The XFT quadrature in discrete Fourier analysis / Rafael G. Campos.
2019
QA403.5 .C36 2019
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Title
The XFT quadrature in discrete Fourier analysis / Rafael G. Campos.
Author
Campos, Rafael G., author.
ISBN
9783030134235 (electronic book)
3030134237 (electronic book)
3030134229
9783030134228
3030134237 (electronic book)
3030134229
9783030134228
Published
Cham, Switzerland : Birkhäuser, [2019]
Language
English
Description
1 online resource.
Call Number
QA403.5 .C36 2019
Dewey Decimal Classification
515/.2433
Summary
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.-- Provided by publisher.
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Source of Description
Description based on online resource; title from digital title page (viewed on June 28, 2019).
Series
Applied and numerical harmonic analysis.
Available in Other Form
Print version 9783030134228
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