[beagle3]

It has nothing to do directly with FFT, which is why it is confusing:

What he is looking for is maximal correlation between two binary series (think "Pearson's r or r-square correlation coefficient"). Now, correlation is just like convolution except one series is flipped around on the time axis. Which means, if you have an efficient way to compute convolutions (and you do, through FFT), you have an efficient way to compute correlations.

(I don't think 5 year olds heard of Pearson's correlation coefficient or convolutions, but ... that's the best I can do).

In many ways, correlation and covariance are more fundamental than convolution - they are closely and directly related to the inner product.

And the only reason to use the FFT here is convenience (i.e., it is fast and simple to compute), but the correlation/convolution property applies to many "transform domains" - Laplace, Z, Cosine, Sine, and a few others (all of which are closely related among themselves, but only a few easy to compute numerically).