Advanced z-transform
In mathematics and signal processing, the advanced z-transform is an extension of the z-transform, to incorporate ideal delays that are not multiples of the sampling time. The advanced z-transform is widely applied, for example, to accurately model processing delays in digital control. It is also known as the modified z-transform.
It takes the form
where
- T is the sampling period
- m (the "delay parameter") is a fraction of the sampling period
Properties
If the delay parameter, m, is considered fixed then all the properties of the z-transform hold for the advanced z-transform.
Linearity
Time shift
Damping
Time multiplication
Final value theorem
Example
Consider the following example where :
If then reduces to the transform
which is clearly just the z-transform of .
References
- Jury, Eliahu Ibraham (1973). Theory and Application of the z-Transform Method. Krieger. ISBN 0-88275-122-0. OCLC 836240.
- v
- t
- e
Digital signal processing
- Detection theory
- Discrete signal
- Estimation theory
- Nyquist–Shannon sampling theorem
- Audio signal processing
- Digital image processing
- Speech processing
- Statistical signal processing
- Z-transform
- Advanced z-transform
- Matched Z-transform method
- Bilinear transform
- Constant-Q transform
- Discrete cosine transform (DCT)
- Discrete Fourier transform (DFT)
- Discrete-time Fourier transform (DTFT)
- Impulse invariance
- Integral transform
- Laplace transform
- Post's inversion formula
- Starred transform
- Zak transform
- Aliasing
- Anti-aliasing filter
- Downsampling
- Nyquist rate / frequency
- Oversampling
- Quantization
- Sampling rate
- Undersampling
- Upsampling