The Directivity Index (DI) allows for quantifying the directivity of a microphone or a non-adaptive array of microphones. The DI indicates how well a target sound source can be extracted in the presence of diffuse background noise. Adaptive microphone arrays have the potential to provide an improved performance for suppressing distracters that are spatially apart from the target sound source. In the absence of performance measures for adaptive microphone arrays, the DI has been used to evaluate adaptive microphone arrays in both anechoic and diffuse noise conditions. For adaptive microphone arrays the DI may not reflect the real-life performance of the array however, with theoretical directivity values that can be driven to infinity for spatially separated target and distracter sound sources in anechoic conditions, while such conditions will hardly be encountered in daily life. On the other hand, adaptive microphone arrays inherently do not have improved performance in diffuse sound fields for which the DI originally has been defined. Starting from the definition of DI a new measure for adaptive arrays is introduced in this paper as an objective measure for quantifying improvements in signal-to-noise based on directivity.
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