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

f ( t ) = cos ⁡ ( ω t )

reduces to the transform which is clearly just the z-transform of