Results 221 to 230 of about 23,128 (265)

CMMSE: On the generalized Fourier transform

2022
In this paper, we introduce the theory of a generalized Fourier transform in order to solve differential equations with a generalized fractional derivative, and we state its main properties. In particular, we obtain the corresponding convolution, inverse and Plancherel formulas, and Hausdorff-Young inequality.
Ricardo Abreu Blaya, José M. Rodríguez, José M. Sigarreta   +2 more
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A generalized Mobius transform and arithmetic Fourier transforms

IEEE Transactions on Signal Processing, 1994
A general approach to arithmetic Fourier transforms (AFT) is developed. The implementation is based on the concept of killer polynomials and the solution of an arithmetic deconvolution problem pertaining to a generalized Mobius transform. This results in an extension of the Bruns (1903) procedure, valid for all prime numbers, and in an AFT that ...
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Beurling Algebras and the Generalized Fourier Transform

Proceedings of the London Mathematical Society, 1996
Primary ideals at \(\infty\) are investigated in Beurling-type Fréchet algebras in the quasianalytic case. They are described by two parameters characterizing the rate of decay of their Fourier transforms at \(\pm\infty\). The so-called generalized Fourier transform is applied to treat related convolution equations. A necessary and sufficient condition
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Generalized Fourier Transform for Stratified Media

Canadian Journal of Physics, 1972
A Fourier-type transform is derived for functions satisfying the scalar wave equation in stratified media. Using this transform, the function is expressed as a sum of two infinite integrals and a discrete term. In electromagnetic theory, the infinite integrals correspond to the radiation and the lateral wave terms and the discrete term corresponds to ...
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Properties of the Multidimensional Generalized Discrete Fourier Transform

IEEE Transactions on Computers, 1979
In this work the generalized discrete Fouriertransform (GFT), which includes the DFT as a particular case, is considered. Two pairs of fast algorithms for evaluating amultidimensional GFT are given (T-algorithm, F-algorithm, and T'-algorithm, F'-algorithm) It is shown that in the case of the DFT of a vector, the T-algorithm represents a form of the ...
Corsini P., Frosini G.
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The generalized discrete fractional fourier transforms

IEEE International Conference on Acoustics Speech and Signal Processing, 2002
In this paper, we develop the generalized discrete fractional Fourier transform (GDFRFT) by factorizing the generalized discrete Fourier transform (GDFT) matrix. Specifically, the eigenvalues and eigenvectors are presented and then used to define the GDFRFT.
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Generalized fourier transform and its applications

Mathematical Notes, 2006
The author studies the generalized Fourier transform treated as an operator on the dual of an arbitrary locally convex space; the kernel of this operator is an entire vector function. Such transforms and their kernels are studied in detail. First of all, the author gives a definition of this operator and establishes its basic properties.
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The fast Fourier transform for general order

Computing, 1978
An elementary and transparent representation of the fast Fourier transform is given. Instead of using the usual and highly algebraic approach it is shown how a Fourier transform of the ordern=p·m can be reduced top Fourier transforms of orderm by performing essentiallym Fourier transforms of orderp on the data.
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Linear and nonlinear generalized Fourier transforms

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006
This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.
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A generalization of the discrete fourier transform

Integral Transforms and Special Functions, 1995
In [2] we have considered a class of integral transforms which generalizs the classical Fourier tranform. We are able now to define a class of discrete tranformations which can be considered as a generalization of the discrete Fourier transform. Furthermore, when our result is considered in connnection with the particular kernel associated with th ...
Carlo Belingeri, Paolo Emilio Ricci
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