Z transform

              Z transform permit the processing of digital signals and discrete systeme.

1. Definition

The Z transform is defined by :

2. Stability in Z

A discrete system whose transfer function is expressed according to Z is stable if all the poles have a module lower than 1.

3. Propriety

3.1. Linearity

3.2. Delay Theorem

It is noticed that to delay a causal signal of N samples is equivalent to multiply its Z transform by.

3.3. Product of convolution

3.4. Multiplication by

3.5. Multiplication by

3.5. Multiplication by

4. Z transform of tests signals

Dirac :

.

Step:

.

5. End value and initial value theorem

Initial value theorem:

End value theorem :

6. Research of original         It's necessary to arrange the initial expression to obtain forms in tables by carrying out operations such as the decomposition in simple elements