Engineering Tables/Z Transform Properties

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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