Showing papers on "Harmonic wavelet transform published in 1973"
TL;DR: In this paper, a method for estimating the magnitude-squared coherence function for two zero-mean wide-sense-stationary random processes is presented, which utilizes the weighted overlapped segmentation fast Fourier transform approach.
Abstract: A method for estimating the magnitude-squared coherence function for two zero-mean wide-sense-stationary random processes is presented. The estimation technique utilizes the weighted overlapped segmentation fast Fourier transform approach. Analytical and empirical results for statistics of the estimator are presented. The analytical expressions are limited to the nonoverlapped case; empirical results show a decrease in bias and variance of the estimator with increasing overlap and suggest a 50-percent overlap as being highly desirable when cosine (Hanning) weighting is used.
521 citations
01 Oct 1973
TL;DR: The smoothed coherence transform is defined and examples of its uses and shortcomings are given and Computation of this function shows promise for measuring time delays between weak broad-band correlated noises received at two sensors.
Abstract: The smoothed coherence transform (SCOT) is defined and examples of its uses and shortcomings are given. Computation of this function shows promise for measuring time delays between weak broad-band correlated noises received at two sensors.
203 citations
TL;DR: Methods for incorporating crystallographic symmetry properties into complex Fourier transforms in a form particularly well suited for use with the Cooley-Tukey fast Fourier transform algorithm are presented.
Abstract: This paper presents methods for incorporating crystallographic symmetry properties into complex Fourier transforms in a form particularly well suited for use with the Cooley-Tukey fast Fourier transform algorithm. The crystallographic transforms are expressed in terms of a small number of one-dimensional special cases. The algebra presented here has been used to write computer programs for both Fourier syntheses and Fourier inversions. Even for some quite large problems (7000 structure factors and 149000 grid points in the asymmetric unit) the rate-limiting step is output of the answers.
199 citations
TL;DR: The theoretical basis for representation of a speech signal by its short-time Fourier transform is discussed and the design tradeoffs necessary to achieve moderate information rate reductions are elucidated.
Abstract: This paper discusses the theoretical basis for representation of a speech signal by its short-time Fourier transform. The results of the theoretical studies were used to design a speech analysis-synthesis system which was simulated on a general-purpose laboratory digital computer system. The simulation uses the fast Fourier transform in the analysis stage and specially designed finite duration impulse response filters in the synthesis stage. The results of both the theoretical and computational studies lead to an understanding of the effect of several design parameters and elucidate the design tradeoffs necessary to achieve moderate information rate reductions.
116 citations
TL;DR: In this article, the Fourier transform of the spin echo using the pulsed gradient, spin echo technique was used to determine the self-diffusion coefficient of each component in a multicomponent system.
115 citations
107 citations
TL;DR: The fast Fourier transform is employed in the most efficient measurement of the Wiener kernels of a non-linear system so far discovered.
Abstract: A new method is presented for the measurement of the Wiener kernels of a non-linear system. The method uses the complex exponential functions as a set of orthogonal functions with which to expand the kernels. The fast Fourier transform is then employed in the most efficient measurement of the kernels so far discovered.
105 citations
TL;DR: In this article, it was shown that the truncation error can also be removed at discrete frequencies, simply by first subtracting a ramp from the step response of a network, with consequent noise enhancement.
Abstract: If the discrete Fourier transform of the step response of a network is taken, a large truncation error results, since only a finite number of samples is used. This error is usually removed by first differentiating the waveform, with consequent noise enhancement. The letter shows that the error may also be removed at discrete frequencies, simply by first subtracting a ramp from the step response.
91 citations
TL;DR: In this paper, the Fast Fourier Transform (FFT) is used for fitting experimental data described by a sum of exponentials, which has been shown to be well suited for use even on a small computer.
42 citations
TL;DR: The advantages and drawbacks of Hadamard transform spectroscopy are examined in detail and existing theory, as reported in the literature, is not consistent with the claims made for the technique.
Abstract: Recent articles have claimed a significant S/N advantage of Hadamard transform spectroscopy over Fourier transform spectroscopy. The scanty published data does not support this assertion, and the possibility that the claim is valid in theory is examined. Existing theory, as reported in the literature, is not consistent with the claims made for the technique. The advantages and drawbacks of Hadamard transform spectroscopy are examined in detail.
TL;DR: It is shown how simple integration rules can be associated with the Fast Fourier Transform technique in order to obtain accurate results without reducing essentially the speed of computation.
