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If the recording is anechoic than this is simple enough: assuming that the distance between the microphones is $d$ than you can estimate the front source as $$x_f(t) = m_f(t-d/c_0) - g \cdot m_r(t)$$ where $m_f(t)$ is the signal from the front microphone, $m_r(t)$ the signal from the rear microphone, $c_0$ the speed of sound and $g$ a gain factor that ...

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