Speech Signal Analysis and Modelling - Digital Speech: Coding for Low Bit Rate Communication Systems - page 75

(a)

(b)

(c)

0.0 1.0 2.0 3.0 4.0

Frequency (kHz)

Figure 4.11 (a) the original speech spectral envelope, (b) the original speech
spectrum and (c) the LPC residual spectrum

LPC coefficients from one frame to the next is also commonly applied to
smooth out transitional effects.
After the LPC inverse filtering, the resultant signal, e(n) , should have a
much lower spectral variation than the original, s(n) . This is illustrated in
Figures 4.10 and 4.11 where the time and frequency domain representation of
a typical frame of s(n) and e(n) are shown. Clearly, the error signal spectrum
is much flatter. This result is not surprising since LPC can be viewed as a
method of short-time spectrum estimation.
Also illustrated in Figure 4.11 is the frequency response or spectral envelope
of the LPC filter. A feature that can be observed is that the LPC spectral
envelope matches the signal spectrum much better in the spectral peaks than
the spectral valleys. This can be expected as our model transfer function,
H(z) , has poles only to model the formant peaks and no zeros to model the
spectral valleys.

4.4 Pitch Prediction

4.4.1 PeriodicityinSpeechSignals
In the previous section, the ability of LPC analysis to remove the adjacent
or neighbouring sample correlations present in speech was described. As
observed, this was equivalent to removing the spectral envelope in the signal