Signals on ℤ(T)


Discrete-time signals were introduced in Chap.  2 and studied in a preliminary form, following a classical approach. In this chapter they are reconsidered as signals defined on ℤ(T) following the UST. Relevant concepts that are specific to this class of signals, in particular the z-transform and the discrete Hilbert transform, are introduced.

Nowadays discrete-time signals represent the most important class because they can be manipulated with the powerful techniques and tools of digital signal processing and multirate systems.


Impulse Response Convergence Region Infinite Impulse Response Finite Impulse Response Filter Discrete Signal 


  1. 1.
    M.G. Bellanger, J.L. Daguet, TDM–FDM transmultiplexer: digital polyphase and FFT. IEEE Trans. Commun. COM-22, 1199–1205 (1974) CrossRefGoogle Scholar
  2. 2.
    A.V. Oppenheim, R.W. Schafer, Digital Signal Processing (Prentice Hall, Englewood Cliffs, 1975) MATHGoogle Scholar
  3. 3.
    A. Papoulis, Circuits and Systems (Holt, Rinehart and Winston, New York, 1980) Google Scholar
  4. 4.
    A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and Series, vol. 5 (Gordon & Breach, New York, 1986) Google Scholar
  5. 5.
    L.R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice Hall, Englewood Cliffs, 1975) Google Scholar
  6. 6.
    P.P. Vaidyanathan, Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial. Proc. IEEE 78, 56–93 (1990) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

There are no affiliations available

Personalised recommendations