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1436 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 16, NO. 8, NOVEMBER 2008
path usually contribute to speech intelligibility. Therefore, we
focus on the estimation of the early speech component
.
The observed microphone signal
can be written as
(5)
Using (4) and (5) the error signal
can be written as
(6)
Using the short-time fourier transform (STFT), we have in the
time–frequency domain
(7)
where
represents the frequency bin and the time frame. In
the next section, we show how the spectral component
can be estimated.
III. G
ENERALIZED POSTFILTER
In this section, the postfilter is developed that is used to
jointly suppress late reverberation, residual echo, and back-
ground noise. When residual echo and noise are suppressed,
Gustafsson et al. [30] and Jeannès et al. [11] concluded that
the best result is obtained by suppressing both interferences
together after the AEC. The main advantage of this approach
is that the residual echo and noise suppression does not suffer
from the existence of a strong acoustic echo component. Fur-
thermore, the AEC does not suffer from the time-varying noise
suppression. A disadvantage is that the input signal of the
AEC has a low signal-to-noise ratio (SNR). To overcome this
problem, algorithms have been proposed where, besides the
joint suppression, a noise-reduced signal is used to adapt the
echo canceller [31].
Here, a modified version of the OM-LSA estimator [32] is
used to obtain an estimate of the spectral component
.
Given two hypotheses,
and , which indicate,
early speech absence and early speech presence, respectively,
we have
Let us define the spectral variance of the early speech compo-
nent, the late reverberant speech component, the residual echo
signal, and the background noise, as
, and , re-
spectively. The a posteriori SIR is then defined as
(8)
and the a priori SIR is defined as
(9)
The spectral variance
of the background noise
can be estimated directly from the error signal , e.g., by
using the method proposed by Martin in [33] or by using the
improved minima controlled recursive averaging (IMCRA) al-
gorithm proposed by Cohen [34]. The latter method was used
in our experimental study. The spectral variance estimators for
and are derived in Sections IV and V, respec-
tively. The a priori SIR cannot be calculated directly since the
spectral variance
is unobservable. Different estimators
can be used to estimate the a priori SIR, e.g., the decision direct
estimator developed by Ephraim and Malah [35] or the recursive
causal or noncausal estimators developed by Cohen [36]. In the
sequel, the decision directed estimator is used for the estima-
tion of the a priori SIR. The decision directed-based estimator
is given by [35]
(10)
where
is the instantaneous SIR
(11)
and
is a lower-bound on the a priori SIR that helps to
reduce the amount of musical noise. The weighting factor
controls the tradeoff between the amount of
noise reduction and transient distortion introduced into the
signal. The weighting factor is commonly chosen close to one,
e.g.,
. A larger value of results in a greater reduction
of musical noise, but at the expense of attenuated speech onsets
and audible modifications of transient components. Although
(10) can be used to calculate the total a priori SIR, it does not
allow to make different tradeoffs for each interference. One can
gain more control over the estimation of the a priori SIR by
estimating it separately for each interference. More information
regarding this and combining the separate a priori SIRs can be
found in Appendix A.
When the early speech component
is assumed to be
active, i.e.,
is assumed to be true, the log spectral am-
plitude (LSA) gain function is used. Under the assumption that
and the interference signals are mutually uncorrelated, the
LSA gain function is given by [14]
(12)
where
(13)
When the early speech component
is assumed to be in-
active, i.e.,
is assumed to be true, a lower-bound
is applied. In many cases, the lower-bound
is used, where specifies the maximum
amount of interference reduction. To avoid speech distortions
is usually set between and dB. However, in
practice the residual echo and late reverberation needs to be
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