corrcoef mistakenly gives 1 for different amplitude waveforms

I'm trying to obtain the crosscorrelation between sets of oscillations for a lag of zero, here is the relevant part of my code:

yintsplit=(linspace(minimumsplit,maximumsplit,2048))'; y2intsplit=(linspace(minimumsplit,maximumsplit,2048))';

zintsplit = interp1(yisplit,zisplit,yintsplit,'spline'); z2intsplit = interp1(y2isplit,z2isplit,y2intsplit,'spline');

[absplit, lagssplit] = xcorr(zintsplit,z2intsplit, [], 'coeff'); zzsplit = absplit(find(lagssplit == 0));

or

absplit = corrcoeff((zintsplit,z2intsplit); zzsplit = absplit(1,2);

When I plot the two sets of oscillations, they are clearly different. They have the same period, but their amplitude is different. But both xcorr and corrcoef give me a cross-correlation of 1! I'm perplexed, I have no idea what the problem is... Can anyone help? Thanks!

Answer 1

[the cyclist]

I did not try executing your code. But two oscillations that vary only by amplitude are perfectly correlated, as this simple example illustrates:

x = (0 : 0.1: pi)';

y1 =   sin(x);
y2 = 2*sin(x);

corrcoef([y1,y2])

figure
subplot(3,1,1), plot(x,y1,'.')
set(gca,'YLim',[0 2.1])
subplot(3,1,2), plot(x,y2,'.')
set(gca,'YLim',[0 2.1])
subplot(3,1,3), plot(y1,y2,'.')
axis square

Answer 2

[S]

Thanks a lot, you're absolutely right.

I subsequently looked into it a bit more, and if anyone needs any more clarification, here it is:

The way normalisation is done by the 'coeff' option in xcorr or by the crosscoeff function is as:

A.B/|A|.|B|

So naturally, as the cyclist points out, if the amplitude is the same but the period different, the cross-correlation will be renormalised to one.

One could however use (and specify) a different renormalisation which would also give an indication of the amplitude difference, which would be

A.B / ((|A|+|B|)/2)

This would have the effect of giving a lower correlation if the two oscillatory forms do not have the same amplitude.