Digital Signal Processing Reference
In-Depth Information
2.2
Challenges for the convolutive case
This section focuses on the problems to be addressed when using the
above mentioned method (“basic method”) to separate signals in the
convolutive case where the mixing matrix is not constant as in the case of IM
but is a function of time. The logical extension of the “basic method” would
be to take the Fourier transform of the signal with an FTT length that is long
enough to ensure that the convolution can be approximated as multiplication
in the frequency domain. Then the “dual update” algorithm can be applied in
each subband independently.
This approach does have several drawbacks. First of all, the algorithm
finds the signal separation within an arbitrary scale factor and arbitrary
permutation. This means that the scale factors and permutations will need to
be consistent between different subbands.
Incorrect
scale factors cause
spectral distortion.
Currently, there is no good method that can come up with consistent scale
factors for all the bands. However, the solution adopted in this study is to
constrain the mixing system's filter structure such that:
where
is the
column vector of
A
(
k
). This was also used in [6].
Permutation estimation:
For finding the correct permutation between bands
several methods have been developed which are detailed and compared in
[12]. Here, we use the inter frequency correlation. The inter frequency
correlation relies on the non-stationarity of the sources [8]. It has been shown
that for non-stationary signals, adjacent sub-bands are correlated. This can be
used in the following equation:
where
P
(
k
) is the permutation matrix and is the envelope of signal
S
(k,n).
The envelope signal is created by passing the absolute values of the
source signals through a low pass filter. The permutation of the first sub-
band is designated as the correct permutation. The permutation of the next
sub-band is estimated by using (16). The source signals at that subband are
permuted according to the resulting
P
(
k
). This is continued for all sub-bands.
