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
where
- 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.
Properties edit
If the delay parameter, m, is considered fixed then all the properties of the z-transform hold for the advanced z-transform.
Linearity edit
Time shift edit
Damping edit
Time multiplication edit
Final value theorem edit
Example edit
Consider the following example where :
If then reduces to the transform
which is clearly just the z-transform of .
References edit
- Jury, Eliahu Ibraham (1973). Theory and Application of the z-Transform Method. Krieger. ISBN 0-88275-122-0. OCLC 836240.