Recall the definition of the z-transform:
Notation:
Z{*} is the z-transform operator, transforming what appears between the brackets to the complex z-domain.
represents the z-transform pair x[n] and X(z).
We will make use of the following z-transform pairs in developing the z-transform properties:
a
and b are real constants, i.e.,
m, n and n0 are integers
| Properties | Proofs | |
|---|---|---|
|
1. |
Multiplication by a constant,
|
 |
|
2. |
Linearity,
|
 |
| 3. | Time shifting,
|
 |
- The ROC is a ring or disk in the z-plane centered on the origin (i.e,
).
