Digital Signal Processing Reference
In-Depth Information
100.0
Original Spectrum
Comb Response
50.0
0.0
0.0
1000.0
2000.0
3000.0
4000.0
Frequency (Hz)
fo
Figure 6.4
Harmonic peak matching method
the original speech prior to its Fourier transformation. The pulses are scaled
by a factor
A
l
(ω
0
)
so as to provide the best possible match with the original
spectrum. The synthetic spectrum
S(m, ω
0
)
is defined by:
A
0
(ω
0
) W
2
M
m
A
1
(ω
0
) W
2
M
m
ω
0
−
.
A
l
(ω
0
) W
2
M
m
S(m, ω
0
)
=
(6.13)
l ω
0
−
.
where
M
is the length of the DFT and
A
l
(ω
0
)
is defined as:
S(m)W
2
π
l ω
0
b
l
M
m
−
m
=
a
l
A
l
(ω
0
)
=
(6.14)
W
2
π
l ω
0
b
l
2
M
m
−
m
=
a
l
A
l
(ω
0
)
is such that the scaled harmonic lobe spectrum
A
l
(ω
0
)W(
2
M
m
lω
0
)
is the best possible match for
S(m)
, using an MSE criterion. The harmonic
−
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