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Catalogue Information
Field name	Details
Dewey Class	515.5
Title	The XFT Quadrature in Discrete Fourier Analysis ([EBook]) / by Rafael G. Campos.
Author	Campos, Rafael G.
Other name(s)	SpringerLink (Online service)
Publication	Cham : Springer International Publishing , 2019.
Physical Details	XIII, 235 pages : 100 illus., 96 illus. in color. : online resource.
Series	Applied and numerical harmonic analysis
ISBN	9783030134235
Summary Note	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.:
Contents note	Introduction -- The ordinary discrete Fourier transform -- XFT: A discrete Fourier transform -- Applications of the XFT -- A discrete fractional Fourier transform.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-13423-5
Links to Related Works	Subject References: Functions of real variables . Integral transforms . Integral Transforms, Operational Calculus . Operational calculus . Real Functions . Special Functions . Authors: author . Campos, Rafael G. . Corporate Authors: SpringerLink (Online service) . Series: Applied and numerical harmonic analysis . Classification: 515.5 . 515.5 (DDC 23) .

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The XFT Quadrature in Discrete Fourier Analysis

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