I am trying to use generalized cross correlation with phase transform (GCC_PHAT) on some audio processing indoor, with the existence of low noise. I ve read here that by canceling the magnitude factor, which what pretty much PHAT does, the result of the correlation will be resistant to reverberation and low noise, but i cannot seem to understand why. I want to know what is the explanation behind that, what is the relationship between reverberation and magnitude ?
First of all, what do you mean by "cancelling the magnitude factor"? According to the paper by Knapp and Carter (1976), the phase transform (PHAT) was developed as an ad hoc technique. What the transform does is place equal emphasis on each frequency (pre-whitening), but according to the paper by Braindstein and Silverman (1997), the PHAT-weight is suboptimal under ideal conditions.
I am also not sure what you mean by "the relationship between reverberation and magnitude". Reverberation is the effect of reflection subject to room geometry/materials. Basically this means that lots of delayed and attenuated copies of the signal is added to the signal itself.