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
whereT is the sampling periodm 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.Example
Consider the following example where :If then reduces to the transform
which is clearly just the z-transform of.