Digital Signal Processing Reference
In-Depth Information
where
θ
k
(t, M
k
)
represents the continuous analogue form of
θ
k
(n)
,and
θ
k
(t, M
k
)
is the second derivative of
θ
k
(t, M
k
)
with respect to
t
.Although
M
k
is integer-valued, since
f (M
k
)
is quadratic in
M
k
, the problem is most
easily solved by minimizing
f (x
k
)
with respect to the continuous variable
x
k
and then choosing
M
k
to be an integer closest to
x
k
. For the generalized case
of SWPM,
f (x
k
)
is minimized with respect to
x
k
and
x
k
min
is given by,
θ
k
i
−
k
ω
i
+
1
−
ω
i
t
0
1
2
π
x
k
min
=
θ
t
0
+
+
kω
i
t
0
(9.29)
2
N
M
k
min
=
x
k
min
+
0
.
5
is substituted in equation 9.27 for
M
k
to solve for
α
k
and
β
k
and in turn to unwrap the cubic phase interpolation function
θ
k
(n)
.
The initial phase
θ
k
i
for the next frame is
θ
k
(N)
, and the above computations
should be repeated for each harmonic, i.e.
k
. It should be noted that there is
no need to synthesize the phases,
θ
k
(n)
in the up-sampled domain, in order
to use the fractional pitch pulse location,
t
0
. It is sufficient to use
t
0
in solving
the coefficients of
θ
k
(n)
,i.e.
α
k
and
β
k
.
9.5 Hybrid Encoder
A simplified block diagramof a typical hybrid encoder that operates on a fixed
frame size of 160 samples is shown in Figure 9.12. For each frame, the mode
that gives the optimum performance is selected. There are three possible
modes: scaled white noise coloured by LPC for unvoiced segments; ACELP
for transitions; and harmonic excitation for stationary voiced segments.
Input Speech
LSF
LPC, LSF &
Quantize
Inverse LPC
Filter
Fractional
Pitch
Initial
Classification
CL1
LPC
Residual
Amps,
Pulse Shape
& Location
Analysis by
Synthesis
Classification
LPC
CL2
SW2
ACELP
Excitation
SW1
Unvoiced
Gain
Excitation Parameters
Specific to Each Mode
Figure 9.12
Block diagram of the hybrid encoder
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