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. It takes the form

\text{[math]}

where

It is also known as the modified Z-transform.

The advanced Z-transform is widely applied, for example to accurately model processing delays in digital control.

Properties

If the delay parameter, m, is considered fixed then all the properties of the Z-transform hold for the advanced Z-transform.

\text{[math]}

\text{[math]}

\text{[math]}

\text{[math]}

\text{[math]}

Consider the following example where $\text{[math]}$ :

\text{[math]}

If $\text{[math]}$ then $\text{[math]}$ reduces to the transform

\text{[math]}

which is clearly just the Z-transform of $\text{[math]}$ .

Eliahu Ibraham Jury, Theory and Application of the Z-Transform Method, Krieger Pub Co, 1973. ISBN 0-88275-122-0.

Digital signal processing

Theory	Detection theory Discrete signal Estimation theory Nyquist–Shannon sampling theorem

Sub-fields	Audio signal processing Digital image processing Speech processing Statistical signal processing

Techniques	Advanced Z-transform Bilinear transform Discrete Fourier transform (DFT) Discrete-time Fourier transform (DTFT) Impulse invariance Matched Z-transform method Z-transform Zak transform

Sampling	Aliasing Anti-aliasing filter Downsampling Nyquist rate / frequency Oversampling Quantization Sampling rate Undersampling Upsampling

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