I'm looking at some code that matches audio templates in a longer audio file. The calculation correlates the power spectra of the template and audio file, maximizing over the possible alignments. This seems sub-optimal to me, because by going over to the power spectrum we're throwing away phase information. Yet when I try doing a full correlation I get worse results. I'm not 100% sure yet my implementation is correct; I could have made a silly mistake.
Is there any reason it could be better correlating the power spectra than doing a full correlation? E.g. is it more noise resistant? (I don't see why it would be. As it happens, I do have something resembling white noise in my test data.)
The only obvious thing I can think is that the power spectral correlation is probably better if the alignment error is >= 1/highest frequencies in signal because then the template and signal will be out of phase. I don't think this should be the case for me: I'm optimizing to within more temporal precision than that.
EDIT: in view of Peter K's comment, I should clarify that I'm using the short time Fourier transform, summing over windows of size around 0.01s. That's how the alignment dependence enters.