Our investigation into the front-end signal processing for maximum likelihood based speaker normalization reveals that in the linear scaling model, it is more appropriate (and evidently more correct) to assume that the spectral envelopes of any two speakers for same sound are linearly scaled versions of one and another, rather than assuming that the whole magnitude spectra (including pitch harmonics) are scaled. The use of the proposed model and its implementation results in about 4% and 7% relative improvement for adults and children respectively on a digit recognition task.