Showing papers on "Fast Fourier transform published in 1991"

Selection of a convolution function for Fourier inversion using gridding (computerised tomography application)

Abstract: In the technique known as gridding, the data samples are weighted for sampling density and convolved with a finite kernel, then resampled on a grid preparatory to a fast Fourier transform. The authors compare the artifact introduced into the image for various convolving functions of different sizes, including the Kaiser-Bessel window and the zero-order prolate spheroidal wave function (PSWF). They also show a convolving function that improves upon the PSWF in some circumstances. >

A two-dimensional Fourier transform method for the measurement of propagating multimode signals

Abstract: A technique for the analysis of propagating multimode signals is presented. The method involves a two-dimensional Fourier transformation of the time history of the waves received at a series of equally spaced positions along the propagation path. The technique has been used to measure the amplitudes and velocities of the Lamb waves propagating in a plate, the output of the transform being presented using an isometric projection which gives a three-dimensional view of the wave-number dispersion curves. The results of numerical and experimental studies to measure the dispersion curves of Lamb waves propagating in 0.5-, 2.0-, and 3.0-mm-thick steel plates are presented. The results are in good agreement with analytical predictions and show the effectiveness of using the two-dimensional Fourier transform (2-D FFT) method to identify and measure the amplitudes of individual Lamb modes.

Spectral methods on triangles and other domains

Abstract: This article shows how to obtain multidimensional spectral methods as a warped product of one-dimensional spectral methods, thus generalizing direct (tensor) products. This generalization includes the fast Fourier transform. Applications are given for spectral approximation on a disk and on a triangle. The use of the disk spectral method for simulating the Navier-Stokes equations in a periodic pipe is detailed. The use of the triangle method in a spectral element scheme is discussed. The degree of approximation of the triangle method is computed in a new way, which favorably compares with the classical approximation estimates.

A digital recursive measurement scheme for online tracking of power system harmonics

Abstract: An optimal measurement scheme for tracking the harmonics in power system voltage and current waveforms is presented. The scheme does not require an integer number of samples in an integer number of cycles. It is not limited to stationary signals, but it can track harmonics with time-varying amplitudes. A review is first presented of the common frequency domain techniques for harmonics measurement. The frequency domain techniques are based on the discrete Fourier transform and the fast Fourier transform. Examples of pitfalls in the common techniques are given. The authors then introduce the concepts of the new scheme. This scheme is based on Kalman filtering theory for the optimal estimation of the parameters of time-varying harmonics. The scheme was tested on simulated and actual recorded data sets. It is concluded that the Kalman filtering algorithm is more accurate than the other techniques. >

The fractional Fourier transform and applications

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

Application of fast-Fourier-transform techniques to the discrete-dipole approximation.

Abstract: We show how fast-Fourier-transform methods can be used to accelerate computations of scattering and absorption by particles of arbitrary shape using the discrete-dipole approximation.

New Fast GPS code-acquisition technique using FFT

Abstract: A new spread-spectrum code-acquisition technique for the navigation systems Navstar/GPS and Glonass is introduced. This technique uses the FFT to compute the correlation function, thereby eliminating the time-consuming code phase shift process. Comparisons with existing systems show a theoretical reduction in acquisition time of about 2000 times.

The interpolated fast Fourier transform: a comparative study

Abstract: The properties of five interpolating fast Fourier transform methods (IFFT) are studied with respect to their systematic errors and their noise sensitivity, for a monofrequency signal. It is shown that windows with small spectral sidelobes do not always result in a better overall performance of the IFFT and that time-domain estimators can be more efficient than the IFFT methods analyzed. It is also, shown that time-domain techniques have a lower Cramer-Rao lower bound than the IFFT methods, which can result in more efficient estimates. >

A finite-difference time-domain near zone to far zone transformation (electromagnetic scattering)

