Since is the convolution of two rectangles the

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Unformatted text preview: = x1_15; x2_30 = zeros(1,length(n_30)); x2_30(1:15) = x2_15; k = 0:5; X = fft(x,6); subplot(2,1,1) stem(n,x) k_30 = 0:29; X1_30 = fft(x1_30,30); X2_30 = fft(x2_30,30); subplot(2,1,2) stem(k,X) iX1_30 = ifft(X1_30,30); iX2_30 = ifft(X2_30,30); %% Problem #4a figure subplot(2,3,1) stem(n_30,x1_30) n_15 = 0:14; x1_15 = zeros(1,length(n_15)); x1_15(1:10) = 1; x2_15 = ones(1,length(n_15)); k_15 = 0:14; X1_15 = fft(x1_15,15); X2_15 = fft(x2_15,15); iX1_15 = ifft(X1_15,15); iX2_15 = ifft(X2_15,15); figure subplot(2,3,1) stem(n_15,x1_15) subplot(2,3,2) stem(k_15,X1_15) subplot(2,3,3) stem(n_15,iX1_15) subplot(2,3,4) stem(n_15,x2_15) subplot(2,3,5) stem(k_15,X2_15) subplot(2,3,6) stem(n_15,iX2_15) subplot(2,3,2) stem(k_30,X1_30) subplot(2,3,3) stem(n_30,iX1_30) subplot(2,3,4) stem(n_30,x2_30) subplot(2,3,5) stem(k_30,X2_30) subplot(2,3,6) stem(n_30,iX2_30) BE 401 Problem Set #8 %% Problem 4c-e X1X2_15 = X1_15.*X2_15; X1X2_30 = X1_30.*X2_30; iX1X2_15 = ifft(X1X2_15,15); iX1X2_30 = ifft(X1X2_30,30); x1convx2_15 x1convx2_30 n_conv_15 = n_conv_30 = = conv(x1_15,x2_15); = conv(x1_30,x2_30); 0:length(x1convx2_15)-1; 0:length(x1convx2_30)-1; figure subplot(2,4,1) stem(k_15,X1X2_15) title('X_1[k] x X_2[k]') xlabel('k') xlim([-1 15]) subplot(2,4,2) stem(n_15,iX1X2_15) subplot(2,4,3) stem(n_conv_15,x1convx2_15) subplot(2,4,4) hold on stem(n_15,iX1X2_15,'r') stem(n_conv_15(1:15),x1convx2_15(1:15),'b') subplot(2,4,5) stem(k_30,X1X2_30) subplot(2,4,6) stem(n_30,iX1X2_30) subplot(2,4,7) stem(n_conv_30,x1convx2_30) subplot(2,4,8) hold on stem(n_30,iX1X2_30,'r') stem(n_conv_30(1:30),x1convx2_30(1:30),'b') 10- 31- 12 9...
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