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

${\displaystyle F(z,m)=\sum _{k=0}^{\infty }f(kT+m)z^{-k}}$

where

• T is the sampling period
• m (the "delay parameter") is a fraction of the sampling period ${\displaystyle [0,T].}$