411 REFERENCE · Wikibooks
Engineering Handbook/Mathematics/Z Transformation
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Z Transformation Properties
{| class="wikitable"
!
! Time domain
! Z-domain
! ROC
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! Notation
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| ROC:
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! Linearity
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| At least the intersection of ROC1 and ROC2
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! Time shifting
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| ROC, except if and if
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! Scaling in the z-domain
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! Time reversal
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! Conjugation
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| ROC
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! Real part
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| ROC
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! Imaginary part
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| ROC
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! Differentiation
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| ROC
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! Convolution
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| At least the intersection of ROC1 and ROC2
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! Correlation
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| At least the intersection of ROC of X1(z) and X2()
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! Multiplication
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| At least
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! Parseval's relation
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|}
Initial value theorem
, If causal
Final value theorem
, Only if poles of are inside unit circle
Z Transformation of Functions
Here:
for , for
for , otherwise
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! !! Signal, !! Z-transform, !! ROC
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