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# hw22 - ENEE 241 02 HOMEWORK ASSIGNMENT 22 Due Tue 05/12...

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ENEE 241 02* HOMEWORK ASSIGNMENT 22 Due Tue 05/12 Problem 22A Consider the FIR filter with coefficient vector b = £ 3 - 2 0 - 2 3 / T . The following MATLAB script computes a segment of the filter output sequence y (1) [ · ] for a periodic input sequence x (1) [ · ] of period L = 5. Specifically, the vector y1 below equals y (1) [ - 1 : 3]. b = [3 -2 0 -2 3].’ ; H = fft(b) ; x1 = [1 4 1 -1 2 ].’ ; X1 = fft(x1) ; Y1 = H.*X1 ; y1 = ifft(Y1) (i) (3 pts.) Display the vector x (1) [0 : 4]. ( It is not the same as x1 , introduced above .) (ii) (5 pts.) Compute y (1) [0 : 4] using a circular convolution, based on the filter’s input-output relationship. For parts (iii) and (iv) below, consider the following MATLAB script, which computes a segment of the filter output sequence y (2) [ · ] for a periodic input sequence x (2) [ · ] of period L = 4. Specifically, the vector y2 equals y (2) [0 : 7]. b = [3 -2 0 -2 3].’ ; H = fft(b,8) ; x2 = [2 5 0 1 2 5 0 1].’ ; X2 = fft(x2) ; Y2 = H.*X2 ; y2 = ifft(Y2) (iii) (2 pts.) Display the vector x (2) [0 : 3]. (iv) (5 pts.) Compute y (2) [0 : 7] using a circular convolution, based on the filter’s input-output relationship.

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hw22 - ENEE 241 02 HOMEWORK ASSIGNMENT 22 Due Tue 05/12...

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