Digital Signal Processing Reference
In-Depth Information
boundaries
a
l
and
b
l
are defined as:
M
2
π
l
ω
0
1
2
a
l
=
−
(6.15)
M
2
π
l
ω
0
1
2
b
l
=
+
=
a
l
+
1
−
1
(6.16)
Finally, the synthetic spectrum
S(m, ω
0
)
for candidate pitch frequency
ω
0
is
compared with the speech spectrum
S(m)
through an MSE measure, given
by:
M
−
1
S(m)
−
S(m, ω
0
)
2
E(ω
0
)
=
(6.17)
m
=
0
The value of
ω
0
minimizing
E(ω
0
)
is then selected as the pitch frequency. Typ-
ical original and synthetic spectra with correct pitch are shown in Figure 6.5.
6.2.3 Time-andFrequency-DomainPDAs
Pitch Estimation using Spectral Autocorrelation
The time domain autocorrelation (temporal autocorrelation, or TA) has been
used in various PDAs. Given a segment of speech signals
s(n)
,0
≤
n
≤
N
−
1,
100.0
Synthetic Spectrum
Original Spectrum
80.0
60.0
40.0
20.0
fo
0.0
0.0
1000.0
2000.0
3000.0
4000.0
Frequency (Hz)
Figure 6.5
Original and synthesized speech spectra used in the spectrum-similarity
PDA method
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