Analysis by Synthesis LPC Coding - Digital Speech: Coding for Low Bit Rate Communication Systems - page 201

s(n)

W(z)

s w (n)

+

−

Excitation
Generator

1/A w (z)

1/P(z) +

^

s(n)

e(n)

Error
Minimization

Figure 7.4 Modified AbS-LPC encoder with the weighting filter moved to the two
branches of the error minimization procedure

where f s is the sampling frequency in Hz. As can be observed from Figure 7.3,
theweighting filter de-emphasizes the frequency regions corresponding to the
formants as determined by the LPC analysis. By allocating larger distortion
in the formant regions, noise that is more subjectively disturbing in the
formant nulls can be reduced. The amount of de-emphasis is controlled by
γ which introduces a broadening effect and must lie between 0 and 1. The
most suitable value of γ is selected subjectively by listening tests; for 8 kHz
sampling, γ is usually around 0.8 to 0.9.
Although the weighting filter can be used as it is in its normal position (after
subtraction of s(n) from s(n) ), it can also be modified in a computationally-

advantageous way by moving it to the two branches contributing to the
subtraction operation, as illustrated in Figure 7.4. This results in a block of
the input samples being weighted only once prior to the AbS search. At the
same time W(z) is combined with the LPC filter to form a modified all-pole
synthesis filter.

ˆ

1
A w (z) =

1
A(z) .W(z)

(7.5)

1

=

p

a i γ i z − i

−

1

i = 1