Showing papers on "Discrete-time Fourier transform published in 1980"
TL;DR: In this article, the authors developed a representation for discrete-time signals and systems based on short-time Fourier analysis and showed that a class of linear-filtering problems can be represented as the product of the time-varying frequency response of the filter multiplied by the short time Fourier transform of the input signal.
Abstract: This paper develops a representation for discrete-time signals and systems based on short-time Fourier analysis. The short-time Fourier transform and the time-varying frequency response are reviewed as representations for signals and linear time-varying systems. The problems of representing a signal by its short-time Fourier transform and synthesizing a signal from its transform are considered. A new synthesis equation is introduced that is sufficiently general to describe apparently different synthesis methods reported in the literature. It is shown that a class of linear-filtering problems can be represented as the product of the time-varying frequency response of the filter multiplied by the short-time Fourier transform of the input signal. The representation of a signal by samples of its short-time Fourier transform is applied to the linear filtering problem. This representation is of practical significance because there exists a computationally efficient algorithm for implementing such systems. Finally, the methods of fast convolution age considered as special cases of this representation.
600 citations
TL;DR: A new structure and a simplified interpretation of short-time Fourier synthesis using synthesis windows is presented and it is shown how this structure can be used for analysis/synthesis applications which require different analysis and synthesis rates, such as time compression or expansion.
Abstract: In this correspondence we present a new structure and a simplified interpretation of short-time Fourier synthesis using synthesis windows. We show that this approach can be interpreted as a modification of the overlap-add method where we inverse the Fourier transform and window by the synthesis window prior to overlap-adding. This simplified interpretation results in a more efficient structure for short-time synthesis when a synthesis window is desired. In addition, we show how this structure can be used for analysis/synthesis applications which require different analysis and synthesis rates, such as time compression or expansion.
315 citations
TL;DR: The effects of aliasing (including pseudoaliasing), picket-fence effect, and leakage in the fast Fourier transform (FFT) are presented.
Abstract: The effects of aliasing (including pseudoaliasing), picket-fence effect, and leakage in the fast Fourier transform (FFT) are presented. A computer program was written to perform the FFT analysis of known inputs. The program has the capability of detecting aliasing by calculating an "aliasing coefficient" (Q), and will increase the sampling frequency and the number of points in the input sequence if aliasing occurs. The term "pseudoaliasing" is a phenomenon which is similar to aliasing (or fold-over) but related to the effects of picket fence and leakage. The "leakage coefficient" (ri) is a quantitative measure of the deviation from the fundamental frequency component with respect to the sampling frequency, when the input sequence has only one frequency component.
265 citations
TL;DR: In this paper, the authors present new discrete Fourier transform methods which are recursive, expressible in state variable form, and involve real number computations, which are especially useful for running Fourier transformation and for general and multirate sampling.
Abstract: This paper presents new discrete Fourier transform methods which are recursive, expressible in state variable form, and which involve real number computations. The algorithms are especially useful for running Fourier transformation and for general and multirate sampling. Numerical examples are given which illustrate the ability of these spectral observers to operate at sampling rates other than the Nyquist rate, to perform one-step-per-sample updating, and to converge to the spectrum in the presence of severe numerical truncation error.
146 citations
TL;DR: In this paper, a usable characterization of the group Fourier transform of Schwartz space on the Heisenberg group H n, in terms of certain asymptotic series was derived.
81 citations
62 citations
TL;DR: A third order Laplace transform whose coefficients can be related to distal impedance, proximal lumen diameter and elastic modulus is results in a blood-velocity/time waveform over the cardiac cycle from the common femoral artery investigated using Fourier transform and curve-fitting techniques.
Abstract: The blood-velocity/time waveform over the cardiac cycle from the common femoral artery is investigated using Fourier transform and curve-fitting techniques. This results in a third order Laplace transform whose coefficients can be related to distal impedance, proximal lumen diameter and elastic modulus. The validity of the method is investigated by determining the coefficients of the Laplace transform, derived from the common femoral waveform, and from these values, reconstructing the waveform and comparing with the original. The Fourier transform, curve fitting, and reconstruction procedures are shown for each waveform so that all stages of the method can be critically assessed.
58 citations
54 citations
TL;DR: It is shown theoretically that, at least for a wide class of functions, such determination is not possible, and the theory developed in this Letter is essentially two dimensional.
Abstract: Is it possible to determine a function with a finite support from the modulus of its Fourier transform? This problem, the so-called phase problem, is studied theoretically and numerically. It is shown theoretically that, at least for a wide class of functions, such determination is not possible. The theory developed in this Letter is essentially two dimensional. Examples are given and studied numerically.
35 citations
TL;DR: The aim of this paper is to show that the three widely and satisfactorily used techniques of Samulon, Nicolson, and Gans, which originate from apparently different ideas, are exactly the same.
