Multimode Speech Coding - Digital Speech: Coding for Low Bit Rate Communication Systems - page 293

synthesis frame boundaries. However if the selected pitch pulse is on the
frame boundary or within a few samples of it, the pulse must be synthesized
smoothly across this boundary, in order to avoid audible artifacts. In such
cases, high resolution PPL and PPS are essential to maintain the phase
continuity across the frame boundaries. It is also possible to compute the
cross-correlation between p u (n u ) and the eight times up-sampled residual
signal, in order to evaluate the best indices i and j . However this requires
more computations and an equally good result is obtained by shifting p u (n u )
in the up-sampled domain and then computing the cross-correlation in the
down-sampled domain, as shown in equations (9.23) and (9.24).
At the offsets, if no pitch pulses are detected, PPL is predicted from the PPL
of the previous frame using the pitch, and PPS is set to equal to the PPS of the
previous frame. This does not introduce any deteriorating artifacts, since the
encoder checks the suitability of the harmonic excitation in the mode selection
process. The prediction of PPL and PPS is particularly useful at offsets with a
resonant tail, where pitch pulse detection is difficult.

9.4.3 SynthesisusingGeneralizedCubicPhaseInterpolation
In the synthesis, the phases are interpolated cubically, i.e. by quadratic inter-
polation of the frequencies. In [2], phases are interpolated for the frequencies
and phases available at the frame boundaries. But in the case of SWPM the
frequencies are available at the frame boundaries and the phases at the pitch
pulse locations. Therefore a generalized cubic phase interpolation formula is
used, to incorporate PPL and PPS.
The phase θ k (n) of the k th harmonic of the i 1 th synthesis frame is given by, +

α k n 2 β k n 3 θ k (n) = θ k i + kω i n + + for 0 ≤ n < N (9.26)

where N is the number of samples per frame and θ k i and ω i are the phase of
the k th harmonic and the fundamental frequency, respectively, at the end of
synthesis frame i ,and α k and β k are given by,
t 0

2 N 3 N 2 α k

θ t 0 −

t 0 θ k i − kω i t 0 + 2 πM k

= (9.27)

β k kω i + 1 − kω i

where t 0 is the fractional pitch pulse location (PPL), θ t 0 is the PPS estimated at
t 0 ,and M k represents the phase unwrapping and is chosen according to the
'maximally smooth' criterion used by McAulay [2]. McAulay chose M k such
that f (M k ) is a minimum,

T

θ k (t, M k ) 2 dt

=

f (M k ) (9.28)

0