Engineering Tables/Z Transform Properties
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Time domain  Zdomain  ROC  

Notation  ROC:  
Linearity  At least the intersection of ROC_{1} and ROC_{2}  
Time shifting  ROC, except if and if  
Scaling in the zdomain  
Time reversal  
Conjugation  ROC  
Real part  ROC  
Imaginary part  ROC  
Differentiation  ROC  
Convolution  At least the intersection of ROC_{1} and ROC_{2}  
Correlation  At least the intersection of ROC of X_{1}(z) and X_{2}()  
Multiplication  At least  
Parseval's relation 
 Initial value theorem

 , If causal
 Final value theorem

 , Only if poles of are inside unit circle