3. Analog Systems and Signal Spaces

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

Published Online: 14 MAY 2004

DOI: 10.1002/047166037X.ch3

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) Analog Systems and Signal Spaces , in Signal Analysis: Time, Frequency, Scale, and Structure, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/047166037X.ch3

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:

  • analog systems;
  • signal spaces;
  • convolution;
  • analog LTI systems;
  • analog signal spaces;
  • modern integration theory;
  • distributions

Summary

This chapter extends linear systems and Hilbert space ideas to continuous domain signals. Noting that an integral over the real line displaces an integral summation, the definitions, theorems, and examples are quite similar in form to their discrete-world cousins. We mainly verify that after replacing summations with integrations we can still construct analog signal spaces that support signal theory. The chapter contains two important applications. The first, called the matched filter, uses the ideas of inner product and orthogonalization to construct an optimal detector for an analog waveform. The second application introduces the idea of a frame. Frames generalize the concept of a basis, and we show that they are the basic tool for numerically stable pattern detection using a family of signal models.