Showing papers on "Discrete Fourier transform published in 1972"

Dynamic stress-intensity factors for finite strip problems

Abstract: Two simple opening-mode finite strip problems are discussed. The discussion is limited to a dynamic steady-state solution within the realms of the classical theory of elasticity. It is shown that by using Fourier transform methods, the problems are reduced to equations of the Wiener-Hopf type. The complete stress and displacement distributions are difficult to obtain, and no attempt is made to arrive at this. By application of the asymptotic properties of the Fourier transform the stress-intensity factor is, instead, derived.

Real-time Fourier transform with a surface-wave convolver

Abstract: The generation of Fourier transforms of electronic signals in real time with an acoustic-surface-wave convolver is demonstrated. Two matched chirps propagating through each other behave as a narrowband filter in wavevector space, with the filter centre moving at a rate proportional to the acoustic velocity and the chirp rate.

A fast Fourier transform algorithm for symmetric real-valued series

Abstract: A new algorithm is presented for calculating the real discrete Fourier transform of a real-valued input series with even symmetry. The algorithm is based on the fast Fourier transform algorithm for arbitrary real-valued input series (FTRVI) [1], [2]. By eliminating all unnecessary steps and storage locations, and by rearranging the intermediate results and the operation sequence, it is possible to reduce the computation time and the required core storage by a factor of 2 as compared to the case of arbitrary real input or by a factor of 4 as compared to the general fast Fourier transform for complex inputs.

Spectral errors resulting from random sampling-position errors in fourier transform spectroscopy.

Abstract: In the design and operation of a two-beam interferometer in Fourier spectroscopy, it is important to known how much the lack of precision in the setting of the optical path differences will affect the measured spectra. This problem has been considered by Surh, and by Sakai, who has given a relation for the stan­ dard deviation in the size of the \"ghost\" lines due to the random error in the sampling of the interferogram of a monochromatic spectral line. We will reformulate and extend the results to apply to a more general spectrum. Consider an interferogram P(x) which is sampled at optical path differences x = jΔx giving values Pj for N, conveniently an even integer, values of the integer j in the range — N/2 ≤ j < N/2. The discrete Fourier transform pair

Interpolation using the fast Fourier transform

Abstract: The fast Fourier transform (FFT) algorithm has had widespread influence in many areas of computation since its "rediscovery" by Cooley and Tukey [1] An efficient and accurate method for interpolation of functions based on the FFT is presented As an application, the generation of the characteristic polynomial in the "generalized eigenvalue problem" [2] is considered

The Application of Filtered Transforms to the General Classification Problem

Abstract: An image classification model based on nearest prototypes in filtered Fourier and Walsh transform domains is presented. A computer simulation of the model applied to handwritten English letters, Russian letters, numerals, and electromagnetic signals is also presented. Experiments to date fail to refute the working hypothesis that generalized harmonic analysis can be used to reliably classify alphabet characters, time-varying signals, and other images.

A Parallel Implementation of the Fast Fourier Transform Algorithm

Abstract: For many real-time signal processing problems, correlations, convolutions, and Fourier analysis must be performed in special-purpose digital hardware. At relatively high levels of performance, it becomes necessary for this hardware to perform some of its computations in parallel. A parallel FFT algorithm is described that segments the fast Fourier transform algorithm into groups of identical parallel operations that can be performed concurrently and independently. A hardware implementation of the algorithm is described in the context of the parallel element processing ensemble (PEPE) previously described by Githens [7], [8].

A real-time processing system and method utilizing discrete fourier transform

Abstract: A method of and device for carrying out real-time processing of electrical signals wherein, after sampling and quantizing the signals which are to be processed, real samples N are subjected to a pre-processing operation in a system in which a time sequence of said N samples of the processed signal is transformed into a sequence of N/2 complex samples Um applied to and processed in a F.F.T. iterative or repetitive algorithm computer unit of conventional design and mode of operation with N/2 points. The computer unit generates D.F.T. coefficients for which there is a symmetrical relationship between the even complex coefficients C2q and the related odd complex coefficients C*N 2q 2p 1.

Fourier transforms of homogeneous distribution

Abstract: © Scuola Normale Superiore, Pisa, 1972, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Fast convolution for recursive digital filters

Abstract: A physically motivated procedure is presented for evaluating the response of recursive digital filters via the fast Fourier transform (FFT). The key idea of the method is to employ a short string of artificial impulses as an alternative representation of the initial conditions implicit in processing a long excitation in segments. The method is computationally more efficient or of wider applicability than existing FFT techniques.

