(New page: ==Solution of Week12 Quiz Question 5== ---- ---- Back to Quiz Pool Back to Lab wiki) |
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| + | a. | ||
| + | |||
| + | <math> | ||
| + | \begin{align} | ||
| + | X[k]&=\sum_{n=0}^3 x[n]e^{-j\frac{2\pi n}{N}k} \\ | ||
| + | &=\sum_{n=0}^3 cos(\frac{n\pi}{2})e^{-j\frac{2\pi n}{N}k} \\ | ||
| + | &=1-e^{-j\pi k}\text{ , }0\le k\le 3 | ||
| + | \end{align} | ||
| + | </math> | ||
| + | |||
| + | b. | ||
Revision as of 13:23, 10 November 2010
Solution of Week12 Quiz Question 5
a.
$ \begin{align} X[k]&=\sum_{n=0}^3 x[n]e^{-j\frac{2\pi n}{N}k} \\ &=\sum_{n=0}^3 cos(\frac{n\pi}{2})e^{-j\frac{2\pi n}{N}k} \\ &=1-e^{-j\pi k}\text{ , }0\le k\le 3 \end{align} $
b.
