Engineering Tables/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