(New page: <math>x[n]={[e^(jπ/17) ]/2j}u(-n) |x[n] |=u[-n] (1/2)^n E_∞=∑_(n=-∞)^∞▒〖|x[n]|^2〗=∑_(n=-∞)^0▒〖[(1/2)^n ]^2=∑_(n=-∞)^0▒〖(1/4)^n=〗〗 ∞ P_∞=lim┬(N→...) |
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|x[n] |=u[-n] (1/2)^n | |x[n] |=u[-n] (1/2)^n | ||
E_∞=∑_(n=-∞)^∞▒〖|x[n]|^2〗=∑_(n=-∞)^0▒〖[(1/2)^n ]^2=∑_(n=-∞)^0▒〖(1/4)^n=〗〗 ∞ | E_∞=∑_(n=-∞)^∞▒〖|x[n]|^2〗=∑_(n=-∞)^0▒〖[(1/2)^n ]^2=∑_(n=-∞)^0▒〖(1/4)^n=〗〗 ∞ | ||
| − | P_∞=lim┬(N→∞)〖1/(2N+1)〗 ∑_(n=-N)^N▒|x[n] |^2 | + | |
| − | + | P_∞=lim┬(N→∞)〖1/(2N+1)〗 ∑_(n=-N)^N▒|x[n] |^2=lim┬(N→∞)〖1/(2N+1)〗 ∑_(n=-N)^N▒〖(1/4)^n=〗 lim┬(N→∞)〖1/(2N+1)〗 ∑_(k=0)^∞▒〖4^k=〗 lim┬(N→∞)〖[1/(2N+1)]〗 [(1-4^(N+1))/(1-4))]=∞ | |
</math> | </math> | ||
Revision as of 18:33, 5 September 2008
$ x[n]={[e^(jπ/17) ]/2j}u(-n) |x[n] |=u[-n] (1/2)^n E_∞=∑_(n=-∞)^∞▒〖|x[n]|^2〗=∑_(n=-∞)^0▒〖[(1/2)^n ]^2=∑_(n=-∞)^0▒〖(1/4)^n=〗〗 ∞ P_∞=lim┬(N→∞)〖1/(2N+1)〗 ∑_(n=-N)^N▒|x[n] |^2=lim┬(N→∞)〖1/(2N+1)〗 ∑_(n=-N)^N▒〖(1/4)^n=〗 lim┬(N→∞)〖1/(2N+1)〗 ∑_(k=0)^∞▒〖4^k=〗 lim┬(N→∞)〖[1/(2N+1)]〗 [(1-4^(N+1))/(1-4))]=∞ $
