Digital Signal Processing Reference
In-Depth Information
2000
15000
1000
10000
0
5000
−
1000
−
2000
0
50
100
150
200
0
1000
2000
3000
4000
(b) Frequency (Hz)
(a) Time (samples)
6000
1
4000
0.5
2000
0
0
−
2000
−
0.5
−
4000
−
6000
−
1
0
1000
2000
3000
4000
50
100
150
(c) Frequency (Hz)
(d) Lag (samples)
Figure 6.7
An example of (a) speech signal of
T
0
8
kHz), (b)
magnitude spectrum, (c) zero-crossing spectrum, and (d) spectral autocorrelation
=
59
-sample (
F
s
=
where
α
is a weighting factor, 0
≤
α
≤
1. The cases of
α
=
0and
α
=
1reduce
T
0
using the
the STA to SA and TA, respectively. The estimated pitch period
STA is the argument maximizing (6.22) as:
T
0
=
arg max
τ
{
R
ST
(τ )
}
(6.23)
Because of the dual relation between the temporal and the spectral autocorre-
lations, it is found that the STA has a useful property for pitch estimation. For
a segment of periodic signal with a pitch period
T
0
,
T
(l)
T
(u)
0
≤
T
0
≤
,
R
ST
(τ )
0
in (6.22) has the strongest peak at
τ
=
T
0
compared with the integer multiple
T
(u)
and submultiple periods of
T
0
,i.e.
τ
=
pT
0
and
T
0
/p
for 2
≤
p
≤
/T
0
and
0
T
0
/T
(l)
2
. In (6.22),
R
S
(τ )
and
R
T
(τ )
terms suppress the undesirable
high peaks for the multiples and submultiples of
T
0
excluding
τ
≤
p
≤
0
=
T
0
.Con-
sequently, the STA for
τ
=
T
0
remains relatively more prominent compared
with those for the rest.
The range of the pitch period can be split into three groups as high (short
pitch period), mid, and low (long pitch period), based on the expected number
of prominent peaks in TA and SA. The minimum pitch period producing a
pitch period submultiple in SA is 2
T
(l)
. The SA can only rarely produce pitch
0
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