(New page: <math>x[n] = 2 + cos(\omega_0 n) + 4sin(\omega_0 n + \frac{\pi}{2})</math> where <math>\omega_0 = \frac{2\pi}{N}</math>. <math>h[n] = x[n] * \delta[n] = </math>) |
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| − | <math> | + | <math>y[n] = x[n] + x[n -1]</math> |
| − | + | <math>h[n] = \delta[n] + \delta[n-1]</math> | |
| − | <math> | + | <math>H[z] = \sum_{k=-\infty}^\infty h[k] z^{-k}</math> |
| + | |||
| + | <math> = \sum_{k=0}^1 h[k] z^{-k}</math> | ||
| + | |||
| + | when k = 0, <math>H[z] = 1</math> | ||
| + | |||
| + | when k = 1, <math>H[z] = z^{-1}</math> | ||
| + | |||
| + | else, <math>H[z] = 0</math> | ||
Latest revision as of 04:35, 26 September 2008
$ y[n] = x[n] + x[n -1] $
$ h[n] = \delta[n] + \delta[n-1] $
$ H[z] = \sum_{k=-\infty}^\infty h[k] z^{-k} $
$ = \sum_{k=0}^1 h[k] z^{-k} $
when k = 0, $ H[z] = 1 $
when k = 1, $ H[z] = z^{-1} $
else, $ H[z] = 0 $
