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

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.

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

Consider the following example where ${\displaystyle f(t)=\cos(\omega t)}$:

If ${\displaystyle m=0}$ then ${\displaystyle F(z,m)}$ reduces to the transform

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