Analysis by Synthesis LPC Coding - Digital Speech: Coding for Low Bit Rate Communication Systems - page 251

The gains g k and β D can then be found by solving the above equation as,

K 1 G 3 − K 2 G 2

g k = (7.111)

G 2 G 1 G 3 −

K 2 G 1 K 1 G 2

G 1 G 3 −

−

β D = (7.112)

G 2

The variables k and D are searched through all combinations using the
above analysis and the combination giving the minimum error is selected for
transmission. Even though, the speech quality increases significantly with
this joint computation of the pitch predictor and secondary excitations, the
search computation required is extremely high. Therefore the pitch lag D is
usually limited to a narrow range (i.e. 2 samples) around the selected value

during the LTP search (and its submultiples) before the codebook vector is
selected in this joint optimization process.

±

7.3.6 CELPwithPost-Filtering
As discussed earlier, the function of the perceptual weighting filter is to shape
the noise spectrum so as to hide it under the speech spectrum [2]. However,
at low rates such as 4.8 kb/s, where the average noise level is relatively large,
it is very difficult to suppress the noise below the masking threshold at all
frequencies. Therefore, in order to improve CELP speech quality at lower
bit rates (or, indeed, all rates), further subjective noise reduction techniques
are required.
As CELP is essentially a waveform type speech coder, the coded speech
can be considered to be the original speech corrupted by additive Gaussian-
type noise. Therefore, any speech enhancement technique that deals with
this problem can be used to reduce the noise. One such method is that of
post-filtering [28]. Adaptive post-filtering (APF) has been used successfully in
enhancing ADPCM-coded speech and APC-type schemes [29]. For AbS-LPC
coders, the APF as reported by Chen [30] and given by equation (7.113), has
been widely accepted.

− µz − 1 ) 1 a i β i z − i

p

( 1 −

i = 1

H apf (z) = (7.113)

1

a i α i z − i

p

−

i = 1

The function of the APF is to attenuate the components in the spectral
valleys. However, to achieve this successfully, the simple all-pole APF used
in earlier schemes is not adequate. If an all-pole APF is used alone, then,