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I am trying to supply a solution for recording a court room and then, use some smart algorithms in order to automatically convert the speech to text.

In order to do that I have three boom microphones, one is near the judge, the second is on A side and the third one on the B side. this way i get 3 different sound sources to convert to text. the problem is that each microphone picks up the other sides also (quietly but they are still there).

I mean that the judge microphone can hear a little bit the A and B sides also. this of course messes with my voice to text algorithm.

Is there any way to subtract from the judge microphone the A side and the B side tracks in order to clean them and hear only the judge?

Then I can apply the same algorithm to A side and To B side also. does anyone knows how to do it?

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That's called source separation, and higher-end conference table systems already do thatcitation needed.

You'll be able to find quite a bit of literature if you search for that term, but an easy approach would be to assume that things are linear (sadly, in audio, that's not really often the case), and that you can simply:

Calibrate the system by only speaking (better: feeding white noise) into one microphone, then calculating the auto- and crosscorrelations between the signals. The cross-correlation functions will directly tell you with what you need to convolve the signal of that one microphone before subtracting it from the signals of the others.

But maybe the solution to that problem is simpler: Microphones come with a directivity; use such that only record what's coming from straight in front of them.

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