LPC gain term

Submitted by rockychaudhary on Sun, 2006-12-10 19:16.

While converting the LPC coeifficients to cepstal cofficients, (as given in "fundamentals of speech recognition" - Rabiner/Juang) we need the term "G", i.e. the LPC gain term. Its also written that this is actually calculated from the speech signal. How ? I have read somewhere that it can be taken as the first autocorrelation coefficients, is it so? please help .........

Thanks in advance....

Submitted by cranen on Mon, 2006-12-11 18:04.

An elaborate description of how the Gain (G) for the LPC model can be computed can be found in

Rabiner, L.R. and Schafer,R.W. (1978) Digital processing of speech signals, Prentice Hall, Englewood Cliffs.
p. 404-406.

The result in formula:
G^2=R_n(0)-Sum_{k=1}^{p} \a_{k} R_{n}(k)
with G gain factor
R_{n}(k) k-th autocorrelation coefficient at
time instant (i.e. sample index) n
a_k LPC coefficients