Authors:
- Presents a new quadrature formula for the fractional Fourier transform
- Many examples are addressed to illustrate the power of the new formula
- Most of the algorithms presented, are implemented in standard packages as MATLAB or MATHEMATICA
- Present the XFT matrix as a finite-dimensional transformation
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
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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Authors and Affiliations
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Science Department, University of Quintana Roo, Chetumal, Mexico
Rafael G. Campos
Bibliographic Information
Book Title: The XFT Quadrature in Discrete Fourier Analysis
Authors: Rafael G. Campos
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-3-030-13423-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-13422-8Published: 11 June 2019
Softcover ISBN: 978-3-030-13425-9Published: 14 August 2020
eBook ISBN: 978-3-030-13423-5Published: 24 May 2019
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XIII, 235
Number of Illustrations: 4 b/w illustrations, 96 illustrations in colour
Topics: Special Functions, Real Functions, Integral Transforms, Operational Calculus