Abstract: In 1965 Cooley and Tukey published an algorithm for rapid calculation of the discrete Fourier transform (DFT), a particularly convenient calculating technique, which can well be applied to impulse-like functions whose beginning and end lie at the same level. Independently, various propositions were made to overcome the truncation error which arises, if a step-like function, i.e. one whose end level differs from its starting level, is treated in the same way. It was argued that they behave differently under the influence of noise, band-limited violation, and other experimental inconveniences. The aim of this paper is to show that the three widely and satisfactorily used techniques of Samulon, Nicolson, and Gans, which originate from apparently different ideas, are exactly the same. An extended DFT and fast Fourier transform (FFT) formula is deduced which is adapted as well to impulse-like as to step-like functions.
28 citations
TL;DR: In this paper, the authors proposed a numerical technique for the computation of Fourier transforms using a bilateral expansion of the unknown transformed function with respect to Laguarre functions using trigonometric interpolation and may be computed very efficiently by means of the Fast Fourier Transform.
Abstract: In this paper we propose a numerical technique for the computation of Fourier transforms. It uses a bilateral expansion of the unknown transformed function with respect to Laguarre functions. The expansion coefficients are obtained via trigonometric interpolation and may be computed very efficiently by means of the Fast Fourier Transform. The convergence of the algorithm is analyzed and numerical results are presented which confirm that it works well.
01 Feb 1980
TL;DR: In this paper, a real-time Fourier spectral analysis algorithm for Fourier analysis is presented, which is recursive, expressable in state variable form, and involves real number computations.
Abstract: New techniques for Fourier spectral analysis are reported, for which ongoing spectral estimates are generated in real time. The algorithms are recursive, expressable in state variable form, and involve real number computations. The ability of these spectral observers to perform one-step-per-sample updating is demonstrated with numerical examples.
TL;DR: Analysis is given for Good's algorithm and for two algorithms that compute the discrete Fourier transform in O(n log n) operations: the chirp-z transform and the mixed-radix algorithm that computes the transform of a series of prime length p in P log p operations.
TL;DR: A decomposition of the Cooley-Tukey algorithm is proposed to allow efficient utilization of core memory and mass storage and the number of input/output operations is greatly reduced, with no increase in the computational burden.
Abstract: We consider the problem of performing a two-dimensional fast Fourier transform (FFT) on a very large matrix in limited core memory. We propose a decomposition of the Cooley-Tukey algorithm to allow efficient utilization of core memory and mass storage. The number of input/output operations is greatly reduced, with no increase in the computational burden. The method is suitable for nonsquare matrices and arrays of three or more dimensions.
TL;DR: A basis for the processing of EEG signals using the discrete, orthogonal set of Walsh functions provides sufficient justification for usage of Walsh spectral features in place of Fourier spectral features, enabling one to take advantage of the vast computational superiority of the fast Walsh transform over the fast Fourier transform.
Abstract: A basis for the processing of EEG signals using the discrete, orthogonal set of Walsh functions is presented. The Walsh power spectrum is examined from the point of view of its statistical properties, especially as it relates to spectral resolution. Features, selected from the spectrum of sleep EEG data are compared to corresponding Fourier features. Each feature set is used to classify the data using a minimum-distance clustering algorithm. The results show that the Walsh spectral features classify the data in much the same way as the Fourier spectral features. This provides sufficient justification for usage ofWalsh spectral features in place of Fourier spectral features, enabling one to take advantage of the vast computational superiority of the fast Walsh transform over the fast Fourier transform.
Patent•
29 Jul 1980TL;DR: In this article, a system for using optical data processing means to create the ambiguity function for two signals is disclosed, where one-dimensional spatial light modulators are employed to code the signals into a beam of substantially coherent light.
Abstract: A system for using optical data processing means to create the ambiguity function for two signals is disclosed. One-dimensional spatial light modulators are employed to code the signals into a beam of substantially coherent light. After the light has been coded with the first one-dimensional signal a Fourier Transform is performed by lens means. A linear phase shifter is placed in the Fourier Transform plane. This has the effect of creating a linear dependence along a second dimension when a second Fourier Transform is performed.
TL;DR: In this paper, conditions for a transform of the DFT structure, defined in a ring of residues of algebraic integers, to map cyclic convolution isomorphically into a pointwise product are presented.
Abstract: Conditions are presented for a transform of the DFT structure, defined in a ring of residues of a ring of algebraic integers, to map cyclic convolution isomorphically into a pointwise product. The conditions are used to verify that a number of potentially useful transforms (which require no general multiplications) satisfy this property. In particular, transforms defined in residue rings of the Gaussian integers, the Eisenstein integers, and a biquadratic domain are studied.
01 Apr 1980
TL;DR: A set of conditions under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform are developed, applicable to mixed-phase one-dimensional and multi-dimensional sequences.
