Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
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TL;DR: It is shown that NCHT is a natural-ordered version of complex Hadamard transform whereas SCHT shows the sequency ordering, which is parallel to their real-valued counterparts, the WHT and thesequency-ordered Walsh transform (SOWT).
14 citations
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01 May 1960TL;DR: The Taylor-Cauchy transform calculus as discussed by the authors is a transform calculus based on the Cauchy integral theorem and Taylor's series in complex form, which can be justified rigorously by the partition theory, essentially transforms a nonlinear differential equation having certain conditions imposed on its linear, nonlinear and driving terms into an algebraic equation.
Abstract: This paper presents a new transform calculus for analyzing a certain class of nonlinear systems. The method, which can be justified rigorously by the partition theory, essentially transforms a nonlinear differential equation having certain conditions imposed on its linear, nonlinear, and driving terms into an algebraic equation. The latter is easily solved recursively owing to its symmetry and convolution properties. The transform pair is based on a combination of the Cauchy integral theorem and Taylor's series in complex form. To illustrate the method a number of examples are solved and a table of transforms is included. Because the results of this transform technique are the same as those given by the partition method under certain circumstances, the two are compared. It is then seen that the solution can be obtained uniquely and exactly. The Taylor-Cauchy transform method can be compared with the Laurent-Cauchy transform method, given in a companion paper, for the solution of linear systems described by differential-difference and sum equations.
14 citations
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TL;DR: In this article, the Stechkin problem of the approximation of derivatives by bounded linear functionals was studied, and exact Kolmogorov-type inequalities for derivatives corresponding to these problems were obtained.
Abstract: The problems of the optimal recovery of the derivatives of functions from inaccurate information about the Fourier transforms of these functions on a finite interval or the entire number line are considered. The Stechkin problem of the approximation of derivatives by bounded linear functionals, which is closely connected to this range of problems, is also studied. Precise Kolmogorov-type inequalities for derivatives corresponding to these problems are obtained.
14 citations
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TL;DR: This correspondence describes a new bit-reversal permutation algorithm based on a trivial symmetry that has not been exploited until now that outperforms the fastest algorithms known to the author.
Abstract: This correspondence describes a new bit-reversal permutation algorithm based on a trivial symmetry that has not been exploited until now. According to timing experiments, this algorithm outperforms the fastest algorithms known to the author. This is of interest for applications using intensive fast Fourier transforms (or fast Hartley transforms) of constant length, such as transform domain adaptive filtering.
14 citations
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01 Nov 1966
TL;DR: The fast Fourier transform is a significant advance over previous methods, in that the number of arithmetic operations is proportional to n log2 n instead of n(2) and one that makes practical the solution of large problems in which data overlay within high speed storage will occur.
Abstract: : The report consists of six ALGOL procedures with comments Procedure FASTTRANSFORM computes the complex finite Fourier transform or its inverse, using a modified version of the fast Fourier transform algorithm proposed by Cooley and Tukey Procedure REALTRANSFORM similarly computes the real Fourier transform and inverse The remaining four procedures are building blocks used in the first two procedures: they may be combined in other ways, for example, to form procedures for computing convolutions and power spectral density function estimates The fast Fourier transform is a significant advance over previous methods, in that the number of arithmetic operations is proportional to n log2 n instead of n(2) Detailed methods of computing this transform are shown here in the language of ALGOL A new approach to organizing the computations is used, one that makes practical the solution of large problems in which data overlay within high speed storage will occur
14 citations