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Adaptive noise cancellation with directional microphones

The spatial correlation function between directional microphones is useful in the design and analysis of the performance of these microphones in actual acoustic noise fields. These correlation functions are well known for omnidirectional receivers, but not well known for directional receivers. This paper investigates the spatial correlation functions for N/sup th/-order differential microphones in spherically isotropic noise fields. The results are used to calculate the amount of achievable cancellation from an adaptive noise cancellation application using combinations of differential microphones to remove unwanted noise from a desired signal. The results are also useful in determining signal-to-noise ratio gains from arbitrarily positioned differential microphone elements in microphone array applications.