Cross-correlation in matlab: symmetrical plot and sign convention

Question

I have two cosine signals in MATLAB both having a frequency of 100 Hz and the second signal has been delayed in time by 0.003 seconds. Both signals have been sampled at 1 Khz. When I use the cross correlation function and plot it to verify the delay between the signals, I expect to see a single point in time at which the signals are aligned but the plot looks symmetrical about the y axis. Why is that?

Also I am not sure about the sign convention here. Does a negative x axis value at the cross correlation peak denote time lag or does a positive x axis value denote time lag?

st=1/1000;
t=[0:999]*st;

s1=cos(2*pi*100*t);
t1=t-(3*st);
s2=cos(2*pi*100*t1);

[c,lags]=xcorr(s1,s2);
plot(lags,c/max(c))

Answer 1

It is not exactly symmetrical. Look where the autocorrelation has a maximal absolute value:

lags(abs(c)==max(abs(c)))

This returns -3, which corresponds to your delay of 0.003 s. The negative sign simply means that your second signal is delayed, not the first. If you swap them when calling xcorr, like that:

[c,lags] = xcorr(s2,s1);
lags(abs(c)==max(abs(c)))

then the answer will be 3. Now it's positive.