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The XFT quadrature in discrete Fourier analysis

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The XFT quadrature in discrete Fourier analysis/ by Rafael G. Campos.
Author:	Campos, Rafael G.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xiii, 235 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Fourier analysis. -
Online resource:	https://doi.org/10.1007/978-3-030-13423-5
ISBN:	9783030134235

The XFT quadrature in discrete Fourier analysis
Campos, Rafael G.

The XFT quadrature in discrete Fourier analysis[electronic resource] /by Rafael G. Campos. - Cham :Springer International Publishing :2019. - xiii, 235 p. :ill., digital ;24 cm. - Applied and numerical harmonic analysis,2296-5009. - Applied and numerical harmonic analysis..

Introduction -- The ordinary discrete Fourier transform -- XFT: A discrete Fourier transform -- Applications of the XFT -- A discrete fractional Fourier transform.

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book's second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.

ISBN: 9783030134235

Standard No.: 10.1007/978-3-030-13423-5doiSubjects--Topical Terms:

639284
Fourier analysis.

LC Class. No.: QA403.5 / .C367 2019

Dewey Class. No.: 515.2433

The XFT quadrature in discrete Fourier analysis
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505 0 $a Introduction -- The ordinary discrete Fourier transform -- XFT: A discrete Fourier transform -- Applications of the XFT -- A discrete fractional Fourier transform.
520 $a This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book's second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.
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