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

where

• T is the sampling period

• m

Properties

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

Linearity

Time shift

Damping

Time multiplication

Final value theorem

Example

:

reduces to the transform

which is clearly just the z.

References