Advanced Z-transform

The modified z-transform is a discrete-time extension of the Z-transform is also able to process the signal values ​​between the sampling points in the integer time-discrete control systems can. The necessary modifications of the Z- transformation were presented in works by Eliahu Ibrahim Jury in 1958. Primary application is in the detection of instabilities according to the discrete-time signal processing of controlled systems, for example in the field of power electronics for high-dynamic electric drive systems.

Definition

The modified Z-transform has for causal signals with positive and integer k the following definition:

The period, and a " delay factor ", which is a part of the period and is in the range.

Graphically represents the modified Z-transform is a unilateral Z- transformation of tracer to obtain the discrete signal sequence, an additional delay element with the delay

Having. For time-invariant properties of the Z-transform apply.

Correspondences

Some of the important correspondence of the modified Z-transform are:

For the correspondences go into the shapes of the Z- transform. The modified Z- transform is thus also referred to as an extended Z- transformation.