Efficient LPC Quantization Methods - Digital Speech: Coding for Low Bit Rate Communication Systems - page 99

where,

and r i r i = u i + jv i = u i − jv i

(5.39)

r i r i u i v i ⇒ r i + = 2 u i and r i × = + = t i

Equating the terms of equations (5.37) and (5.16),

S 0 = 1 (5.40)

T 0 = 1 (5.41)

S p + 1 =− 1 (5.42)

T p + 1 = 1 (5.43)

1
2 (T i +

α i = S i ) (5.44)

1
2 (T i

α p + 1 − i = − S i ) (5.45)

for i = 1 , ... ,P/ 2

5.4.2 LPCSynthesisFilterMethod
An LPC synthesis can be constructed directly using the LSF coefficients. The
filter is derived from the following,

H(z) = 1 /A p (z) = 1 / [1 + (A p (z) − 1 ) ] (5.46)

1

=

1 + 1 / 2[ (P p + 1 (z) − 1 ) + (Q p + 1 (z) − 1 ) ]

i.e.

A p (z) − 1 = 1 / 2[ (P p + 1 (z) − 1 ) + (Q p + 1 (z) − 1 ) ] (5.47)

p/ 2

z 2 ) = 1 / 2 ( 1 − z) ( 1 − 2cos ω i z + − 1

i = 1

p/ 2

z 2 ) + ( 1 + z) ( 1 − 2cos θ i z + − 1 (5.48)

i = 1

Let u i =− 2cos ω i ,v i =− 2cos θ i