01

Nanoparticles of carboxymethyl cellulose acetate butyrate complexed with the poorly soluble antiviral drug acyclovir (ACV) were produced by precipitation process and the formulation process and properties of nanoparticles were investigated. Two different particle synthesis methods were explored—a conventional precipitation method and a rapid precipitation in a multi-inlet vortex mixer. The particles were processed by rotavap followed by freeze-drying. Particle diameters as measured by dynamic light scattering were dependent on the synthesis method used. The conventional precipitation method did not show desired particle size distribution, whereas particles prepared by the mixer showed well-defined particle size ~125-450 nm before and after freeze-drying, respectively, with narrow polydispersity indices. Fourier transform infrared spectroscopy showed chemical stability and intactness of entrapped drug in the nanoparticles. Differential scanning calorimetry showed that the drug was in amorphous state in the polymer matrix. ACV drug loading was around 10 wt%. The release studies showed increase in solution concentration of drug from the nanoparticles compared to the as-received crystalline drug.

Dimension-Factorized Range Migration Algorithm for Regularly Distributed Array Imaging

PubMed Central

Guo, Qijia; Wang, Jie; Chang, Tianying

2017-01-01

The two-dimensional planar MIMO array is a popular approach for millimeter wave imaging applications. As a promising practical alternative, sparse MIMO arrays have been devised to reduce the number of antenna elements and transmitting/receiving channels with predictable and acceptable loss in image quality. In this paper, a high precision three-dimensional imaging algorithm is proposed for MIMO arrays of the regularly distributed type, especially the sparse varieties. Termed the Dimension-Factorized Range Migration Algorithm, the new imaging approach factorizes the conventional MIMO Range Migration Algorithm into multiple operations across the sparse dimensions. The thinner the sparse dimensions of the array, the more efficient the new algorithm will be. Advantages of the proposed approach are demonstrated by comparison with the conventional MIMO Range Migration Algorithm and its non-uniform fast Fourier transform based variant in terms of all the important characteristics of the approaches, especially the anti-noise capability. The computation cost is analyzed as well to evaluate the efficiency quantitatively. PMID:29113083

Simulation of foulant bioparticle topography based on Gaussian process and its implications for interface behavior research

NASA Astrophysics Data System (ADS)

Zhao, Leihong; Qu, Xiaolu; Lin, Hongjun; Yu, Genying; Liao, Bao-Qiang

2018-03-01

Simulation of randomly rough bioparticle surface is crucial to better understand and control interface behaviors and membrane fouling. Pursuing literature indicated a lack of effective method for simulating random rough bioparticle surface. In this study, a new method which combines Gaussian distribution, Fourier transform, spectrum method and coordinate transformation was proposed to simulate surface topography of foulant bioparticles in a membrane bioreactor (MBR). The natural surface of a foulant bioparticle was found to be irregular and randomly rough. The topography simulated by the new method was quite similar to that of real foulant bioparticles. Moreover, the simulated topography of foulant bioparticles was critically affected by parameters correlation length (l) and root mean square (σ). The new method proposed in this study shows notable superiority over the conventional methods for simulation of randomly rough foulant bioparticles. The ease, facility and fitness of the new method point towards potential applications in interface behaviors and membrane fouling research.

Quantitative subsurface analysis using frequency modulated thermal wave imaging

NASA Astrophysics Data System (ADS)

Subhani, S. K.; Suresh, B.; Ghali, V. S.

2018-01-01

Quantitative depth analysis of the anomaly with an enhanced depth resolution is a challenging task towards the estimation of depth of the subsurface anomaly using thermography. Frequency modulated thermal wave imaging introduced earlier provides a complete depth scanning of the object by stimulating it with a suitable band of frequencies and further analyzing the subsequent thermal response using a suitable post processing approach to resolve subsurface details. But conventional Fourier transform based methods used for post processing unscramble the frequencies with a limited frequency resolution and contribute for a finite depth resolution. Spectral zooming provided by chirp z transform facilitates enhanced frequency resolution which can further improves the depth resolution to axially explore finest subsurface features. Quantitative depth analysis with this augmented depth resolution is proposed to provide a closest estimate to the actual depth of subsurface anomaly. This manuscript experimentally validates this enhanced depth resolution using non stationary thermal wave imaging and offers an ever first and unique solution for quantitative depth estimation in frequency modulated thermal wave imaging.

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.

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.

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.

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

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.