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＜E-Book＞
The XFT Quadrature in Discrete Fourier Analysis / by Rafael G. Campos
(Applied and Numerical Harmonic Analysis. ISSN:22965017)

Edition	1st ed. 2019.
Publisher	(Cham : Springer International Publishing : Imprint: Birkhäuser)
Year	2019
Size	XIII, 235 p. 100 illus., 96 illus. in color : online resource
Authors	*Campos, Rafael G author SpringerLink (Online service)
Subjects	LCSH:Special functions LCSH:Functions of real variables LCSH:Mathematical analysis FREE:Special Functions FREE:Real Functions FREE:Integral Transforms and Operational Calculus
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-030-13423-5

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