Efficient LPC Quantization Methods - Digital Speech: Coding for Low Bit Rate Communication Systems - page 103

bit-rate speech coders. Therefore the overall success of a given speech coding
scheme depends greatly on the quality of the LSF quantizer used.
Scalar schemes can be used, as they present very low complexity and
storage requirements. However they cannot make use of the high intra-frame
correlation exhibited by LSF vectors and, hence, they are very rarely used due
to their poor performance. Vector quantization (VQ) schemes can be used
to exploit intra-frame correlations. VQ exploits the redundancies in the LSF
vector well and can provide high quality quantization for a relatively limited
number of bits per frame of speech. As a result, they are widely used in
modern speech coders. The following sections investigate the use of VQ for
LSF quantization and ways of maximizing the performance of such schemes
in several coder configurations.

5.6.1 DistortionMeasures
In order to achieve good performance quantization of LSF parameters, it is
necessary to have a way of linking the quantization error to the distortion
in perceptual quality. Due to the complex relationship that exists between a
set of LSF coefficients and the frequency response of the corresponding LPC
filter, using a Mean-Square Error (MSE) measurement may not lead to an
optimal performance of the quantizer.
A widely-used technique for computing the distortion that exists between
the original set of LSFs and their quantized version is the Log Spectral
Distortion measure. However a Weighted Mean-Square Error (WMSE) mea-
surement may also lead to good results if an appropriate weighting function
is used.

5.6.2 SpectralDistortion
The mean square log spectral distortion, which will be referred to simply as
spectral distortion (SD), is defined as:

π

1
π

10 log 10 S (w) ] 2 sd = [10 log 10 S(w) − (5.54)

0

where S(w) and S (w) are the frequency responses of the LPC filter derived
from the original and quantized LSFs, respectively. S(w) can therefore be
defined as:

2

S(w) = 1 / | A(w) | (5.55)

which leads to,

p

a k e − jwk

2

S(w) = 1 / | 1 − | (5.56)

k = 1