Efficient LPC Quantization Methods - Digital Speech: Coding for Low Bit Rate Communication Systems - page 105

computed for every bin of each FFT output. This is, of course, not a problem
when estimating the performance of a quantizer off-line, but severely limits
its use in a real-time coder.
On the other hand, simple MSE techniques have much lower complexity
and can easily be implemented in real-time coders. However the basic MSE
methods do not take into account the different perceptual effect of each of the
LSFs, and this may lead to poor performance of the quantizer. One simple
way to reduce this problem is to introduce an appropriate weighting function
in the calculation of the MSE (WMSE). The WMSE between the LSF vector f
and the candidate vector f (frequencies are in Hz) is given by:

− f ) T W( f

d( f , f ) − f )

= ( f (5.58)

where W is a positive diagonal matrix. This is equivalent to:

p

− f n ) 2

d( f , f ) = w n ( f n (5.59)

n = 1

where w is a positive weighting vector.
Theweighting vector renders contributions of certain elements more impor-
tant than others in the summation process. The weighting vector is usually a
function of the original LSF vector, and therefore needs to be computed only
once per quantization (i.e once for every frame). A correctly chosen weighting
function will improve the perceptual quality of the quantization but finding a
suitable weighting function is difficult, as it needs to be related to perceptual
quality. Various weighting functions have been investigated in the literature
and the most popular ones are presented here.

Paliwal-Atal
This LSF weighting method is based on the frequency response of the original
LPC filter [9]. The weights are calculated as:

c n [ P( f n ) ] τ w n = (5.60)

where P( f n ) is the LPC power spectrum associated with the original set of
LSFs, f n is the n th LSF. τ is a constant used to determine the relative importance
of the LSF and is experimentally set to 0.3. Finally, the fact that the human ear
cannot resolve high frequencies very well is used in introducing the factor c n ,
which reduces the influence of the last two LSFs in the summation.

1 . 0for1 ≤ n ≤ 8

c n = 0 . 8forn=9

0 . 4forn=10

(5.61)