SPlpcLSdist
Routine

double SPlpcLSdist (const float pc1[], const float pc2[], int Np, int Ncep)
Purpose

Calculate the RMS log LPC spectral distance measure
Description
This function calculates Markel and Gray's RMS log LPC spectral distance
measure. Consider the prediction error filter A(z),
Np k
A(z) = 1  SUM p(k) z .
k=1
The power spectrum corresponding to the allpole LPC filter is
S(w) = 1 / A(w)^2 ,
where A(w) is shorthand 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
meansquare 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.

Reference:

A. H. Gray, Jr. and J. D. Markel, "Distance measures for speech
processing", IEEE Trans. Acoustics, Speech, and Signal Processing,
vol. ASSP24, pp. 380391, October 1976.
Parameters

< double SPlpcLSdist

Resultant distance measure (dB units). 0 dB corresponds to identical
sets of predictor coefficients.

> const float pc1[]

Predictor coefficients corresponding to the first spectrum

> const float pc2[]

Predictor coefficients corresponding to the second spectrum

> int Np

Number of predictor coefficients in each of pc1 and pc2

> int Ncep

Number of cepstral coefficients used for the distance calculation
(maximum 150). This number does not include the zero'th cepstral
coefficient. A recommended number is 3*Np.
Author / revision
P. Kabal
/ Revision 1.15 2003/05/09
See Also
SPlpcISdist
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