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<math>\ a_5 = \frac{1}{10} \sum_{0}^{9} x[n](-1)^n</math> | <math>\ a_5 = \frac{1}{10} \sum_{0}^{9} x[n](-1)^n</math> | ||
| + | |||
| + | a_5 = \frac{1}{10} | ||
Revision as of 14:03, 26 September 2008
1. x[n] is a real and even signal
2. x[n] has period N = 10 and Fourier coefficients $ \ a_k $
3. $ \ a_{11} = 5 $
4. $ \ \frac{1}{10} \sum_{n=0}^{9}|x[n]|^2 = 50 $
From #2 gives the period of N=10, from that can deduce that the frequency $ \ w = k\frac{2\pi}{10} $ and if assume k=1 then the frequency $ \ w=\frac{\pi}{5} $
- 2 also gives the equation $ x[n] = \sum_{0}^{9} a_{k} e^{-jkn\pi /5 } $
$ \ a_5 = \frac{1}{10} \sum_{0}^{9} x[n]e^{-j\pi n} $
$ \ a_5 = \frac{1}{10} \sum_{0}^{9} x[n](-1)^n $
a_5 = \frac{1}{10}