TL;DR: A hybrid special-purpose computer based on a recursive algorithm for discrete Walsh transform computations is described, which uses feedback in time to reduce the required number of summing junctions to N, the number of data points to be transformed.
Abstract: A hybrid special-purpose computer based on a recursive algorithm for discrete Walsh transform computations is described. The device uses feedback in time to reduce the required number of summing junctions to N, the number of data points to be transformed. Computations are completed in 700 ?s when N = 256.
TL;DR: Concepts of group theory are used to explain the difference between two major fast Fourier transform algorithms and the relation between FFT and fast Walsh transforms.
Abstract: Concepts of group theory are used to explain the difference between two major fast Fourier transform (FFT) algorithms and the relation between FFT and fast Walsh transforms.
TL;DR: The effects of severely quantising the multiplication coefficients in the fast Fourier transform have been studied in this article, where it was shown that rounding these off to the nearest power of 2 produces power-spectrum errors of as little as 0.08% (maximum) for a pure sinewave sampled at 64 points.
Abstract: The effects of severely quantising the multiplication coefficients in the fast Fourier transform have been studied. Rounding these off to the nearest power of 2 produces power-spectrum errors of as little as 0.08% (maximum) for a pure sinewave sampled at 64 points.
TL;DR: Spectral modes for the generalized transform are developed in this paper, which are invariant to cyclic shift of the input sequence and possess sequency resolution in their squared terms, however, they cannot be called energy spectra as there are cross terms, some of which are negative.
Abstract: Spectral modes for the generalized transform are developed. These spectra are invariant to cyclic shift of the input sequence and possess sequency resolution in their squared terms. They cannot, however, be called energy spectra as there are cross terms, some of which are negative.
Journal Article•
TL;DR: An assembler language program for a PDP 11 20 (1) computer has been written for on-line data acquisition and analysis of asymmetric interferograms obtained by far infrared Foutier transform spectroscopy as discussed by the authors.
TL;DR: Various pre-processing and post-processing techniques that reduce the errors and favourably change the distribution of errors in the reconstructed signal or reduce the effective bit-rate without affecting the errors inThe reconstructed signal are discussed.
Abstract: In digital signal processing in the transform domain, it is important to study the effects of quantization in the transform domain on the signal reconstructed by inverse transformation. Adaptive quantization schemes are developed earlier for Fourier transform domain and Hadamard transform domain, using the knowledge that in the transform domain adaptive set-dependent bounds can be obtained on the sample amplitudes. This paper discusses various pre-processing and post-processing techniques that reduce the errors and favourably change the distribution of errors in the reconstructed signal or reduce the effective bit-rate without affecting the errors in the reconstructed signal.
TL;DR: This work has sought a way to make the Fourier transform hologram require less dynamic range, by reducing the dynamic range of a high-dynamic-range pattern with out changing the pattern.
Abstract: Fourier transform holography has proved useful in infor mation storage, data processing, pattern recognition, image enhancement, interferometry, and several other fields.The properties that make the Fourier transform of such interest are its relationship to the spatial frequen cies in the input wavefront and its relative compactness. At the same time the Fourier transform pattern presents some significant technical problems. These arise almost entirely from the tremendous range in amplitudes encoun tered in a typical Fourier transform. In the effort to alle viate these problems I have sought a way to make the Fourier transform hologram require less dynamic range. The Fourier transform pattern itself is determinate. Changes that modify that pattern would reduce its use fulness. Therefore, the problem is: How can we reduce the dynamic range of a high-dynamic-range pattern with out changing the pattern? That at least one class of solu-
TL;DR: In this article, an improved form of the Fourier optical method is developed by the use of symmetric transforms, and is suited to problems involving a repeated Fourier transform, which is used for the classification of laser velocimeters into scattering and reference beam systems, and the analysis indicates that for the systems considered the signals cannot be made coherent (ie additive) when a cloud of many thousands of particles is present in the measuring volume.
Abstract: An improved form of the Fourier optical method is developed by the use of symmetric transforms, and is suited to problems involving a repeated Fourier transform. The method is used for the classification of laser velocimeters into scattering and reference beam systems, and the analysis indicates that for the systems considered the signals cannot be made coherent (ie additive) when a cloud of many thousands of particles is present in the measuring volume. There is always a statistical cancelling of signals due to random phase effects.