cross correlation plot- symmetry about y axis

I have two cosine signals 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 sort of symmetrical about the y axis. Why is that? Any help would be much appreciated.

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(abs(c)))

Answer 1

[Honglei Chen]

You have a cosine signal with multiple periods. So when you move back and forth for a period, you get another match. Guaranteed the delay that matches the two exactly should produce the highest peak but nevertheless there will be other peaks when you delay/advance multiple periods.