# How to extract noise when the noise on three data sets are near identical?

I have a microphone array with three microphones placed in a small equilateral triangle. During recording, there is a lot of noise introduced by an ADC. However, I am not interested in reducing this noise before sampling - for learning, I want to remove this noise digitally as best as possible, given that the noise on each channel is near identical.

Given that their noise is near identical, I imagine it would be possible to correlate the signals in some way, even in the presence of a stronger signal with slight time delays. If possible, how can I remove this noise?

• I would think this Q&A could give you some insight; in your case your signal of interest is likely the narrow band and the noise the wide band signal: dsp.stackexchange.com/questions/37902/… Mar 18 '17 at 0:48

Given the three measurements $y1$, $y2$ and $y3$ coming from three unknown signals $x1$, $x2$ and $x3$, which we could assume additive to some unknown common noise $x4$, we can write: $$y1=x1+x4\\ y2=x2+x4\\ y3=x3+x4$$ or equivalently: $$y=Ax\\ A=[1,0,0,1;0,1,0,1;0,0,1,1]$$ Again, assuming a enough noisy signal, we can have an standard Recursive Least Squares algorithm for solving the standard LS projection recursively: $$\hat x=(A^TA)^{-1}A^Ty$$ This way, and if and only if the additive noise and the noisy signal suficciencies are met, you will solve for your three signals, and your coupled noise.