Revision as of 14:12, 26 September 2008 by Mfrankos (Talk)

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} $

  1. 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} $

$ \ x[n] = a_0 + a_1e^{j\pi/ 5(1)n} +a_2e^{j\pi/ 5(2)n}+a_3e^{j\pi/ 5(3)n}+a_4e^{j\pi/ 5(4)n}+\frac{1}{10}e^{j\pi/ 5(5)n} $

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Sees the importance of signal filtering in medical imaging

Dhruv Lamba, BSEE2010