Analysis by Synthesis LPC Coding - Digital Speech: Coding for Low Bit Rate Communication Systems - page 240

With this α 01 , the two functions q 0 (n) and q 1 (n) are now orthogonal. In order
to build the other functions q i (n) , linearly independent p i (n) are added one at
a time until all are constructed. This can be formulated in general as

k − 1

q k (n) = p k (n) − α jk q j (n) (7.80)

j = 0

where,

L − 1

p k (n)q j (n)

=

n 0

α jk = , j = 0 , 1 , ... ,k − 1 (7.81)

L − 1

q j (n)

n = 0

Therefore, the basic task in VSE is to obtain s opt (n) by deriving the set of

orthogonal vectors s i (n) and their optimum scaling factors a i .Theoptimum
excitation x opt (n) can then be derived by passing

ˆ

ˆ s opt (n) through the combined

LPC and perceptual-weighting inverse filter.
In VSE, it is very important to construct the basis vectors in a perceptu-
ally advantageous way and training is required. As in CELP with Gaussian
excitation, in VSE linear prediction (VSELP), the pitch filter is treated as an
adaptive codebook for lag values less than the subframe size and, hence,
it is not included in the codebook search process. Finally, the total excita-
tion is obtained by adding the gain-scaled secondary excitation Gx opt (n) to
the pitch predictor excitation. A block diagram of vector processing of a
VSELP coder where the scaling factors a i are assumed to be ± 1isshownin

Figure 7.23.
The M basis vectors, [ x i (n) ] i = 1 , are first synthesized to give M synthetic
basis vectors [ s i (n) ] i = 1 . These are then made orthogonal to the pitch predictor

contribution signal via the Gram-Schmidt orthogonalization process to get
[ s i (n) ] i = 1 . This ensures that the secondary excitation does not cover the vector
space that has already been covered by the pitch predictor contribution.
After orthogonalization, the individual basis vector scaling factors a i are
computed to form a M th element vector, a .Thevector a is then quantized
as

ˆ

± 1. The final synthetic signal from the excitation, ˆ s opt (n) , is obtained by

first summing up the properly signed ( 1) orthogonal basis vectors and

then gain scaling the summed vector. In order to obtain the quantized
secondary excitation,

±

s opt (n) is then inverse-filtered with the combined LPC
and perceptual-weighting filters at the encoder. At the decoder, as there is
no need for the perceptual-weighting filtering, only the LPC inverse filtering
is used. The overall scaling factor is obtained as in standard CELP. The final

ˆ