Blind Signal Separation
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