Analysis by Synthesis LPC Coding - Digital Speech: Coding for Low Bit Rate Communication Systems - page 252

s p (n)

Modified
Inverse
Filter

Modified
Synthesis
Filter

High-Pass
Filter

s o (n)

s po (n)

g(n)

Power
Normal-
isation

Figure 7.26 Block diagram of the adaptive post-filter

although the perceived noise level is lowered, the output speech is severely
low-pass, giving a muffling effect. In order to compensate for this low-pass
effect the spectral tilt of the all-pole APF can bemodified such that its response
is somewhere between an all-pass response and the signal spectrum. The best
APF combination was found to be that shown in Figure 7.26.
The simple high-pass filter in the first stage provides a slightly high-pass
spectral tilt and thus helps to reduce muffling. The pole-zero second-stage
filter provides 'shaping' of the spectral envelope. Finally, a gain control is
added to scale the post-filtered speech such that it has roughly the same
power as the unfiltered noisy speech. This is necessary as the cascaded
filters are not unity gain filters. One technique used to normalize the output
signal power is to estimate the power of the un-filtered and filtered speech
separately, then determine an appropriate scaling factor based on the ratio
of the two estimated power values. The speech power is estimated by an
exponential-average gain estimator, i.e. the two estimated power values δ o
and δ p are given by,

δ o (n) ζδ o (n s o (n)

ˆ

= − 1 ) + ( 1 − ζ) (7.114)

δ p (n) ζδ p (n s p (n)

= − + −

ζ) ˆ 1 ) ( 1 (7.115)

where s p (n) is the post-filtered

speech. A suitable leakage factor ζ is 0.96. At each sampling instant, δ o (n) and
δ p (n) are computed as above, then the ratio and the square root are computed
in order to obtain the gain factor g(n)

s o (n) is the original synthetic speech and ˆ ˆ

δ o (n)/δ p (n) . Therefore, the final

=

post-filtered speech is given by

ˆ ˆ

s po (n) = g(n) s p (n) (7.116)

The above procedure is quite computationally-intensive as it requires a
divide and square root operation per sample. Therefore, instead of the