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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. | ||
+ | Source: Lecture notes by Professor Mimi |
Latest revision as of 13:22, 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.
Source: Lecture notes by Professor Mimi