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I have 3 speech files of the same speech recorded by 3 different microphones at the same time.

I'm only concerned to improve the speech quality (in terms of SNR and intelligibility) by combining the 3 speech files that I have.

Is there any method to solve the problem? What is the term used for it?

The techniques that I found involving multiple microphones was related to microphone array, but I'm interested to work with randomly placed microphones.

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The easiest approach would just be averaging – since noise on these three microphones should at least partially be uncorrelated, that would improve SNR.

However, that requires that the three microphones are

  1. synchronously sampled (i.e. the $n4th sample from each microphone happened "exactly" at the same time) and
  2. in the same distance from the desired source of sound.

Since both 1. and 2. are usually not fulfilled, you'll have to look into adapting to that – the result is a beamformer. This might be a term often linked to regularly spaced microphone arrays, but that's not a mathematical requirement – you'd just start by detecting the phase/time offset between the strongest (or, better: the desired) source of sound on each of your microphone channels, and then align (read: fractional delay) the channels in a manner that maximizes SNR for that. This inherently leads to a geometric beam shape, though it usually is but a singular value decomposition of a receive signal matrix (that's where "beamforming" and "MIMO processing" meet).

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