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ENEE241hw13 - ENEE 241 02 HOMEWORK ASSIGNMENT 13 Due Tue...

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ENEE 241 02* HOMEWORK ASSIGNMENT 13 Due Tue 05/10 Problem 13A Consider the FIR filter with coe ffi cient vector b = 1 3 0 - 3 - 1 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 = 6. Specifically, the vector y1 below equals y (1) [ - 1 : 4]. b = [1 3 0 -3 -1].’ ; H = fft(b,6) ; x1 = [1 2 4 -1 -2 -4].’ ; X1 = fft(x1) ; Y1 = H.*X1 ; y1 = ifft(Y1) (i) (3 pts.) Display the vector x (1) [0 : 5]. ( It is not the same as x1 , introduced above .) (ii) (5 pts.) Compute y (1) [ - 1 : 4] by hand using a circular convolution, or, equivalently, using 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 = 3. Specifically, the vector y2 equals y (2) [ - 1 : 4]. b = [1 3 0 -3 -1].’ ; H = fft(b,6) ; x2 = [2 -1 5 2 -1 5].’ ; X2 = fft(x2) ; Y2 = H.*X2 ; y2 = ifft(Y2) (iii) (2 pts.) Display the vector x (2) [0 : 2]. (iv) (5 pts.) Compute y (2) [ - 1 : 4] by hand using a circular convolution, based on the filter’s input-output relationship. (v) (5 pts.) Fully explain the relationship between y3 computed below and y2 computed earlier. b = [1 3 0 -3 -1].’ ; H = fft(b,6) ; H = H(1:2:6) ; x3 = [2 -1 5].’ ; X3 = fft(x3) ; Y3 = H.*X3 ; y3 = ifft(Y3) Problem 13B Consider the FIR filter with impulse response given by h [ n ] = b 0 δ [ n ] + b 1 δ [ n - 1] + b 2
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