# Extracting common signal from 4 sets of observations

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

• I would say the autocorrelation could help you Apr 11 '14 at 11:18
• Independant component analysis or Principal component analysis may help you Apr 11 '14 at 11:56

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