< Electronics Communication < Signal Processing < Signal Transformation
Z Transform Properties
Time domain | Z-domain | ROC | |
---|---|---|---|
Notation | ROC: | ||
Linearity | At least the intersection of ROC1 and ROC2 | ||
Time shifting | ROC, except if and if | ||
Scaling in the z-domain | |||
Time reversal | |||
Conjugation | ROC | ||
Real part | ROC | ||
Imaginary part | ROC | ||
Differentiation | ROC | ||
Convolution | At least the intersection of ROC1 and ROC2 | ||
Correlation | At least the intersection of ROC of X1(z) and X2() | ||
Multiplication | At least | ||
Parseval's relation |
- Initial value theorem
- , If causal
- Final value theorem
- , Only if poles of are inside unit circle
Z Transform Table
Here:
- for , for
- for , otherwise
Signal, | Z-transform, | ROC | |
---|---|---|---|
1 | |||
2 | |||
3 | |||
4 | |||
5 | |||
6 | |||
7 | |||
8 | |||
9 | |||
10 | |||
11 | |||
12 | |||
13 | |||
14 | |||
15 | |||
16 | |||
17 | |||
18 | |||
19 | |||
20 |
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