# What is obtained from the cross correlation plot?

Let’s assume that we have two audio signals, x(t) and y(t) affected by the noise as shown below. And we would like to cross-correlate these two signals and the cross-correlation plot is shown as below.

In this correlation plot there is a peak value around -11 msec. I am trying to understand how we interpret this peak in this plot? What does it mean? Please also explain me what do we obtain from the Fourier transform of the correlation function.

• This shows that $x(t)$ and $y(t)$ are very likely to be noisy versions of the same audio signal except that one of the signals (which one depends on what your definition of correlation is) is delayed by about 11 msec with respect to the other signal. That is, $x(t) = a(t) + n_1(t)$ while $y(t) = a(t-\tau) + n_2(t)$ for some $a(t)$. It also suggests that $a(t)$ is not a sustained musical note such as the A at 440 Hz that is sounded while the orchestra is tuning up before a performance. If it were, there would be multiple tall peaks and a broader spread of the crosscorrelation function. – Dilip Sarwate Jun 9 '14 at 12:51
• @DilipSarwate Why not make that an answer? – Phonon Jun 10 '14 at 0:21