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==H(z)== | ==H(z)== | ||
| − | <math>H(z) = \sum_{m=-\infty}^{\infty}h[m] e^{-j \omega m} = \sum_{m=-\infty}^{\infty} u[m] e^{-j \omega m} = \sum_{m=0}^{\infty} e^{-j \omega m}</math> | + | <math>H(z) = \sum_{m=-\infty}^{\infty}h[m] e^{-j \omega m} = \sum_{m=-\infty}^{\infty} u[m] e^{-j \omega m} = \sum_{m=0}^{\infty} e^{-j \omega m} = \sum_{m=0}^{\infty} (\frac{1}{e^{j \omega}})^m</math> |
Revision as of 18:47, 23 September 2008
DT LTI System
$ y[n] = \sum_{n=-\infty}^{\infty}x[n] \; \; $ (DT integral)
h[n]
$ h[n] = \sum_{n=-\infty}^{\infty}\delta [n] = u[n] $
H(z)
$ H(z) = \sum_{m=-\infty}^{\infty}h[m] e^{-j \omega m} = \sum_{m=-\infty}^{\infty} u[m] e^{-j \omega m} = \sum_{m=0}^{\infty} e^{-j \omega m} = \sum_{m=0}^{\infty} (\frac{1}{e^{j \omega}})^m $
