In cepstral speech analysis, it is relatively easy to understand why subtracting the mean removes any "channel" effects (including that of recording equipment and the vocal tract). There is a good explanation of that here. But why does dividing by the variance (after the mean has been subtracted) also give a similar (additional) improvement?
Subtraction in the quefrency-domain corresponds to de-multiplication in the frequency domain, which corresponds to de-convolution in the time domain. Can a similar analogy or explanation be given for division in the quefrency-domain?