Efficient LPC Quantization Methods - Digital Speech: Coding for Low Bit Rate Communication Systems - page 90

A 0

A p A p−1

X
Input
Terminal

Y
Output
Terminal

+1/−1

k p k p−1

Lossless Z

− −

(k 0 = − 1)

Z −1 Z −1

Z −1

B 0

With loss B p B p−1

Figure 5.4 PARCOR structure of LPC synthesis

The PARCOR representation is an equivalent version and its digital form is
asshowninFigure5.4,where,

A p − 1 (z) = A p (z) + k p B p − 1 (z) (5.10)

z − 1 [ B p − 1 (z) B p (z) = − k p A p − 1 (z) ] (5.11)

z − 1 ,and where A 0 (z) = 1and B 0 (z) =

z − (p + 1 ) A p (z − 1 )

B p (z) = (5.12)

The PARCOR representation as shown in Figure 5.4 is stable for < 1for

all i . In Figure 5.4, the transfer function, TF, from X to Y is H p (z) ,andfromY
to Z is B p (z) , therefore the TF from X to Z is given by equation (5.13) where
R p (z) is the ratio filter,

| k i |

R p = B p (z)/A p (z) (5.13)

The PARCOR synthesis process can be viewed as sound wave propagation
through a lossless acoustic tube, consisting of p sections of equal length but
nonuniform cross sections. The acoustic tube is open at the terminal corre-
sponding to the lips and each section is numbered from the lips. Mismatching
between the adjacent sections p and ( p 1) causes wave propagation reflec-

tion. The reflection coefficients are equal to the p th PARCOR coefficient k p .
Section p

+

1, which corresponds to the glottis, is terminated by a matched
impedance. The excitation signal applied to the glottis drives the acoustic
tube.
In PARCOR analysis, the boundary condition at the glottis is impedance-
matched. Now consider a pair of artificial boundary conditions where the
acoustic tube is completely closed or open at the glottis. These conditions
correspond to k p + 1

+

= 1and k p + 1 =− 1, a pair of extreme values for the