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Blind
Signal Separation
Abstract:
The separation of independent sources from mixed observed data
is a fundamental and challenging problem. In many practical
situations, observations may be modelled as linear mixtures
of a number of source signals, ie. a linear multi-input multi-output
system. A typical example is speech recordings made in an acoustic
environment in the presence of background noise and/or competing
speakers. Other examples include EEG signals, passive sonar
applications and cross-talk in data communications. In this
paper, we propose iterative algorithms to solve the nxn linear
time invariant system under two different constraints. Some
existing solutions for 2x2 systems are reviewed and compared.
Here is a simple case
with two sources s1(k),s2(k) and two mixing transfer functions
H1(z), H2(z) to produce two mixed inputs x1(k), x2(k). The
objective of the problem is to estimate separating transfer
functions W1(z), W2(z) from x1(k) and x2(k) only, such that
y1(k) and y2(k) would each contain s1(k) or s2(k) only.
ie. Y1(z)=S1(z)G1(z),
Y2(z)=S2(z)G2(z). A normalising process is needed.
An
iterative algorithm is developed to estimate W1(z), W2(z).
Here is an example.
a) s1(k) b) s2(k)
c) x1(k) d) x2(k)
e) y1(k) f) y2(k)
The mixing transfer
functions H1(z), H2(z) were 5 taps each.
The model can be
extended to multi-sources multi-inputs model. Algorithm has
been devised to solve such problem.
a)
Source 1 b) Source 2 c)Source 3
a)
Observation 1 b) Observation 2 c) Observation 3
a)
Output 1 b) Output 2 c) Output 3
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