Showing papers on "Fast Fourier transform published in 1989"

Fast algorithm for spectral analysis of unevenly sampled data

Abstract: On montre que les transformations de Fourier rapides peuvent servir pour faire des calculs sur ordinateur de l'ordre de 10 2 N Log N

The LOT: transform coding without blocking effects

Abstract: An exact derivation of an optimal lapped orthogonal transform (LOT) is presented. The optimal LOT is related to the discrete cosine transform (DCT) in such a way that a fast algorithm for a nearly optimal LOT is derived. Compared to the DCT, the fast LOT requires about 20-30% more computations, mostly additions. An image coding example demonstrates the effectiveness of the LOT in reducing blocking effects; the LOT actually leads to slightly smaller signal reconstruction errors than does the DCT. >

Windows and interpolation algorithms to improve electrical measurement accuracy

Abstract: An FFT-based measurement technique, which can be easily used to determine accurately the frequency, amplitude, and phase of all the harmonic and interharmonic components of a distorted signal, is examined Suitable windows and interpolation algorithms are examined in order to reduce undesirable effects due to spectral leakage caused by a sampling process that is not synchronized Several results concerning the application of different windows on a set of simulated signals are compared to verify the capability of the proposed procedure The influence of the noise is examined to study the filtering properties of the weighting functions >

Implementation of the three-dimensional turning bands random field generator

Abstract: Numerical techniques to generate replicates of spatially correlated random fields are often used to synthesize sets of highly variable physical quantities in stochastic models of naturally heterogeneous systems. Within the realm of hydrologic research, for example, such tools are widely used to develop hypothetical rainfall distributions, hydraulic conductivity fields, fracture set properties, and other surface or subsurface flow parameters. The turning bands method is one such algorithm which generates two- and three-dimensional fields by combining values found from a series of one-dimensional simulations along lines radiating outward from a coordinate origin. Previous work with two-dimensional algorithms indicates that radial lines evenly spaced about the unit circle lead to enhanced convergence properties. The same can be said for the three-dimensional models, but it is more difficult to choose an arbitrary number of evenly spaced lines about the unit sphere. The current investigation shows that the use of larger numbers of randomly oriented lines (100) can enhance the performance of the three-dimensional algorithm. This improved performance is needed to effectively simulate problems characterized by full three dimensionality and/or anisotropy in either Monte Carlo or single-realization applications. Use of a large number of lines will also reduce the presence of a distortion effect manifested as linelike patterns in the field. Increased computational costs can be reduced by employing a fast Fourier transform technique to generate the line processes.

Algorithms for Discrete Fourier Transform and Convolution

Abstract: Contents: Introduction to Abstract Algebra.- Tensor Product and Stride Permutation.- Cooley-Tukey FFF Algorithms.- Variants of FFT Algorithms and Their Implementations.- Good-Thomas PFA.- Linear and Cyclic Convolutions.- Agarwal-Cooley Convolution Algorithm.- Introduction to Multiplicative Fourier Transform Algorithms (MFTA).- MFTA: The Prime Case.- MFTA: Product of Two Distinct Primes.- MFTA: Transform Size N = Mr. M-Composite Integer and r-Prime.- MFTA: Transform Size N = p2.- Periodization and Decimation.- Multiplicative Character and the FFT.- Rationality.- Index.

A pipelined FFT processor for word-sequential data

Abstract: A modified fast Fourier transform algorithm is described together with a real-time pipelined implementation. The approach is particularly suited to sequentially presented input data. The method can be used for both mixed and uniform radix number implementations. For example, for the radix-4 implementation, the method requires less data memory and only 1/3 of the number of complex multipliers of a conventional design. >

The generalized method of characteristics for waveform relaxation analysis of lossy coupled transmission lines

Abstract: The transient response of lossy coupled transmission lines is simulated by iterative waveform relaxation analyses of equivalent disjoint networks constructed with congruence transformers, fast Fourier transform (FFT) waveform generators, and characteristic impedances synthesized by the Pade approximation. A two order reduction of CPU time and one order savings in computer memory are achieved. A lossy directional coupler is simulated for illustration. >

