Efficient LPC Quantization Methods - Digital Speech: Coding for Low Bit Rate Communication Systems - page 119

parameters to be quantized, so as to maximize the efficiency of the quantizer.
The MSVQ was shown above to provide better performance than the SVQ,
mostly because it makes better use of the correlations between the elements
of an LSF vector, i.e. the intra-frame correlations as shown in Table 5.2.
However, LSF vectors are extracted at a typical update rate of 20ms and
speech characteristics often remain similar for longer than 20ms. Therefore,
successive LSF vectors are correlated (see Table 5.3) and a good quantizer
should make use of these similarities to improve the quantization accuracy.
The inter-frame correlation can be exploited in various ways, the most
popular ones being the use of a predictor and joint quantization of several
sets of LSFs.

5.9.1 LSFPrediction
A popular approach to exploiting the inter-frame correlations of LSF vectors
is the use of prediction. Instead of quantizing an LSF vector directly, the
difference between a predicted vector and the actual LSF vector is quantized
and transmitted. If the predictor is good, then the residual signal should
be easier to quantize than the original LSF vector. It is common practice
to remove the long-term mean of each LSF before applying prediction. The
residual LSF is given by:

f n − f n r n = (5.74)

where f n is the prediction vector. The decoded LSF vector is then given by,

f n

+ f n = ˆ r n (5.75)

where r n is the quantized value of r n .

This obviously implies that the decoder should have knowledge of f n .
Therefore, the prediction used should be a function of some parameters
available at both the decoder and the encoder. One of the simplest predictors
assumes that a set of LSFs can be predicted using the previous quantized set
of LSFs, scaled by a weighting factor,

ˆ

f n = α n f k − 1

(5.76)

n

This will be referred to as an LSF differential quantizer (LSF-DQ). The
computation of the prediction gain ismade difficult by the fact that knowledge
of the quantizer (codebook) is necessary to compute the prediction. One way
around this problem is to assume that the final quantizer will be quite good
and therefore f k − 1

n can be approximated by f k − n in the equation above. The
optimal factors α n can then be determined by maximizing the prediction gain