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Signals on ℝ/ℤ(Tp)

  • Gianfranco Cariolaro

Abstract

Continuous-time periodic signals were introduced in Chap.  2, and in this chapter they are reconsidered as signals defined on ℝ/ℤ(T p ), that is, on a proper quotient group which takes periodicity into account. After the previous analysis of signals defined on ℝ, most of the concepts become obvious. The general rule for the passage from ℝ to ℝ/ℤ(T p ) is to limit the analysis to one period, that is, to a cell of ℝ modulo ℤ(T p ).

Keywords

Fourier Coefficient Periodic Signal Quotient Group Fourier Series Expansion Symmetry Pair 
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References

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    A. Papoulis, The Fourier Integral and Its Applications (McGraw–Hill, New York, 1962) MATHGoogle Scholar
  3. 3.
    J.G. Proakis, Digital Communications, 3rd edn. (McGraw–Hill, New York, 1995) Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

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