Digital Signal Processing Reference
In-Depth Information
where the superscript
t
indicates the frame index,
η
is the smooth adaptation
factor, e.g. 0.95, and
Y
is the noisy spectrum. In the case of speech presence,
usually indicated by a VAD, it does not update the noise variance. HD-based
noise adaptation has been widely used in speech enhancement.
11.3.2 SoftDecision-basedNoiseAdaptation
The SD-based noise estimation, the estimated noise given by
Y
k
,isformu-
lated as,
E(D
k
|
Y
k
)
=
E(D
k
|
Y
k
,H
0
)p(H
0
|
Y
k
)
+
E(D
k
|
Y
k
,H
1
)p(H
1
|
Y
k
)
={
p(H
0
|
Y
k
)
+
p(H
1
|
Y
k
)G
D,k
}
Y
k
(11.48)
where
E(D
k
|
Y
k
,H
0
)
=
Y
k
,
E(D
k
|
Y
k
,H
1
)
=
G
D,k
Y
k
. The probability of speech
presence
p(H
1
|
Y
k
)
.
The optimal noise gain
G
D,k
can be derived from the Wiener estimator
W
in
the time domain. It can be shown that
W
Y
k
)
is defined in equation (11.39) and
p(H
0
|
Y
k
)
=
1
−
p(H
1
|
R
dd
)
−
1
,inwhich
R
dd
and
R
xx
denote the covariance matrices of the noise and speech signals resulting
in the filter frequency response given by,
=
R
dd
(R
xx
+
2
)
E(
|
D
k
|
G
D,k
=
E(
|
X
k
|
2
)
+
E(
|
D
k
|
2
)
1
=
(11.49)
1
+
ξ
k
where
ξ
k
is the
apriori
SNR which can be estimated using the decision-
directed method defined in equation (11.6). Here, the estimation of noise gain
G
D
is an independent task within the noise estimation process which may
be used in other kinds of enhanced spectral estimation techniques, such as
MMSE, MMSE-LSA, etc. The noise variance of the SD-based method may be
estimated in a recursive manner as given below,
D
(t)
D
(t
−
1
)
E(D
(t)
Y
(t
k
)
2
)
2
)
2
|
|
=
|
|
+
−
|
|
|
E(
ηE(
(
1
η)
(11.50)
k
k
k
11.3.3 MixedDecision-basedNoiseAdaptation
In order to alleviate the problems in the HD- and SD-based methods, the
MD-based method is proposed [20] for noise adaptation as
D
(t
−
1
)
k
Y
(t)
k
2
)
2
if
Y
(t)
H
0
and
(t)
ηE(
|
|
+
(
1
−
η)
|
)
|
;
∈
≤
θ
D
(t)
k
2
)
=
D
(t
−
1
)
k
E(D
(t)
k
Y
(t
k
)
|
E(
|
|
2
)
+
(
1
2
if
Y
(t)
H
0
and
(t)
>θ
ηE(
|
|
−
η)
|
|
;
∈
D
(t
−
1
)
k
2
)
E(
|
|
;
otherwise
(11.51)
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