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Given two identical microphones arranged in an ideal XY pattern, recording a single sound source at equal distance from both capsules, the two signals obtained are equal in amplitude, perfectly in phase with each other, and distorted identically by microphone frequency response. Therefore, other than small differences that result from noise, what exactly causes the difference between the left and right channel, such that when heard, a stereo field is perceived?

I ask because I am developing an audio synthesis application, and need a way to simulate real stereophonic sound given a single input signal.

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The XY pattern is used with directional microphones (usually cardioid) pointed in different directions. Cardioid microphones reject signal coming from different directions. Therefore, even if the mics somehow occupied the same space, they would still be hearing different things (as long as they are pointed in different directions).

Your statement that "the two signals obtained are equal in amplitude" is therefore incorrect: when instruments are mic'ed using the XY pattern, there are differences in amplitude if the sound source (including reverberant reflections of sound from surfaces in the room) are coming "off axis" of the stereo pair.

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