2. Discrete Systems and Signal Spaces

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

Published Online: 14 MAY 2004

DOI: 10.1002/047166037X.ch2

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 Systems and Signal Spaces, in Signal Analysis: Time, Frequency, Scale, and Structure, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/047166037X.ch2

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



  • discrete systems;
  • signal spaces;
  • operations;
  • linear systems;
  • translation invariant systems;
  • convolutional systems;
  • inner product spaces;
  • Hilbert spaces


This chapter begins with a practical exploration of the types of operations that one can perform on signals. Many of these simple systems will arise again and again as we develop methods for processing and interpreting discrete and continuous signals. In modern audio technology, more and more of the processing stages operate on digital signal information. The compact disc player is a wonderful example, embodying many of the systems that we cover in this chapter. Its processed signals take many forms: discrete engravings on the disc, light pulses, digital encodings, analog voltages, vibration of the loudspeaker membrane, and finally sound waves.