(New page: <math>x\left[n\right]=\sqrt{n} </math> ---- <math>E_{\infty}=\sum_{n=-\infty}^{\infty} \left | x \left[ n \right ] \right | ^2 = \lim_{N \rightarrow \infty } \sum_{n=-N}^{N} \left | x...) |
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| − | <math>x\left[n\right]=\sqrt{n} </math> | + | <math>x\left[n\right]= \sqrt{n}*u \left [ n \right ] </math><br> |
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<math>E_{\infty}=\sum_{n=-\infty}^{\infty} \left | x \left[ n \right ] \right | ^2 = \lim_{N \rightarrow \infty } \sum_{n=-N}^{N} \left | x \left[ n \right ] \right | ^2</math><br> | <math>E_{\infty}=\sum_{n=-\infty}^{\infty} \left | x \left[ n \right ] \right | ^2 = \lim_{N \rightarrow \infty } \sum_{n=-N}^{N} \left | x \left[ n \right ] \right | ^2</math><br> | ||
| − | <math>E_{\infty}=\sum_{n=-\infty}^{\infty} \left | \sqrt{n} | + | <math>E_{\infty}=\sum_{n=-\infty}^{\infty} \left | \sqrt{n}*u \left [ n \right ] \right | ^2</math><br> |
| − | <math>E_{\infty}=\underbrace{\sum_{n=-\infty}^{-1} \left | \sqrt{n} \right | ^2}_{0} + \sum_{n=0}^{\infty} \left | \sqrt{n} | + | <math>E_{\infty}=\underbrace{\sum_{n=-\infty}^{-1} \left | \sqrt{n}*u \left [ n \right ] \right | ^2}_{0} + \sum_{n=0}^{\infty} \left | \sqrt{n}*u \left [ n \right ] \right | ^2</math><br> |
<math>E_{\infty}=\sum_{n=0}^{\infty} n = \lim_{N \rightarrow \infty } \sum_{n=0}^{N} n</math><br> | <math>E_{\infty}=\sum_{n=0}^{\infty} n = \lim_{N \rightarrow \infty } \sum_{n=0}^{N} n</math><br> | ||
<math>E_{\infty}= \lim_{N \rightarrow \infty } \frac{N \left ( N+1 \right ) }{2} =\infty</math><br> | <math>E_{\infty}= \lim_{N \rightarrow \infty } \frac{N \left ( N+1 \right ) }{2} =\infty</math><br> | ||
Revision as of 07:34, 22 June 2009
$ x\left[n\right]= \sqrt{n}*u \left [ n \right ] $
$ E_{\infty}=\sum_{n=-\infty}^{\infty} \left | x \left[ n \right ] \right | ^2 = \lim_{N \rightarrow \infty } \sum_{n=-N}^{N} \left | x \left[ n \right ] \right | ^2 $
$ E_{\infty}=\sum_{n=-\infty}^{\infty} \left | \sqrt{n}*u \left [ n \right ] \right | ^2 $
$ E_{\infty}=\underbrace{\sum_{n=-\infty}^{-1} \left | \sqrt{n}*u \left [ n \right ] \right | ^2}_{0} + \sum_{n=0}^{\infty} \left | \sqrt{n}*u \left [ n \right ] \right | ^2 $
$ E_{\infty}=\sum_{n=0}^{\infty} n = \lim_{N \rightarrow \infty } \sum_{n=0}^{N} n $
$ E_{\infty}= \lim_{N \rightarrow \infty } \frac{N \left ( N+1 \right ) }{2} =\infty $
$ P_{\infty}=\lim_{N \rightarrow \infty } \frac{1}{2N + 1} \sum_{n=-N}^{N} \left | x \left[ n \right ] \right | ^2 $
$ P_{\infty}=\lim_{N \rightarrow \infty } \frac{1}{2N + 1} \sum_{n=-N}^{N} \left | \sqrt{n} \right | ^2 $
$ P_{\infty}=\lim_{N \rightarrow \infty } \frac{1}{2N + 1} \frac{N \left ( N+1 \right ) }{2}=\infty $
