Standard Article

Fourier and Other Mathematical Transforms

  1. Ronald N. Bracewell

Published Online: 15 DEC 2009

DOI: 10.1002/3527600434.eap144.pub2

Encyclopedia of Applied Physics

Encyclopedia of Applied Physics

How to Cite

Bracewell, R. N. 2009. Fourier and Other Mathematical Transforms. Encyclopedia of Applied Physics. 1149–1175.

Author Information

  1. Stanford University, Electrical Engineering Department, Stanford, CA, USA

Publication History

  1. Published Online: 15 DEC 2009

This is not the most recent version of the article. View current version (10 MAR 2015)

Abstract

The article contains sections titled:

  • 1
    Introduction
  • 2
    The Fourier Transform
  • 3
    Continuous versus Discrete Transforms
  • 4
    Some Common Transforms
  • 5
    The Laplace Transform
  • 6
    Convergence Conditions
  • 7
    Why Transforms are Useful
  • 8
    Fields of Application
  • 9
    The Hartley Transform
  • 10
    The Fast Fourier Transform
  • 11
    The Fast Hartley Algorithm
  • 12
    The Mellin Transform
  • 13
    The Hilbert Transform
  • 14
    Multidimensional Transforms
  • 15
    The Hankel Transform
  • 16
    The Abel Transform
  • 17
    Tomography and the Radon Transform
  • 18
    The Walsh Transform
  • 19
    The Z Transform
  • 20
    Convolution
  • 21
    Summary

Keywords:

  • convolution;
  • Fourier transform;
  • Abel transform;
  • integral;
  • Laplace transform