Applied and Numerical Harmonic Analysis

The XFT Quadrature in Discrete Fourier Analysis

Authors: Campos, Rafael G.

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  • 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
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eBook $59.99
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  • ISBN 978-3-030-13423-5
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Hardcover $109.99
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  • ISBN 978-3-030-13422-8
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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.


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-030-13423-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-030-13422-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The XFT Quadrature in Discrete Fourier Analysis
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-13423-5
DOI
10.1007/978-3-030-13423-5
Hardcover ISBN
978-3-030-13422-8
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XIII, 235
Number of Illustrations
4 b/w illustrations, 96 illustrations in colour
Topics