7. Discrete Fourier Transforms

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

Published Online: 14 MAY 2004

DOI: 10.1002/047166037X.ch7

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) Discrete Fourier Transforms, in Signal Analysis: Time, Frequency, Scale, and Structure, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/047166037X.ch7

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

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Keywords:

  • discrete Fourier transforms;
  • discrete-time Fourier transform;
  • sampling theorem

Summary

We have already discovered a rich theory of frequency transforms for analog signals, and this chapter extends the theory to discrete signals. We begin frequency transforms for discrete signals by covering the discrete Fourier transform (DFT). Later, we develop the principles underlying the famous sampling theorem of Shannon and Nyquist. This result effectively builds a frequency analysis bridge between the world of analog signals and the world of discrete signals.