Analysis by Synthesis LPC Coding - Digital Speech: Coding for Low Bit Rate Communication Systems - page 218

problemcan also be solved by employing backward forms of LPC analysis, i.e.
using quantized (or past) samples only, to estimate the LPC coefficients as in
the 16 kb/s LD-CELP (G.728) proposed for the ITU standard [15]. However,
such backward techniques can only operate successfully at around 16 kb/s,
because the prediction accuracy reduces rapidly with the increase in the
quantization noise of the encoded speech.

7.3.2 PitchPrediction
Pitch prediction is an essential part of all CELP coders. Since the early versions
of CELP had Gaussian-noise-populated excitation codebooks, pitch filtering
was required to introduce the necessary pitch of the voiced speech parts. The
order of the pitch filter is usually less than the order of the LPC filter and is
giveninitsgeneralformas,

I

β i z ( − D − i) P(z) = 1 − (7.26)

i =− I

The pitch predictor in CELP generates long-term correlation, either due to
the actual pitch excitation or other long-term similarities. Thus the term
'long-term predictor' (LTP) is usually preferred to 'pitch predictor', which
is somewhat misleading in describing the action of this filter for unvoiced
speech and even, to some extent, for voiced speech when D is equal to
pitch multiples. In CELP and other AbS-LPC schemes, the LTP analysis
is usually performed in a closed loop [16] with single or multiple taps.
In CELP, one is interested in minimizing the error between the weighted
original and the synthesized output speech. By this definition, analysis of
the signal to derive the desired LTP parameters must minimize the error
between the weighted original and the synthesized speech, and not mini-
mize the LTP prediction error (or second residual) as is the case in older
analysis and synthesis systems. Assuming that the LPC parameters have
already been calculated, the remaining undetermined parameters are Gx(n) ,
D ,and β k . Although these parameters can be obtained by exhaustively
searching for all Gx(n) as well as the LTP parameters, the procedure becomes
very computationally-intensive and thus suboptimal solutions have to be
used. One way of reducing the complexity is by obtaining the LTP and
Gx(n) in two sequential steps. First we assume Gx(n) is zero, and cal-
culate the LTP parameters such that e(n) is minimized. Next the LTP is
held constant and Gx(n) is computed. Thus, let the codebook excitation
be zero, i.e.

x(n) = 0 , 0 ≤ n ≤ L − 1 (7.27)