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The XFT Quadrature in Discrete Fourier Analysis

  • Rafael G. Campos
Book

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Rafael G. Campos
    Pages 1-2
  3. Rafael G. Campos
    Pages 3-37
  4. Rafael G. Campos
    Pages 39-118
  5. Rafael G. Campos
    Pages 119-184
  6. Rafael G. Campos
    Pages 185-203
  7. Back Matter
    Pages 205-235

About this book

Introduction

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.

Keywords

fourier transform discrete fourier transform fast fourier transform fractional fourier transform fast linear canonical transform differentiation matrices partial differentiation matrices discrete rotations discrete translations

Authors and affiliations

  • Rafael G. Campos
    • 1
  1. 1.Science DepartmentUniversity of Quintana RooChetumalMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-13423-5
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-13422-8
  • Online ISBN 978-3-030-13423-5
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site
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