Interpolation techniques for real-time multifrequency waveform analysis

Abstract: It is well-known that in discrete-Fourier-transform- (DFT-) based waveform analysis of multifrequency signals, spectral parameter accuracy can be increased by windowing the time samples and interpolating the DFT coefficients. It is shown that some relationships used in interpolation are affected very little by the number of processed samples, so that only the characteristics of the analyzed signal and the required accuracy affect the choice of this parameter. In particular, this makes the approach well suited for real-time analysis of signals with slowly time-varying spectra. Polynomial approximations of some relationships reduce the processing effort and, allow a greater freedom in the choice of the window functions, improving both accuracy and frequency resolution. >

A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform

Abstract: A numerical scheme to obtain radar cross section (RCS) of three-dimensional bodies of resonant size (BRS) with arbitrary geometry and material composition is described. The RCS is obtained by solving the electric-field integral equation (EFIE) using the conjugate gradient-fast Fourier transform method (CG-FFT). The choice of a suitable set of basis and testing functions to discretize the EFIE leads to a very accurate and computationaly efficient CG-FFT procedure. This accuracy is checked by comparison with RCS measurements or predictions by other methods. As compared to the moment method, this CG-FFT scheme avoids the storage of large matrices and reduces the computer time by orders of magnitude. >

Interpolation by the FFT revisited-an experimental investigation

Abstract: A numerical investigation into the accuracy of interpolation by, fast Fourier transform (FFT), using a sinusoidal test signal, is described. The method is precisely defined, including a previously unnoticed detail which makes a significant difference to the accuracy of the result. The experiments show that, with no input windowing, the accuracy of interpolation is almost independent of sinusoidal wavelength very close to the Nyquist limit. The resulting RMS error is inversely proportional to input sequence length and is very low for sequence lengths likely to be encountered in practice. As wavelength passes through the Nyquist limit, there is a sudden increase in error, as is expected from sampling theory. If the sequence ends are windowed by short, cosine half-bells, accuracy is further improved at longer wavelengths. In comparison, small-kernal convolution methods, such as linear interpolation and cubic convolution, perform badly at wavelengths anywhere near the Nyquist limit. >

CPS transform correlation receiver and method

Abstract: A method for rapid acquisition of multiple GPS signals builds upon fast Fourier transformation of input GPS signals to simultaneously track multiple satellites and derive psuedorange measurements that are suitable for navigation solution. The method utilizes 2M samples of the reference signal with N samples of the signal set from the satellites (one millisecond of actual data) to directly compute the fractional psuedorange values for four (4) or more satellites. The FFT process is incorporated with a process to determine an integer psuedorange. The integer psuedorange is then combined with a fractional psuedorange to define the GPS navigation solution.

Automatic and reliable estimation of glottal closure instant and period

Abstract: The authors present an automatic and reliable algorithm for determining glottal closure instant (GCI). As a byproduct, nonstationary fundamental period estimation is achieved. The computation includes twelve-pole speech linear-prediction analysis, cross correlation, and both direct and inverse fast Fourier transforms (or a convolution). Maximum-likelihood epoch determination is used as the basis for locating GCIs, and the Hilbert transformation is applied to improve performance and reliability. A description of the system and the voiced/unvoiced/mixed (V/UV/M) decision procedure is given. The results show that the algorithm works in noise-free, noisy, and very noisy signals for vowels as well as for voiced constants. The proposed pitch estimation only needs a very short frame length and gives accurate results at voice onset. >

Speckle photography fringe analysis: assessment of current algorithms.

Abstract: The accuracy and reliability of four fringe analysis algorithms have been assessed, using Young's fringe patterns calculated from computer generated speckle patterns. The 1-D integration, 1-D autocorrelation, 2-D Fourier transform, and 2-D Walsh transform methods all estimated the two in-plane displacement components with negligible systematic error; the random errors were found to vary in proportion to sigma(2)/VR (speckle diameter = sigma, fringe visibility = V, and radius of laser probe beam = R), with the lowest errors given by the 2-D Fourier transform method.

Single spatial light modulator joint transform correlator

Abstract: We describe a joint Fourier transform image correlator that employs thresholding at both the input plane and the Fourier plane. This suggests using a single binary spatial light modulator (SLM) to read in sequentially the binarized input signal and the binarized Fourier transform interference intensity. The performance of the single SLM joint Fourier transform correlator (JTC) is compared with that of the classical JTC in the areas of correlation peak intensity, peak-to-sidelobe ratio, signal-to-noise ratio (SNR), and correlation width. We show that the single SLM JTC outperforms the classical JTC in all such areas. Using a single binary SLM results in significant reduction in cost, size and complexity of the system.

