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
- 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 transform
which is clearly just the Z-transform of .