What is the significance of the first zero up-crossing of a cross-correlation? The signals being correlated are cosines signals with some phase difference.

EDIT 1 : Cross-correlation plot attached. The signals are cosines with phase difference and may be with some low frequency components.

Sampling frequency of the measured signal is taken as 50Hz

Cross correlation obtained using:

Cxx=fftshift(ifft(fft(x,N).*conj(fft(y,N))))/(norm(x) * norm(y));

enter image description here

  • $\begingroup$ I'm not quite sure what you mean by the "first zero upcrossing" of the cross correlation. Can you post a picture? $\endgroup$
    – Jim Clay
    Commented Jun 12, 2013 at 2:20
  • $\begingroup$ Well, the first peak occurs at the lag at which the wave constructively interferes with itself, and the first negative peak occurs at the lag at which it destructively interferes with itself, so the first zero crossing is... the midpoint between those? $\endgroup$
    – endolith
    Commented Jun 13, 2013 at 17:30
  • 1
    $\begingroup$ @endolith A minor emendation: zero crossings occurs between positive and negative peaks, but don't need to occur at midpoints between the two. $\endgroup$ Commented Jul 4, 2013 at 18:24

1 Answer 1


Not sure what you are asking specifically. The cross correlation of two cosine waves is just another cosine. The triangular envelope in the picture is simply a consequence of the limited length of the signals.

The phase of the cross-correlation cosine is given by the phase difference of the two input cosines. This phase difference determines the position of the zero crossings. So in effect the position of that zero crossing is some metric of the phase difference of the input signals


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