You may be asking what is the need to know Z-transform. What is Z-transform, anyway? Before we define it, let us know its use. Z-transform is very useful in the analysis of discrete-time signals and systems. We will see later that it is extremely powerful in the design of digital filters. It tells us everything about an LTI discrete-time system – its stability, its frequency response, the filter structure, etc. Therefore, it is a must for us to know what Z-transform is. By the way, Z-transform plays a similar role for the discrete-time signals and systems as does Laplace transform for the continuous-time counterparts.

Supplementary material (497 kb)


  1. 1.
    Churchill RV, Brown JW (1990) Introduction to complex variables and applications, 5th edn. McGraw-Hill, New YorkGoogle Scholar
  2. 2.
    Jury EI (1973) Theory and application of the z-transform method. Robert E. Krieger, HuntingtonGoogle Scholar
  3. 3.
    Milne-Thomson LM (1951) Calculus of finite differences. Macmillan, LondonGoogle Scholar
  4. 4.
    Mitra SK (2011) Digital signal processing: a computer-based approach, 4th edn. McGraw Hill, New YorkGoogle Scholar
  5. 5.
    Oppenheim AV, Shafer RW (1989) Discrete-time signal processing. Prentice-Hall, Englewood CliffsGoogle Scholar
  6. 6.
    Oppenheim AV, Willsky AS, Young IT (1983) Signals and systems. Prentice-Hall, Englewood CliffsGoogle Scholar
  7. 7.
    Rabiner LR, Gold B (1975) Theory and application of digital signal processing. Prentice-Hall, Englewood CliffsGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • K. S. Thyagarajan
    • 1
  1. 1.Extension ProgramUniversity of California, San DiegoSan DiegoUSA

Personalised recommendations