Cross-Correlation with Multichannel Input

Generate three 11-sample exponential sequences given by $$0.4^n$$, $$0.7^n$$, and $$0.999^n$$, with $$n\ge 0$$. Use stem3 to plot the sequences side by side.

N = 11;
n = (0:N-1)';

a = 0.4;
b = 0.7;
c = 0.999;

xabc = [a.^n b.^n c.^n];

stem3(n,1:3,xabc','filled')
ax = gca;
ax.YTick = 1:3;
view(37.5,30)

Compute the autocorrelations and mutual cross-correlations of the sequences. Output the lags so you do not have to keep track of them. Normalize the result so the autocorrelations have unit value at zero lag.

[cr,lgs] = xcorr(xabc,'coeff');

for row = 1:3
    for col = 1:3
        nm = 3*(row-1)+col;
        subplot(3,3,nm)
        stem(lgs,cr(:,nm),'.')
        title(sprintf('c_{%d%d}',row,col))
        ylim([0 1])
    end
end

Restrict the calculation to lags between $$-5$$ and $$5$$.

[cr,lgs] = xcorr(xabc,5,'coeff');

for row = 1:3
    for col = 1:3
        nm = 3*(row-1)+col;
        subplot(3,3,nm)
        stem(lgs,cr(:,nm),'.')
        title(sprintf('c_{%d%d}',row,col))
        ylim([0 1])
    end
end

Compute unbiased estimates of the autocorrelations and mutual cross-correlations. By default, the lags run between $$-(N-1)$$ and $$N-1$$.

cu = xcorr(xabc,'unbiased');

for row = 1:3
    for col = 1:3
        nm = 3*(row-1)+col;
        subplot(3,3,nm)
        stem(-(N-1):(N-1),cu(:,nm),'.')
        title(sprintf('c_{%d%d}',row,col))
    end
end