- T is the sampling period
- m (the "delay parameter") is a fraction of the sampling period
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.
If the delay parameter, m, is considered fixed then all the properties of the Z-transform hold for the advanced Z-transform.
Final value theorem
Consider the following example where
If then reduces to the Z-transform
which is clearly just the Z-transform of
- Eliahu Ibraham Jury, Theory and Application of the Z-Transform Method, Krieger Pub Co, 1973. ISBN 0-88275-122-0.