Np -k
A(z) = 1 - SUM p(k) z .
k=1
The power spectrum corresponding to the all-pole LPC filter is
S(w) = 1 / |A(w)|^2 ,
where A(w) is short-hand notation for A(exp(jw)). The RMS log LPC spectral distance measure for two filters A1(z) and A2(z) is given by
pi
D = sqrt{ int (10 log[|A1(w)|^2] - 10 log[|A2(w)|^2])^2 dw } .
-pi
The power spectrum is the Fourier transform of the (infinite) set of autocorrelation coefficients. The cepstrum for the autocorrelation coefficients is given by inverse Fourier transform of the log power spectrum. Equivalently the cepstral coefficients are the Fourier series coefficients for the (periodic) log power spectrum.
The RMS log LPC spectral distance measure is equivalent to the root mean-square difference between the cepstral coefficients corresponding to the two LPC filters. This routine finds the cepstral coefficients corresponding to the two sets of input predictor coefficients. Theoretically, this requires an infinite number of cepstral coefficients. This routine calculates an approximation to the distance from two finite length sets of cepstral coefficients.