Revision as of 16:51, 18 July 2008 by Krtownse (Talk)

Problems

1)a)If a discrete time singal x[n] is periodic with period N, then the Fourier series coefficients $ a_k $ of the signal x[n] is also periodic with period N. For the periodic signal x[n], find the values of $ a_0,a_1,...,a_{N-1}. $ Express your answer in a + jb form.

$ x[n]=1 - 2je^{5+j(3\pi/2*n+\pi/4)} $

1)b)

Solutions

1)a) Change the equation to look like a forier series. $ x[n]=1-2je^{5+j(3\pi/2*n+\pi/4)}= $ $ x[n]=1 - 2je^{\pi/4}e^{5}e^{j(3\pi/2)*n}= $ $ x[n]=1 + (\sqrt{2}e^{5} - j\sqrt{2}e^5)e^{j(3\pi/2*n)} $

find the period N. $ \omega_0=3\pi/2 $. $ P=2\pi/\omega_0=4/3 $. The LCM of 1 and 4/3 is 12. Therefore N=12

Choose values of $ a_k $ that match the forier series repersentation of x[n]

$ x[n]=\sum_{k=<n>}^{}a_ke^{jk(2\pi/12)n} $

$ a_0=1 $

$ a_9=\sqrt{2}e^{5} - j\sqrt{2}e^5 $


--Krtownse 15:53, 18 July 2008 (EDT)

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BSEE 2004, current Ph.D. student researching signal and image processing.

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