Abstract: An efficient time-domain near-zone-to-far-zone transformation for FDTD (finite-difference-time-domain) computations is presented. The approach is to keep a running accumulation of the far-zone time-domain vector potentials due to the tangential electric and magnetic fields on a closed surface surrounding the scatterer at each time step. At the end of the computation, these vector potentials are converted to time-domain far-zone fields. Many far-zone bistatic directions can be included efficiently during one FDTD computational run. Frequency domain results can be obtained via fast Fourier transform. Wideband results for scattering from a perfectly conducting plate were obtained from a single FDTD computation transformed to the frequency domain, and compared with moment method results. This approach is significantly more efficient than computing many FDTD results using sinusoidally varying excitation if a wide frequency band is of interest. Coupled with recent advances in computing FDTD results for frequency-dependent materials, wideband results for far-zone scattering from targets including frequency-dependent materials can be obtained efficiently. >

Computationally efficient algorithms for cyclic spectral analysis

Abstract: Two computationally efficient algorithms for digital cyclic spectral analysis, the FFT accumulation method (FAM) and the strip spectral correlation algorithm (SSCA), are developed from a series of modifications on a simple time smoothing algorithm. The signal processing, computational, and structural attributes of time smoothing algorithms are presented with emphasis on the FAM and SSCA. As a vehicle for examining the algorithms the problem of estimating the cyclic cross spectrum of two complex-valued sequences is considered. Simplifications of the resulting expressions to special cases of the cross cyclic spectrum of two complex-valued sequences, such as the cyclic spectrum of a single real-valued sequence, are easily found. Computational and structural simplifications arising from the specialization are described. >

Linear FM signal parameter estimation from discrete-time observations

Abstract: The authors consider the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations An estimation algorithm is proposed, and its asymptotic (large sample) performance is analyzed The algorithm is computationally simple, consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima The variance of the estimates is shown to be close to the Cramer-Rao lower bound when the signal-to-noise ratio is 0 dB and above The authors applied the algorithm to the problem of estimating the kinematic parameters of an accelerating target by pulse-Doppler radar A representative test case was used to exhibit the usefulness of the algorithm for this problem, and to verify the analytical results by Monte Carlo simulations >

A Fast Algorithm for the Evaluation of Legendre Expansions

Abstract: An algorithm is presented for the rapid calculation of the values and coefficients of finite Legendre series. Given an n-term Legendre expansion, the algorithm produces its values at n Chebyshev nodes on the interval $[-1,1]$ for a cost proportional to $n\log n$. Similarly, given the valuesof a function f at n Chebyshev nodes, the algorithm produces the n-term Legendre expansion of the polynomial of degree $n - 1$ that is equal to f at these nodes. The cost of the algorithm is roughly three times that of the Fast Fourier Transform of length n, provided that calculations are performed to single precision accuracy. In double precision, the ratio is approximately 5.5.The method employed admits far-reaching generalizations and is currently being applied to several other problems.

A Fast Algorithm for the Evaluation of Legendre Expansions.

Abstract: An algorithm is presented for the rapid calculation of the values and coefficients of finite Legendre series. Given an n-term Legendre expansion, the algorithm produces its values at n Chebyshev nodes on the interval $[-1,1]$ for a cost proportional to $n\log n$. Similarly, given the valuesof a function f at n Chebyshev nodes, the algorithm produces the n-term Legendre expansion of the polynomial of degree $n - 1$ that is equal to f at these nodes. The cost of the algorithm is roughly three times that of the Fast Fourier Transform of length n, provided that calculations are performed to single precision accuracy. In double precision, the ratio is approximately 5.5.The method employed admits far-reaching generalizations and is currently being applied to several other problems.

DFT/FFT and Convolution Algorithms: Theory and Implementation

Abstract: From the Publisher: This readable handbook provides complete coverage of both the theory and implementation of modern signal processing algorithms for computing the Discrete Fourier transform. Reviews continuous and discrete-time transform analysis of signals and properties of DFT, several ways to compute the DFT at a few frequencies, and the three main approaches to an FFT. Practical, tested FORTRAN and assembly language programs are included with enough theory to adapt them to particular applications. Compares and evaluates various algorithms.

