Analysis by Synthesis LPC Coding - Digital Speech: Coding for Low Bit Rate Communication Systems - page 200

method is the use of a weighting filter in AbS-LPC schemes. This weighting
filter is given by,

A(z)
A(z/γ )

W(z) = (7.3)

p

a i z − i

−

1

i = 1

= , 0 ≤ γ ≤ 1

p

a i γ i z − i 1 −

i = 1

This weighting filter is the same as that proposed by Atal [2] for APC
schemes and a typical plot of its frequency response is shown in Figure 7.3.
The effect of the factor γ does not alter the centre formant frequencies but
just broadens the bandwidth of the formants by f given by,

f s
π ln γ Hz)

f =− (7.4)

15.0

Original Envelope

5.0

γ = 0.98

-5.0

γ = 0.95

γ = 0.90

-15.0

γ = 0.80

γ = 0.70

-25.0

γ = 0.50

-35.0

-45.0

0.0 1.0 2.0 3.0 4.0

Frequency (kHz)

Figure 7.3 Typical plots of weighting filter spectra compared with the original
speech envelope