PS7_sol - EE341, Autumn 2007 Problem Set 7 SOLUTION Reading...

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Unformatted text preview: EE341, Autumn 2007 Problem Set 7 SOLUTION Reading for this problem set: Chapter 12 of Signals, Systems, and Transforms . 1. The signal x ( t ) = 5 cos(8 t ) is sampled eight times with T = 0 . 1s, starting at t = 0. solution (a) Compute the DFT of this sequence. x [ n ] = [5 cos(8 . 0) , 5 cos(8 . 1) , 5 cos(8 . 2) , 5 cos(8 . 3) , 5 cos(8 . 4) , 5 cos(8 . 5) , 5 cos(8 . 6) , 5 cos(8 . 7)] = [5 . ,- 4 . 05 , 1 . 55 , 1 . 55 ,- 4 . 05 , 5 . ,- 4 . 05 , 1 . 55] X [ k ] = 7 summationdisplay n =0 x [ n ] e- j 2 kn 1 8 = 7 summationdisplay n =0 x [ n ] e- jkn 1 4 = [2 . 5 , 2 . 65 + j . 8 , 3 . 45 + j 2 . 15 , 15 . 45 + j 12 ,- 5 . 6 , 15 . 45- j 12 , 3 . 45- j 2 . 15 , 2 . 65- j . 8] (b) Use MATLAB to show a graph that confirms part (a). Include your code. % create vector of 5cos(8*pi*t_i), with t_i = {0, 0.1, 0.2, ... 0.7} for n=1:8 x(n) = 5 * cos(8 * pi * (n-1)/10); end x % display x % take the DFT of x, and display X = fft(x,8) stem(abs(X)); stem(angle(X));...
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PS7_sol - EE341, Autumn 2007 Problem Set 7 SOLUTION Reading...

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