A fast algorithm for the implementation of filter banks based on 'time domain aliasing cancellation'

Abstract: Several data compression techniques are in competition for coding high-quality audio signals (sampling rate >or=32 kHz) down to a 64 kb/s bit rate. The authors concentrate on the subband/transform coding scheme using filter banks known as time domain aliasing cancellation (TDAC). This scheme first involves a window on a set of N data, overlapping by N/2 with the previous one, followed by a TDAC transform. First, it is shown that the transform turns out to be a doubly odd DCT, for which a fast algorithm is provided. Then, it is shown how the windowing and the overlap can be merged with the first step of the first algorithm. The total number of operations (multiplications plus additions) required by this algorithm for computing a length-N TDAC plus windowing is exactly N log/sub 2/ N. Implementation considerations are provided. >

Superresolution techniques for time-domain measurements with a network analyzer

Abstract: Superresolution techniques for time delay estimation are proposed and applied to frequency-domain data measured with a network analyzer. A MUSIC (multiple signal classification) algorithm preprocessed by spatial smoothing is used. The spatial smoothing preprocessing is performed to destroy signal coherence, and the decorrelation performance is examined in detail. The expression which gives an individual response is given. Using this expression, it is possible to eliminate unwanted signals that appear as ripples in the frequency domain. Experimental results show that the frequency bandwidth required by the MUSIC algorithm to resolve distinct time-domain responses and eliminate unwanted signals is much narrower than that required by the FFT (fast Fourier transform). Thus, the MUSIC algorithm is applicable to the time-domain measurements with the network analyzer and has much higher resolution capability than the conventional FFT techniques. The MUSIC algorithm is one of the most promising methods of enhancing the accuracy of measurement for narrowband devices such as antennas. >

Linear and nonlinear algorithms for identification in H ∞ with error bounds

Abstract: In this paper, a linear and a nonlinear algorithm are presented for the problem of system "identification in H∞", posed by Helmicki, Jacobson and Nett. We derive some error bounds for the linear algorithm which indicate that if the model error is not too high, then this algorithm has good guaranteed error properties. The linear algorithm requires only FFT (fast Fourier transform) computations. A nonlinear algorithm, which requires an additional step of solving a Nehari best approximation problem, is also presented that has the robust convergence property.

Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis

Abstract: The Fourier transform technique, originally developed for spatial fringe pattern analysis, has been applied to the analysis of a temporal fringe signal obtained by a wavelength-shift interferometer used for absolute distance measurements. It has been shown that the error caused by the nonlinear and time-varying current-wavelength characteristic of the laser diode can be removed by combining the Fourier transform technique with the reference technique. A novel technique for distance measurement based on multiple-beam interferometry has been proposed, and an experimental demonstration is given for a three-beam interferometer that includes a reference reflector as an integral part of the system. Error sources and the limitation of the technique are discussed.

A finite-element-boundary-integral method for scattering and radiation by two- and three-dimensional structures

Abstract: A hybrid finite-element-boundary-integral formulation for scattering and radiation by 2-D and 3-D composite structures is described. In contrast to other hybrid techniques involving the finite-element method, the method is in principle exact, and can be implemented using low O(N) amounts of storage. This is of particular importance for large-scale applications, and is a characteristic of the boundary chosen to terminate the finite-element mesh, usually as close to the structure as possible. A general description of the method, without reference to any specific geometry or application, is given. A number of 2-D and 3-D applications are then considered, to demonstrate its accuracy, efficiency, and capabilities. Of particular concern in these applications is the choice of the fictitious boundary enclosing the structure. Boundaries of a certain class lead to convolutional boundary integrals, which can be evaluated by the fast Fourier transform without generating a matrix, thus retaining the O(N) storage requirement. >

Fast and accurate near-field-far-field transformation by sampling interpolation of plane-polar measurements

