Showing papers on "Hartley transform published in 1973"
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
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 paper, a non-recursive transform equation for the Fourier transform of a discrete Walsh function with a rectangular pulse was developed, which is a function of the bits of the Gray code number for the order of the Walsh function.
Abstract: Convolution of a discrete Walsh function with a rectangular pulse simplifies the derivation of an expression for the Fourier transform of a Walsh function. The nonrecursive transform equation that is developed is a function of the bits of the Gray code number for the order of the Walsh function.
33 citations
01 Jan 1973
TL;DR: The algorithm for Lie transforms proposed in this article reduces the number of Poisson brackets to be evaluated in a part of the implementation of the Analytical Lunar Theory by a factor of three.
Abstract: The algorithm for Lie transforms proposed here reduce the amount of computation to be carried out in particular but typical problems of Perturbation Theory. In conjunction with the formulas for inverting and composing Lie transforms it is shown to reduce by a factor of three the number of Poisson brackets to be evaluated in a part of the implementation of the Analytical Lunar Theory.
32 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.
23 citations
TL;DR: In this article, an algorithm for the inverse Laplace transform is developed. But the algorithm is not suitable for the case of the Fast Fourier transform and the results are unsatisfactory.
Abstract: The analytic methods for evaluating the time response of irrational transfer functions are incomplete. The graphical approaches for solving the problem are inaccurate. This paper attempts to attack the general inverse Laplace transform problem under the new light shed by the Fast Fourier transform. An algorithm for the inverse Laplace transform is developed. Several typical but difficult cases are studied and the results are extraordinarily satisfactory.
18 citations
9 citations
TL;DR: In this article, the generalized atomic scattering factors were applied to Patterson maps based on satellite reflections of a plagioclase feldspar and the results were applied in a subsequent paper.
Abstract: The intensities of `difference reflections' of crystals with supercells or of crystals with a modulated structure are formulated using `generalized atomic scattering factors'. The Fourier transform of the structure factors of a single set of difference reflections is the sum of the convolutions of the point functions representing average atomic positions, with the transforms of the generalized atomic scattering factors. The Patterson function of one set of difference reflections is the sum of the convolutions of the point functions representing average interatomic vectors, with the convolutions of the transforms of the generalized atomic scattering factors. These results are applied in a subsequent paper to Patterson maps based on the satellite reflections of a plagioclase feldspar.
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.