Abstract: In this paper, we develop a set of conditions under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform. These conditions are applicable to mixed-phase one-dimensional and multi-dimensional sequences. Under the specified conditions, we also present several algorithms which may be used to reconstruct a sequence from its phase.
TL;DR: In this article, a new method of determining Fourier coefficients is described, which is the substitution of algebraic addition to replace the integration operation in Fourier analysis, and is applicable to every periodic function that satisfies Dirichlet conditions.
Abstract: A new method of determining Fourier coefficients is described. The advantage of the method is the substitution of algebraic addition to replace the integration operation in Fourier analysis. The method is applicable to every periodic function that satisfies Dirichlet conditions. Several waveforms of converter voltages and currents are analyzed as examples for the method.
TL;DR: In this paper, a unified derivation for three known expressions for the Fourier decomposition of a scalar function on spheres is presented, which is put in a common framework for easy comparison and are contrasted in a table.
Abstract: A unified derivation for three known expressions for the Fourier decomposition of a scalar function on spheres is presented. The expressions are put in a common framework for easy comparison and are contrasted in a table. One expression is shown to be superior.
DOI•
01 Feb 1980TL;DR: An algorithm is presented, for the computation of multidimensional Fourier and Fourier-like discrete transforms, which offers substantial savings in the number of multiplications over the conventional fast Fourier transform method.
Abstract: An algorithm is presented, for the computation of multidimensional Fourier and Fourier-like discrete transforms, which offers substantial savings in the number of multiplications over the conventional fast Fourier transform method Implementation of this algorithm, and the use of it to compute discrete Fourier transforms of real sequences, are also described
TL;DR: In this paper, the possible line distortions and signal-to-noise and resolution enhancement ratios in the Ernst filter are explicitly derived and the general limitation inherent in the digital transformation on the minimum linewidth obtainable by any convolution filter is also derived.
Patent•
IBM1
TL;DR: In this article, an apparatus for computing the two-dimensional discrete Fourier transform (DFT) of an image comprised of N×N samples is presented. But it is not shown how to compute the one-dimensional DFT of the image.
Abstract: An apparatus for computing the two-dimensional discrete Fourier transform (DFT) of an image comprised of N×N samples. The samples within each row are respectively multiplied by W-n.sbsp.1, n1 =0, 1, . . . , N-1 and stored in a memory 17. A device 20 derives therefrom N polynomials of N terms by means of a polynomial transform. The terms of each of these polynomials are multiplied by Wn.sbsp.1 and a device 28 computes the one-dimensional DFT thereof, thereby providing the N2 terms of the transform of said image.
IBM1
TL;DR: A variant of the Cooley-Tukey algorithm due to Stockham is derived and vectorized and is shown to be on a par with the Pease algorithm.
Abstract: A variant of the Cooley-Tukey algorithm due to Stockham is derived and vectorized and is shown to be on a par with the Pease algorithm. The Stockham algorithm is then proposed for the entire computation of the two-dimensional fast Fourier transform on a vector computer.
DOI•
01 May 1980
TL;DR: In this article, the power spectra may be computed via a discrete fourier transform with severely rounded-off trigonometric terms, and recently the ultimate round-off to rectangular waves has been proposed.
Abstract: Power spectra may be computed via a discrete fourier transform with severely rounded-off trigonometric terms, and recently the ultimate round-off – that is to rectangular waves – has been proposed.1 A comparison is made between this and a 3 level round-off, +1, −1 and 0.
01 Apr 1980
TL;DR: This paper develops a closed-form expressions for these spectral estimators when the estimates are constrained to be discrete and relatively simple expressions result which can be used to compare the two methods in a straightforward manner.
Abstract: Two different methods for extrapolating a given time-limited data sequence have been proposed. The first uses a linear prediction model and the second is based on a bandlimited constraint. In both cases, the extrapolated sequence is constrained to equal the initial data on the given interval and to provide an estimate of the data outside that interval. A high resolution spectral estimate which contains both gain and phase information is then computed from a Fourier Transform of the extrapolated sequence. This paper develops a closed-form expressions for these spectral estimators when the estimates are constrained to be discrete. In this case, relatively simple expressions result which can be used to compare the two methods in a straightforward manner.
TL;DR: An all-spherical-mirror system for applications in coherent image processing is described and analyzed and the Fourier transform properties of this one-to-one system are acceptable for many applications.
Abstract: An all-spherical-mirror system for applications in coherent image processing is described and analyzed. This one-to-one system is panchromatic and can be made to have minimal cosmetic defects. Such a system offers advantages such as multiple wavelength operations and the introduction of minimal scattering noise into the final image. A sample design that is diffraction-limited (for f/8) over the entire area of a standard 35-mm slide is given. The Fourier transform properties of this system are acceptable for many applications.