Finding Frequency Differences In Differing Amplitude Signals
Sounds to me like you need to look at the signals in the frequency domain.  Take the Fourier transform of each signal (use an FFT), and look at the spectrum.  I'm not sure if you've got signals with just a single frequency (a tone) or with many frequencies, but in either case if they have the same frequencies in them then the spectra should look the same (except for one being larger than the other).

If you're unfamiliar with frequency domain concepts, I'd suggest you read up on them first.  The wikipedia page on Fourier transforms is pretty large, so I'm not sure how good that would be as an introduction, but there are a large number of books on the topic and many websites too.