Dynamic Analysis by Extra Fast Fourier Transform

Abstract: A method based on the Discrete Fourier Transform (DFT) is presented for evaluating the dynamic response of any discrete, time invariant, linear system to an excitation, the spatial distribution of which is constant and the timewise variation of which may be represented by a string of equally spaced impulses of arbitrary magnitudes. In addition to being faster and more efficient than available DFT approaches, the method may be adopted to the processing of arbitrarily long excitations as a series of short, independent segments. The length of the individual segments may be chosen to optimize computational efficiency. The method consists of taking advantage of the periodicity implicit in the DFT approach and evaluating first the response of the system to a periodic extension of the excitation. A simple corrective solution is then superposed which converts the periodic response to the desired transient response. The method is illustrated by two numerical examples.

Method of an apparatus for processing of signals to transform information between the time domain and frequency domain

Abstract: A method of and apparatus for signal processing to transform information between the time domain and frequency domain (Fourier transform) wherein a time-varying electromagnetic signal to be analyzed and a series of radio frequency pulses are applied to a piezoelectric medium so as to interact at predetermined positions, and generate sampling pulses which are subsequently combined in the medium in a fashion to provide the discrete Fourier transform of the time-varying signal.

An algorithm for the on-line computation of fourier spectra

Abstract: An on-line method to compute the spectra associated with the Fourier transform M of a data sequence is developed, whereM and N are finite positive integers. This method provides a simple means of generating time-frequency-amplitude plots of Fourier power and phase spectra. Such plots may be used to display Fourier spectra for pedagogical purposes, and in the general area of the classification of transient waveforms whose durations are unknown. An illustrative example is included.

Summability and Fourier analysis.

Abstract: Let s = {sn} be an infinite sequence of complex numbers, that is, a continuous function on the discrete additive semigroup of natural numbers N. The sequence s has a continuous extension s to βN, the Stone-Cech compactification of N (s takes the value if s is unbounded). Throughout the paper, the symbol βZ denotes the Stone-Cech compactification of the space Z, and the continuous extension of a function / defined on Z to βZ will be denoted by f; for a description of the Stone-Cech compactification we refer the reader to [2, pp. 82-93], We impose the norm

On generalized Walsh functions and transform

Abstract: This paper is basically tutorial in nature. Hence, its purpose is to introduce the Walsh set of functions, Walsh transform and some of the basic properties of these two formulations. The method of defining Walsh functions as products of Rademacher functions is adopted here. These functions are then extended to the generalized Walsh functions; and consequently the Walsh transform is introduced. The notion of a delta function for Walsh analysis is developed along the lines of the classical Fourier analysis. And finally, relations connecting Walsh and Fourier transforms are derived.

A Theory for Optimal MTI Digital Signal Processing: Part 1. Receiver Synthesis

Abstract: : A classical problem in radar theory is the detection of moving targets in a ground clutter plus receiver noise background. Improvements in clutter rejection have recently been made by replacing analog MTI processors by their digital equivalents as this eliminates many of the problems associated with the maintenance of the analog hardware. In an attempt to determine the ultimate improvements possible using this new technology, the MTI problem was formulated as a classical detection problem and solved using the generalize likelihood ratio test. By manipulating the likelihood ratio, the receiver could be interpreted as a clutter filter in cascade with a doppler filter bank. The performance of the optimum receiver was evaluated in terms of the output signal- to-interference ratio and compared with well-known MTI processors. It was shown that near-optimum performance can be obtained using a sliding weighted Discrete Fourier Transform (DFT).

Automated design of large-signal amplifiers for minimum distortion

Abstract: A technique for the design of large-signal amplifiers for minimum distortion is presented. This technique takes advantage of the frequency-domain aspects of the problem by using the fast Fourier transform.

Digital Bandpass Beamforming with the Discrete Fourier Transform

Abstract: : A method is developed to form beam spectral estimates from a set of signals sampled from hydrophone outputs of an acoustic array. The signals must be frequency band limited over an interval (Wo,Wo+W) and sampled over a time interval T. A savings of (Wo/W) + 1 in data storage and computation time is realized over conventional beam forming analysis methods employing sampling rates equal to twice the highest frequency in the signal band. Any set of delays ti may be used and the beamforming error determined as long as ti

A note on the spectral analysis of periodic functions

Abstract: An analysis of the Fourier transform for a truncated cosine waveform is given that illustrates the dependence of the transform on the phase as the period of the waveform becomes large with respect to the record length. The effects of sampling on the transform are then discussed and illustrated.

