Digital Signal Processing Reference
In-Depth Information
10.3.2 NoiseEstimationBasedonSLR
Depending on the characteristics of the noise source, the short-time spectral
amplitudes of the noise signal can fluctuate strongly from frame to frame. In
order to cope with time-varying noise signals, the variance of the noise spec-
trum is adapted to the current input signal by a soft decision-based method.
The speech absence probability (SAP) of the
k
th
spectral bin,
p(H
0
,k
|
Y
k
)
,can
be calculated by Bayes' rule as:
p(H
0
,k
)p(Y
k
|
H
0
,k
)
1
|
=
H
1
,k
)
=
p(H
0
,k
Y
k
)
(10.8)
p(H
1
,k
)
p(H
0
,k
)p(Y
k
|
H
0
,k
)
+
p(H
1
,k
)p(Y
k
|
1
+
p(H
0
,k
)
k
where
p(H
1
,k
)
p(H
0
,k
)
, and the unknown
apriori
speech absence proba-
bility (PSAP),
p(H
0
,k
)
, is estimated in an adaptive manner given by:
=
1
−
p(H
(n)
p(H
(n
−
1
)
0
,k
−
β)p(H
(n)
Y
(n
k
),H
(L)
,H
(U)
0
ˆ
0
,k
)
=
MIN
{
MAX
{
β
ˆ
)
+
(
1
0
,k
|
}
}
(10.9)
0
where
β
is a smoothing factor, e.g. 0.65. The lower and upper limits,
H
(L)
0
and
H
(U
0
, of the PSAP are determined through experiments, e.g. 0.2 and 0.8. Note
that, for SLR,
k
is applied to the calculation of the SAP instead of LR,
k
.
The variance of the noise spectrum of the
k
th
spectral component in the
n
th
frame,
λ
(n)
N,k
, is updated in a recursive way as:
λ
(n)
N,k
=
ηλ
(n
−
1
)
N
(n)
k
Y
(n
k
)
2
+
(
1
−
η)E(
|
|
|
(10.10)
N,k
where
η
is a smoothing factor, e.g. 0.95. The expected noise power-spectrum
E(
|
N
(n)
k
Y
(n
k
)
is estimated by means of a soft-decision technique [18] as:
2
|
|
N
(n)
k
Y
(n
k
)
=
N
(n)
k
Y
(n
k
)
+
N
(n)
k
Y
(n
k
)
2
2
2
E(
|
|
|
E(
|
|
|
H
0
,k
)p(H
0
,k
|
E(
|
|
|
H
1
,k
)p(H
1
,k
|
Y
(n)
k
Y
(n)
k
λ
(n
−
1
)
N,k
Y
(n)
k
2
p(H
0
,k
|
=|
|
)
+
p(H
1
,k
|
)
(10.11)
Y
(n
k
)
. During some tests, it is observed that
SLR-based adaptation is useful for the estimation of the noise spectra with
high variations, such as a babble noise source.
Y
(n
k
)
=
where
p(H
1
,k
|
1
−
p(H
0
,k
|
10.3.3 Comparison
The effect of the smoothing factor
κ
in equation (10.6) is shown in Figure 10.16.
Note that the case of
κ
0 reduces equation (10.6) to the LR-based method. It
is obvious from the results that the detection accuracy increases with increase
in
κ
, at the offset regions without serious degradations in the performance
=
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