From: "Bruno L. Giordano"
I am looking for "general" metrics of the acoustical (not perceived)
similarity between mono signals independent of a features extraction
stage (e.g., peak level, harmonicity etc.).
Ideally, this metric would operate on a low-level representation of the
signal (ideally the waveform).
I am doing work which involves measuring similarity for machine
learning applications. One standard method (eg in evolutionary
computation) is to take a mean square error over the magnitude or
power spectrum: ie for two signals x and y of length N, window them
and take the DFT of each window and then take the magnitude of each
bin, to produce two sequences of spectra, X_i and Y_i: the distance is
d(x, y) = sum_i (sum_n (X_i[j] - Y_i[j]) ^2)
You can indeed define a purely time-domain distance measure:
d(x, y) = sum_n (x[n] - y[n]) / N
but it seems to be pretty useless: eg if we construct y by
phase-inverting x, we get a very large distance between them, even
though they sound exactly the same.
As you know, in other applications (such as automatic classification),
the extraction of features is more common.
I'd be interested to hear more about your application and why you
don't want to extract features?