Rapid calculation of selected fourier spectrum ordinates

Abstract: The use of Fourier spectrum techniques in earthquake engineering has grown rapidly in recent years because of the economy of programs using the Fast Fourier Transform (FFT) and the widespread use of Fourier techniques in other fields of engineering and science. Typically, the standard FFT programs take 2N equally spaced data points in the time domain as input and produce as output 2N-1 Fourier amplitude spectrum ordinates equally spaced in the frequency domain from 0 cps to the maximum frequency permitted by the digitization interval. By appropriate choice of filters, sampling interval and length of record, the FFT approach can be adapted to most purposes, but there is occasionally a need to calculate a few spectrum points in narrow frequency bands or to analyze, over selected frequency bands, records of longer duration than can be accommodated conveniently by standard FFT programs. The technique presented below permits such calculations to be made rapidly and accurately. In addition, the method helps in the interpretation of Fourier spectra used in earthquake engineering because it is developed from the point of view of elementary vibration theory. The first part of the text reviews the relation between the response of an undamped, single degree-of- freedom oscillator subjected to the same accelerogram. This review shows that the calculation of the Fourier amplitude and phase spectrum ordinates is equivalent to finding the potential and kinetic energies of an undamped oscillator at the end of the excitation. The analysis is then extended to include an associated free vibration problem useful in the interpretation of Fourier spectra. The next portion of the study shows that these final response values can be calculated rapidly and accurately by reducing the accelerogram, regardless of length, to an equivalent excitation with a duration of one natural period, and by further reduction to two excitations - one for displacement and one for velocity - of only one-quarter period duration. The response of the oscillator to the shortened excitations can then be calculated by standard methods. The next section is devoted to the development of a subroutine for calculating ordinates of Fourier amplitude spectra by this approach, and to the presentation of examples of its use. The study concludes with a discussion of possible applications and extensions of the method.

Efficient Data Transformation in Time-Domain Spectrometry

Abstract: In applications of time-domain spectrometry, in which frequency-domain information is obtained by means of Fourier transformation of time-domain excitation and response signals, results are often required at a number M of evenly spaced frequencies, where M is considerably smaller than N, the number of amplitude samples from which the discrete Fourier transform is formed. Under such conditions the modified form of fast Fourier transformation described offers markedly greater computing efficiency than the standard form.

A method of computer generation of correlated Gaussian pseudo-random numbers☆

Abstract: A METHOD is described for generating stationary and non-stationary sequences of pseudo-random Gaussian numbers with given correlation from sequences of independent bounded pseudo-random numbers with arbitrary distributions. The method is based on computing the discrete Fourier transform of the initial sequence, modified in accordance with the required energy spectrum. As a result of using the fast Fourier transformation algorithm, after N log 2N computer operations, N Gaussian numbers can be generated with a given energy spectrum of arbitrary shape; not more than N numbers of the initial sequence are expended in these operations. The method is useful for generating large blocks of high-quality correlated Gaussian numbers.

Spectral Analysis of Unequally Spaced Data Samples

Abstract: : Most of the theory and practice of digital spectral analysis is based on use of the discrete Fourier transform, which by definition requires a set of data values measured at equally spaced times. In the paper the authors consider the analysis of data that are only approximately on an equally spaced grid and that in addition suffers from the problem of missing observations. In this case, the discrete Fourier transform is not directly applicable, and the authors consider several alternative approaches. The authors then consider in detail the measurement of the frequency of a single sinusiodal function in the presence of noise, using an approach based on minimizing the residual squared error after fitting. (Author)

Some considerations of the discrete Fourier and Walsh-Hadamard transforms

Abstract: In this Paper, we summarize a set of properties of the discrete Fourier transform (DFT) and compare them with corresponding properties of the Walsh-Hadamard transform (WHT) [see Table I]. It is hoped that such a summary will assist in observing the analogy between Walsh-Hadamard and discrete Fourier analyses for those who are relatively more familiar with the latter.

A comparison of the fast Fourier and trigonometric Fourier algorithms

Abstract: The Cooley–Tukey fast Fourier algorithm and the factored trigonometric Fourier algorithm are compared for four typical crystallographic problems. With general PL/1 programs the execution speed of the fast Fourier algorithm ranged from 4.7 to 19 times faster than the trigonometric algorithm. In addition the PL/1 fast Fourier program was 1.8 times faster than a space group specific, fixed axial length trigonometric Fourier FORTRAN program. Our results indicate that the fast Fourier is the most efficient algorithm available for crystallographic Fourier series calculations, with efficiency increasing as one goes to larger problems.