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where C is a closed counterwise countour inside the ROC of the Z- transform and around the origin. | where C is a closed counterwise countour inside the ROC of the Z- transform and around the origin. | ||
| − | <math> = \sum_{poles a_i ( X(Z) Z ^ (n-1))} | + | <math> = \sum_{poles a_i ( X(Z) Z ^ (n-1))} Residue ( X(Z) Z ^ (n-1)) \ </math> |
| − | <math> = \sum_{poles a_i}</math> | + | <math> = \sum_{poles a_i ( X(Z) Z ^ (n-1))} Coefficient of degree (-1) term on the power series expansion of ( X(Z) Z ^ (n-1)) about a_i \ </math> |
Revision as of 05:32, 23 September 2009
Inverse Z-transform
$ x[n] = \oint_C {X(Z)}{Z ^ (n-1)} , dZ \ $
where C is a closed counterwise countour inside the ROC of the Z- transform and around the origin.
$ = \sum_{poles a_i ( X(Z) Z ^ (n-1))} Residue ( X(Z) Z ^ (n-1)) \ $ $ = \sum_{poles a_i ( X(Z) Z ^ (n-1))} Coefficient of degree (-1) term on the power series expansion of ( X(Z) Z ^ (n-1)) about a_i \ $
