Speech Signal Analysis and Modelling - Digital Speech: Coding for Low Bit Rate Communication Systems - page 80

Original

LPC Residual

Pitch Residual

0.0 100.0 200.0 300.0 400.0 500.0

Time (Samples)

Figure 4.13 Time domain plots of original, LPC and pitch residuals

In order to determine the optimum τ , values of the lags are tested between
τ min and τ max , and the lag which minimizes the error E is the optimal value.
Having found τ ,thegain β can be found. A plot of the LPC residual and the
signal after pitch inverse filtering is shown in Figure 4.13. It is clear that the
pitch residual (secondary excitation) no longer possesses the sharp pulse-like
characteristics of the residual, i.e. it looks much whiter than the LPC residual.
Similar formulations can also be given for multiple-tap pitch filters.
A typical plot of τ and β for a block of voiced, unvoiced and transitional
speech is shown in Figures 4.14 and 4.15. As can be observed, during voiced
regions (refer to the steady regions in Figure 4.14), β stays close to unity,
whereas during transitional regions β fluctuates significantly.
Aswell as a single-tapfilter, the three-tappitchfilter givenby equation (4.66)
is commonly used. Here I

= 1 which forms the pitch prediction based on

three past samples at τ − 1 , τ , τ + 1.

1

P 3 (z) = (4.66)

1

β j z − (j + τ) 1 −

=−

j 1

A multiple-tap pitch filter tends to provide better performance than the
single-tap, but with increased complexity and larger capacity requirement
for the extra two filter taps β − 1 and β 1 .