# When comparing different signals, how can I normalize their amplitude?

I am comparing two sound signals in the frequency domain. As they can have been recorded in different volumes I need to normalize them. My initial approach was to divide each sample by the mean absolute value of all samples. I done this in the frequency domain (after a fft).

Now I realize that this can be the wrong approach, I could normalize in the time domain or I even could use the average power (amplitude squared). Each approach could yield different results. Of all those possibilities I still don't know which is more suitable to my case.

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I think your answer depends on what you are trying to compare. You could normalize by total power (which is the same as integrating amplitude square in frequency space as integrating the amplitude squared in time). But if you are interested in something like volume in a particular frequency bin you might want to normalize differently. Dividing by mean absolute value is probably not ideal. –  Alice Jul 20 '11 at 19:43
@Alice Not exactly a frequency bin but I am comparing the volume of the same frequencies ranges in different music. Why would I normalize it differently? How would I proceed? –  Jader Dias Jul 20 '11 at 20:07
Those ` quotes you used cause what's between them to be regarded as a verbatim code snippet -- you probably intended to have normal single ' quotes around that instead? –  joriki Jul 20 '11 at 21:09
@XML One possibility is that you can filter your signal, say with a bandpass filter. Then look at the power within the bandpass. A series of band pass filters gives a series of powers in each bandpass. This is essentially a mixer. Matlab signal processing toolbox can do this for you. However your question may involve how the listener determines volume and this is a perception question as our ears are not equally sensitive at all frequencies (and there is interesting phenomena such as masking). This is not even physics, even less so math. –  Alice Jul 21 '11 at 1:48
@joriki I intended to use double quotes. –  Jader Dias Jul 21 '11 at 11:41