(New page: <math> x[n] = \begin{cases} 1, & n = 4 \\ 2, & n = 5 \\ 3, & n = 2 \\ 0, & \mbox{else} \end{cases} </math> This is equivalent to <math> \begin{align} x[n] &= u[n-4] + 2u[n-5] + 3u[n-2...) |
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\begin{align} | \begin{align} | ||
x[n] &= u[n-4] + 2u[n-5] + 3u[n-2] \\ | x[n] &= u[n-4] + 2u[n-5] + 3u[n-2] \\ | ||
| − | X(z) & | + | & {\color{blue} \text{I think you mean } \delta[n-4] + 2\delta [n-5] + 3\delta [n-2]}, \\ |
| − | + | {\color{blue} \text{and thus } X(z)} &{\color{blue}= z^{-4} + 2z^{-5} + 3z^{-2} , \text{ which converges for any finite }z\neq 0.}\\ | |
| − | + | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
[[2010_Fall_ECE_438_Boutin|Back to 438 main page]] | [[2010_Fall_ECE_438_Boutin|Back to 438 main page]] | ||
Revision as of 07:45, 18 September 2010
$ x[n] = \begin{cases} 1, & n = 4 \\ 2, & n = 5 \\ 3, & n = 2 \\ 0, & \mbox{else} \end{cases} $
This is equivalent to
$ \begin{align} x[n] &= u[n-4] + 2u[n-5] + 3u[n-2] \\ & {\color{blue} \text{I think you mean } \delta[n-4] + 2\delta [n-5] + 3\delta [n-2]}, \\ {\color{blue} \text{and thus } X(z)} &{\color{blue}= z^{-4} + 2z^{-5} + 3z^{-2} , \text{ which converges for any finite }z\neq 0.}\\ \end{align} $