Abstract: An optimal sampling interpolation algorithm which allows the accurate recovery of plane-rectangular near-field samples from the knowledge of the plane-polar ones is developed. This enables the standard near-field-far-field (NF-FF) transformation, which takes full advantage of the fast Fourier transform (FFT) algorithm, to be applied to plane-polar scanning. The maximum allowable sample spacing is also rigorously derived, and it is shown that it can be significantly greater than lambda /2 as the measurement place moves away from the source. This allows a remarkable reduction of both measurement time and memory storage requirements. The sampling approach is compared with that based on the bivariate Lagrange interpolation (BLI) method. The sampling reconstruction agrees with the exact results significantly better than the BLI, in spite of the significantly lower number of required measurements. >

Digital measurement of voltage flicker

Abstract: The author deals with cyclic variations in the envelope of voltage waveforms. European power utilities have done substantial work already in their characterization, based on the effects on visual perception. They have also established a norm for the calculation of an instantaneous flicker level, a short-term severity coefficient, and a long-term severity coefficient. The measurement techniques that they propose are basically designed for analog instrumentation. Digital implementations of the analog design are neither cost effective nor optimal in performance. The author proposes a method for direct calculation of flicker level from digital measurements of voltage waveforms. The direct digital implementation uses a fast Fourier transform (FFT) as the first step in the computation. A pruned FFT, customized for the flicker level computation, is also proposed. >

Simulation of Multivariate Nonstationary Random Processes by FFT

Abstract: The fast Fourier transform (FFT) technique is utilized to simulate a multivariate nonstationary Gaussian random process with prescribed evolutionary spectral description. A stochastic decomposition technique facilitates utilization of the FFT algorithm. The decomposed spectral matrix is expanded into a weighted summation of basic functions and time‐dependent weights that are simulated by the FFT algorithm. The desired evolutionary spectral characteristics of the multivariate unidimensional process may be prescribed in a closed form or a set of numerical values at discrete frequencies. The effectiveness of the proposed technique is demonstrated by means of three examples with different evolutionary spectral characteristics derived from past earthquake events. The closeness between the target and the corresponding estimated correlation structure suggests that the simulated time series reflect the prescribed probabilistic characteristics extremely well. The simulation approach is computationally efficient, p...

Harmonic power flow determination using the fast Fourier transform

Abstract: Multichannel data acquisition systems and commercially available digital signal processing software packages make the determination of harmonic power flow possible provided the limitations of the analysis techniques are understood. The authors describe how data from a typical acquisition system can be processed using the fast Fourier transform and discuss possible errors (e.g. those due to leakage) and how to avoid them using techniques such as skewing correction and windowing. Guidelines on the practical application of the transform in analyzing measured data are presented. The analysis method has been used successfully to analyze data obtained at a traction (railway supply) substation which had a sixth-harmonic resonance caused by the interaction of a harmonic filter and the only supply system. >

Stokes formula using Fast Fourier Techniques

Abstract: For geoid computations with FFT usually a flat earth approximation is assumed However FFT can also be used with the spherical Stokes formula With a relative small approximation in the computation of spherical distances the Stokes integral can be transformed into a 2D-convolution integral, which can be solved by multiplication of the 2D-spectra Test computations show that the effect of the approximation in FFT is in the order of only a few cm for an area up to 1500 × 1500 km and increasing to 15 cm for 3500 × 3500 km

Block, multistride vector, and FFT accesses in parallel memory systems

Abstract: A discussion is presented of the use of dynamic storage schemes to improve parallel memory performance during three important classes of data accesses: vector accesses in which multiple strides are used to access a single vector, block accesses, and constant-geometry FFT accesses. The schemes investigated are based on linear address transformations, also known as XOR schemes. It has been shown that this class of schemes can be implemented more efficiently in hardware and has more flexibility than schemes based on row rotations or other techniques. Several analytical results are shown. These include: quantitative analysis of buffering effects in pipelined memory systems; design rules for storage schemes that provide conflict-free access using multiple strides, blocks, and FFT access patterns; and an analysis of the effects of memory bank cycle time on storage scheme capabilities. >