Database Reference
In-Depth Information
Table 10.1
Feature extraction for audio signal
Input
Audio signal,
s
(
t
)
=
{
}
,
Output
Feature vector,
f
m
0
,
˃
},{
ʱ
,
b
1
,
l
,
b
2
,
l
l
=
1
,
2
,...,
L
−
1
,
where
m
0
0
1
,
l
and
0
are the mean and standard deviation of the wavelet coefficients in
the low-frequency subband,
˃
are the model parameters obtained
from wavelet coefficients from the
l
-th high-frequency subband, and
L
is the
decomposition level.
{
ʱ
,
b
1
,
l
,
b
2
,
l
}
1
,
l
Computation
1. Apply DWT to
s
and obtain wavelet coefficients of the low-frequency
subband
{
w
(
i
)
}
Low
and the high-frequency subband
{
w
(
i
)
}
High
,
l
,
l
=
1
,
2
,...,
L
−
1
2. Compute
(
t
)
w
(
i
)
}
{
m
0
,
˃
}
from
{
0
Low
3. Compute
{
ʱ
,
b
1
,
l
,
b
2
,
l
},
l
=
1
,
2
,...,
L
−
1
1
,
l
begin
initialize
l
ₐ
0
w
(
i
)
}ₐ{
w
(
i
)
}
do
l
ₐ
l
+
1,
{
l
begin
initialize
[
b
1
,
b
2
]
and
[
ʱ
1
,
ʱ
2
]
,
j
ₐ
0
High
,
(
EM algorithm
)
do
j
ₐ
j
+
1
E-step
: compute the expected value of the hidden variable for each
wavelet coefficient
z
(
i
1
w
(
i
)
|
b
1
(
j
))
ʱ
1
(
j
)
p
(
=
ʱ
1
(
j
)
p
(
w
(
i
)
|
b
1
(
j
))+
ʱ
2
(
j
)
p
(
w
(
i
)
|
b
2
(
j
))
z
(
i
2
w
(
i
)
|
ʱ
2
(
j
)
p
(
b
2
(
j
))
=
ʱ
1
(
j
)
p
(
w
(
i
)
|
b
1
(
j
))+
ʱ
2
(
j
)
p
(
w
(
i
)
|
b
2
(
j
))
M-Step
: update the parameters
[
b
1
,
b
2
]
and a
priori
probabilities
[
ʱ
1
,
ʱ
2
]
,
z
(
i
)
1
N
∑
i
(
j
)
=
1
ʱ
1
(
j
+
1
)=
N
z
(
i
)
2
N
∑
(
j
)
i
=
1
ʱ
(
j
+
1
)=
,
2
N
w
(
i
)
z
(
i
)
1
N
∑
(
j
)
i
=
1
b
1
(
j
+
1
)=
z
(
i
)
1
N
∑
(
j
)
i
=
1
z
(
i
)
2
w
(
i
)
N
∑
i
=
(
j
)
1
b
2
(
j
+
1
)=
,
z
(
i
)
2
N
∑
(
j
)
i
=
1
where
N
is the number of wavelet coefficients.
until
convergence is reached
return
[
ʱ
,
b
1
,
b
2
]
1
end
until
l
=
L
return
{
ʱ
1
,
l
,
b
1
,
l
,
b
2
,
l
},
l
=
1
,
2
,...,
L
−
1
end
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