6. Generalized Fourier Transforms of Analog Signals

  1. Ronald L. Allen1 and
  2. Duncan W. Mills2

Published Online: 14 MAY 2004

DOI: 10.1002/047166037X.ch6

Signal Analysis: Time, Frequency, Scale, and Structure

Signal Analysis: Time, Frequency, Scale, and Structure

How to Cite

Allen, R. L. and Mills, D. W. (2003) Generalized Fourier Transforms of Analog Signals, in Signal Analysis: Time, Frequency, Scale, and Structure, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/047166037X.ch6

Author Information

  1. 1

    San José, California, USA

  2. 2

    Mountain View, California, USA

Publication History

  1. Published Online: 14 MAY 2004
  2. Published Print: 19 DEC 2003

ISBN Information

Print ISBN: 9780471234418

Online ISBN: 9780471660378

SEARCH

Keywords:

  • generalized Fourier transforms;
  • analog signals;
  • distribution theory;
  • generalized functions;
  • linear systems;
  • frequency domain;
  • filters;
  • modulation

Summary

This chapter provides tools for studying the frequency content of important signals – sinusoids, constants, the unit step, and the like – for which the standard Fourier analysis in Chapter 5 does not work. We apply the generalized transform to the study of communication systems. We also consider the design of basic frequency selective linear, translation-invariant systems – filters.