Z-transform
Sign in to saveIn 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.
Article
28 sectionsContents
- 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
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.
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.