Performance analysis of frequency-domain block LMS adaptive digital filters

Abstract: The performance of the frequency-domain block least-mean-square (FBLMS) adaptive digital filters, whose filter weights are updated efficiently using the fast Fourier transform, is investigated. In particular, the convergence of the unconstrained FBLMS algorithm with reduced complexity, which is obtained by removing the constraint that has been known to be required in adjusting the frequency-domain weights based on overlap-save sectioning, is analyzed. The performance of the self-orthogonalizing FBLMS algorithm with improved convergence speed, in which different convergence factors normalized by frequency-domain power estimates are used for different frequency components of the weights, is also studied. >

Impulse Response Method for Frequency-Dependent Pipeline Transients

Abstract: An effective numerical method is presented to compute transients in piping systems in which frequency-dependent parameters influence the response. Frequency-dependent friction is utilized as the parameter-of-concern herein, however, the procedure can accommodate other factors such as frequency-dependent wavespeed equally well. The method, a variation in the impulse response method, is developed from the frequency response analysis and incorporates the fast Fourier transform

A neural net approach to discrete Hartley and Fourier transforms

Abstract: The authors present an electronic circuit, based on a neural (i.e. multiply connected) net to compute the discrete Fourier transform (DFT). They show both analytically and by simulation that the circuit is guaranteed to settle into the correct values within RC time constants (on the order of hundreds of nanoseconds), and they compare its performance to other on-chip DFT implementations. >

Comparison of probabilistic production cost simulation methods

Abstract: The authors present the results of an investigation of the relative computational speeds and solution qualities of six different probabilistic production cost simulation methods for power systems. The six methods are: the piecewise linear approximation (PLA), segmentation, equivalent energy function (EEF), cumulant, mixture of normal approximation (MONA), and fast Fourier transform (FFT) methods. For energy calculations, considering both speed and accuracy, it is concluded that if accuracy is paramount then the EEF method with the MW interval chosen to be the maximum common divisor of the block capacities is preferred. If speed is paramount, then either MONA or cumulants is preferred. >

An FFT based technique for suppressing narrow-band interference in PN spread spectrum communications systems

Abstract: Analyses and performance predictions of an FFT-based narrowband interference suppression filter for use in PN (pseudonoise) spread-spectrum communications systems are presented. The received baseband signal is processed in fixed-length blocks, transformed to the frequency domain with an FFT, filtered there by using an appropriate weighting, and then transformed back to the time domain. A general expression for the symbol matched filter signal-to-noise ratio (SNR) is given in terms of signal parameters and filter weighting coefficients. An optimal (maximum SNR) filter scheme and several suboptimal thresholding algorithms are discussed. Performance predictions, based on a realistic high-frequency interference model, are presented for these algorithms and FFT-based architecture. >

Integral transform method

Abstract: A method of performing an integral transform operation (such as a Fast Fourier Transform), wherein the underlying algorithm is partitioned to provide an efficient sequence of data operations. Preferably the address calculations are performed separately from the data calculations, and the algorithm is partitioned so that the microcode sequence for all but the last few data calculations is constant. Thus, the bandwidth at the interface to the numeric processor is conserved, and control storage in the numeric processor is also efficiently conserved. Moreover, the preferred partition for performing Fast Fourier Transform manipulates data in reasonably large subsets (e.g. 8 floating-point words at a time). This turns out to use less data bandwidth than would be required using smaller data subsets.

An analog speech scrambling system using the FFT technique with high-level security

Abstract: A full-duplex analog speech-scrambling system is proposed for application to mobile communication systems and public switched telephone networks. The scrambling algorithm is based on the rearrangement of the fast Fourier transform (FFT) coefficients accompanied by adaptive dummy spectrum insertion and companding operation. The simulation results indicate that the scrambled speech has no residual intelligibility and the descrambled speech quality is satisfactory. The hardware unit is implemented by using seven advanced digital signal processor chips, including those for an adaptive equalizer and an echo canceller for full-duplex operation. The performance is proven to be satisfactory. >

