Put the microphone into a parabolic cup to make the microphone directional then add closed-cell foam to the edge of the cup to seal out ambient noise. This makes a great first approximation. Then add 180-degree phase shift and feed it in appropriately to cancel remaining ambient. This is done with a simple op amp.
After proper cup design and experimenting, If noise cancelling is needed, As a first experiment, I would put both microphones in the cup. One toward the heart and one 90-degrees to the heart (ambient mic). Connect the ambient to the (+) input of op amp as shown. Then use the pot to attenuate the mic to the right cancelling level.
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