10. Time-Frequency Signal Transforms

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

Published Online: 14 MAY 2004

DOI: 10.1002/047166037X.ch10

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) Time-Frequency Signal Transforms, in Signal Analysis: Time, Frequency, Scale, and Structure, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/047166037X.ch10

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:

  • time-frequency signal transforms;
  • Gabor transforms;
  • short-time Fourier transforms;
  • discretization;
  • quadratic time-frequency transforms;
  • Balian–Low theorem

Summary

In this chapter we first explore the basic ideas of the transform, working with its original analog formulation. Next, we develop the idea of the time-frequency–plane. We generalize the Gabor transform further to include general window functions. Finally, we derive the discretization of the Gabor transform.