Summary of Facts About ROC/ROAC of a Z-Transform
| Characteristics of System | How to know? | |
| Causal | The transfer function of the system converges at z= infinity. Z=infinity is included in ROC. (Fact 4) | |
| BIBO Stable | ROC of the transfer function includes the unit circle.(Fact 7) | |
| Frequency Response of the system is well-defined | Unit circle is inside ROC of transfer function.(Fact 7) | |
| FIR Filter | ROC of transfer function is the whole complex plane except z=0 and/or z=infinity.(Fact 1) | |
| Right-Sided | ROC is abs(Z)> number.(Fact 3) | |
| Left-Sided | ROC is abs(Z)<number or 0<abs(Z)<number. (Fact 5) | |
| Both-Sided | ROC includes the whole complex plane(Fact 3 and 5) | |
| Neither Left-Sided nor Right-Sided | number<abs(Z)<number (Fact 6) |
Note: abs(Z) is absolute value of Z.
Source: Lecture notes by Professor Mimi