A new quadrature sampling and processing approach

Abstract: A quadrature sampling and array signal processing technique that differs from earlier approaches in that is processes the data before the Hilbert transformation is presented. A fast Fourier transformation (FFT) technique that performs the discrete Fourier transformation (DFT) on the sampled data directly without Hilbert transformation is proposed for frequency-domain signal processing. For array signal processing, the proposed approach does not perform Hilbert transformation prior to signal combining. It features high processing speed, low distortion, and hardware simplicity. Error analyses, performance evaluation, and computer simulation results are included. >

Split-radix algorithms for length-p/sup m/ DFT's

Abstract: The split-radix algorithm for the discrete Fourier transform (DFT) of length-2/sup m/ is considered. First, the reason why the split-radix algorithm is better than any single-radix algorithm on length-2/sup m/ DFTs is given. Then, the split-radix approach is generalized to length-p/sup m/ DFTs. It is shown that whenever a radix-p/sup 2/ outperforms a radix-p algorithm, then a radix-p/p/sup 2/ algorithm will outperform both of them. As an example, a radix-3/9 algorithm is developed for length-3/sup m/ DFTs. >

Intracerebral dipole sources of EEG FFT power maps

Abstract: The described method opens a way to compute intracerebral source localizations of ongoing EEG activity. A sine-cosine diagram of the Fourier-transformed data is constructed for each frequency point, forming a "FFT constellation" of entries. Into the FFT constellation of each diagram, a straight line is fitted which produces the least squared deviation sum between the original entry positions and their orthogonal projections onto that line. The map landscape described by the voltages between the projected positions ("FFT approximation") is the least error compromise landscape of all possible landscapes during the paradigmatic cycle of the given FFT frequency. The map thus constructed can be used in the usual dipole source localization procedures. There is one for each FFT frequency point. The squared forward solution of the fitted dipole source and the squared FFT approximation map are "power maps" which are very similar to the original power map. For an average-reference power map with two peaks, the source tends to lie between the peaks; a power map with one peak might show closely neighboring maximal and minimal potential values in the FFT approximation, indicative of a tangential source close to the surface.

Richardson-Lucy/maximum likelihood image restoration algorithm for fluorescence microscopy: further testing.

Abstract: A maximum likelihood based iterative algorithm adapted from nuclear medicine imaging for noncoherent optical imaging was presented in a previous publication with some initial computer-simulation testing. This algorithm is identical in form to that previously derived in a different way by W. H. Richardson , “ Bayesian-Based Iterative Method of Image Restoration,” J. Opt. Soc. Am.62, 55– 59 ( 1972) and L. B. Lucy , “ An Iterative Technique for the Rectification of Observed Distributions,” Astron. J.79, 745– 765 ( 1974). Foreseen applications include superresolution and 3-D fluorescence microscopy. This paper presents further simulation testing of this algorithm and a preliminary experiment with a defocused camera. The simulations show quantified resolution improvement as a function of iteration number, and they show qualitatively the trend in limitations on restored resolution when noise is present in the data. Also shown are results of a simulation in restoring missing-cone information for 3-D imaging. Conclusions are in support of the feasibility of using these methods with real systems, while computational cost and timing estimates indicate that it should be realistic to implement these methods. It is suggested in the Appendix that future extensions to the maximum likelihood based derivation of this algorithm will address some of the limitations that are experienced with the nonextended form of the algorithm presented here.

Electromagnetic scattering by a dielectric body with arbitrary inhomogeneity and anisotropy

Abstract: The scattering problem for a dielectric body is formulated in terms of the electric field integral equation where the scatterer is of general shape, inhomogeneity, and anisotropy. On applying the pulse-function expansion and the point-matching technique, the integral equation is solved using an efficient procedure involving the conjugate-gradient method and the fast Fourier transform (FFT). The solution procedure runs parallel to that of the two-dimensional case previously presented by the author (see ibid., vol.AP-35, p.1418-25, Dec. 1987). Most of the work presented involves generalizing two-dimensional Green's function and operations into corresponding three-dimensional ones. >

A Parallel FFT on an MIMD Machine.

Abstract: Abstract In this paper we present a parallelization of the Cooley- Tukey FFT algorithm that is implemented on a shared-memory MIMD (non-vector) machine that was built in the Dept. of Computer Science, Tel Aviv University. A parallel algorithm is presented for one dimension Fourier transform with performance analysis. For a large array of complex numbers to be transformed, an almost linear speed-up is demonstrated. This algorithm can be executed by any number of processors, but generally the number is much less than the length of the input data.