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| − | ! Summary of Facts About ROC/ROAC of a Z-Transform!! | + | ! Summary of Facts About||ROC/ROAC of a Z-Transform!! |
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| − | | '''Characteristics of System''' || '''How to know?''' | + | | '''''Characteristics of System''''' || '''''How to know?''''' |
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| Causal|| The transfer function of the system converges at z= infinity. Z=infinity is included in ROC. (Fact 4) | | Causal|| The transfer function of the system converges at z= infinity. Z=infinity is included in ROC. (Fact 4) | ||
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| Neither Left-Sided nor Right-Sided || number<abs(Z)<number (Fact 6) | | Neither Left-Sided nor Right-Sided || number<abs(Z)<number (Fact 6) | ||
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| + | | Note: abs(Z) is absolute value of Z. | ||
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| + | | Reference: Lecture notes by Professor Mimi | ||
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Revision as of 12:51, 3 December 2017
| 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. | ||
| Reference: Lecture notes by Professor Mimi |
