基于Matlab的循環(huán)卷積計算

1、題目：x(n) = x(O), x(1), x(2) = 1,3,2, h(n) = h(0), h(1), h(2), h(3)=4,3,2,1(1) 計算 y(n) = x(n) * h(n);(2) 分別計算出x(n)與h(n)4點、5點和6點的循環(huán)卷積。解：(1) matlab 代碼：X = 1 3 2; H = 4 3 2 1; Y = Con v(H,X);figure(1); nX = 0:le ngth(X)-1; nH = 0:Ie ngth(H)-1;nY = 0:le ngth(Y)-1;SUbPlot(3,1,1);stem( nX,X);xlabel('Tim

2、e in dex n'); ylabel('Amplitude');title('x (n)');grid on;subplot(3,1,2);stem( nH,H);xlabel('Time in dex n'); ylabel('Amplitude');title('h( n)');grid on;subplot(3,1,3);stem( nY,Y);xlabel('Time in dex n'); ylabel('Amplitude');title('y( n)

3、= x(n )*h( n)');grid on;結(jié)果如下：H =4321151913_ - _,5¾E<T-UTimtr*d rUfIe17pr a '-a3 仃 flF jf,rfl.i2 于 I3uc(2) matlab 代碼：X = 1 3 2; H = 4 3 2 1;N4 = 4; N5 = 5; N6 = 6;figure(2);%4點循環(huán)卷積X4 = fft(X,N4); H4 = fft(H,N4); yy = X4.* H4;Y4 = ifft(yy,N4);nY4 = O:Ie ngth(Y4)-1;SUbPlot(3,1,1);stem(

4、nY4 ,Y4);grid on; xlabel('Time index n'); ylabel('Amplitude');title('y(n)-4 點循環(huán)卷積');%5點循環(huán)卷積X5 = fft(X,N5); H5 = fft(H,N5); yy = X5.* H5;Y5 = ifft(yy,N5);nY5 = 0:le ngth(Y5)-1;subplot(3,1,2);stem( nY 5,Y5);grid on; xlabel('Time index n'); ylabel('Amplitude');ti

5、tle('y(n)-5 點循環(huán)卷積');%6點循環(huán)卷積X6 = fft(X,N6); H6 = fft(H,N6); yy = X6.* H6;Y6 = ifft(yy,N6);nY6 = 0:le ngth(Y6)-1;subplot(3,1,3);stem( nY 6,Y6);grid on; xlabel('Time index n'); ylabel('Amplitude'); title('y(n)-6 點循環(huán)卷積');結(jié)果如下:X =132H =4321Y4 =11171913Y5 =6.000015.000019.000013.000