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I am working on a signal processing assignment where I need to find out one common time domain signal from 4 observation. The math is like this:

\begin{array}{lcl} y_1(t) & = & a_1(t)*x(t) + b_1(t) \\ y_2(t)& = & a_1(t)*x(t) + b_1(t) \\ . & & \\ . & & \\ y_n(t) & = & a_n(t)*x(t) + b_n(t)\end{array}

where:

$n$ is up to 4 in my case, and $x(t)$ is my signal of interest which I want to extract from observed signals $y_n(t)$.

What is the general direction I should take in doing background study for this kind of application?

Thanks, K

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  • $\begingroup$ I would say the autocorrelation could help you $\endgroup$ – Engine Apr 11 '14 at 11:18
  • $\begingroup$ Independant component analysis or Principal component analysis may help you $\endgroup$ – tobassist Apr 11 '14 at 11:56
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Because you have a set of linear equations, why don't you set up a linear system (for each data point) and solve the system (using SVD for example) to obtain the solution?

Write in the the matrix form such as $Y=\beta X$ where $\beta$ are known and $X$ is unknown.

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