Z-transform

Also known as unilateral Z transform, Z transform, one-sided Z-transform

In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex valued frequency-domain (the z-domain or z-plane) representation.

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Article

28 sections

Contents

History
Definition
Bilateral Z-transform
Unilateral Z-transform
Inverse Z-transform
Direct evaluation by contour integration
Expansion into a series of terms in the variables ''z'' and ''z''<sup>−1</sup>
Partial-fraction expansion and table lookup
Example
Region of convergence
Example 1 (no ROC)
Example 2 (causal ROC)
Example 3 (anticausal ROC)
Examples conclusion
Properties
Table of common Z-transform pairs
Relationship to Fourier series and Fourier transform
Relationship to Laplace transform
Bilinear transform
Starred transform
Linear constant-coefficient difference equation
Transfer function
Zeros and poles
Output response
See also
References
Further reading
External links

It can be considered a discrete-time counterpart of the Laplace transform (the s-domain or s-plane). This similarity is explored in the theory of time-scale calculus.