PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 535

figure(2)

corr = xcorr(f1n,f2n);

N= length (corr);

m = 0:1:N-1;

subplot (3,1,1)

stem(m,corr);title(‘Convolution and correlation plots’);

ylabel(‘Amplitude’);

subplot(3,1,2)

conv1=conv(f1n,f2n _ rev);

stem(m,conv1)

xlabel(‘time index n’);ylabel(‘Amplitude’);

subplot(3,1,3)

conv2=conv(f1n _ rev,f2n);

stem(m,conv2);

xlabel(‘time index n’);ylabel(‘Amplitude’);

figure(3) % auto-correlations

mm=-31:31;

aut _ corr1=xcorr(f1n,f1n);aut=xcorr(f1n);

aut _ corr2=xcorr(f2n,f2n);

plot(mm,aut _ corr1,mm,aut _ corr2,mm,aut);

title(‘Auto-correlation plots’);

ylabel(‘Amplitude’);

legend(‘R11’,’R22’,’R1’)

figure(4) % frequency analysis

DFT _ corr = fft(corr,256);

DFT _ f1n = fft(f1n,256);

DFT _ f2n = fft(f2n,256);

DFT _ 12 = conj(DFT _ f1n).*DFT _ f2n;

k=1:1:256;

subplot (2,1,1)

plot (k/256,abs(DFT _ 12));title(‘abs[conj[fft(f1n)]*fft(f2n)] vs. W ’)

ylabel(‘Magnitude’)

subplot(2,1,2)

plot(k/256,abs(DFT _ corr));title(‘abs[fft(xcorr(f1(n),f2(n)))] vs. W’)

xlabel(‘W’); ylabel(‘Magnitude’)

figure(5)

subplot (2,1,1)

error1 = corr-conv1;

bar(m,error1);title(‘error1=corr[f1(n),f2(n)]-conv[f1(n),f2(-n)]’)

ylabel(‘Amplitude’);

subplot(2,1,2)

error2 = abs(abs(corr)-abs(conv2));

bar(m,error2)

title (‘error2=abs[abs[corr[f1(n),f2(n)]]-abs[conv[f1(-n),f2(n)]]]’)

xlabel (‘time index n’); ylabel(‘Amplitude’)

The script fi le conv_corr is executed, and the results are as follows:

>> conv _ corr