The complex-valued correlation coefficient accounts for binaural detection
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Binaural hearing is one of the principal mechanisms enabling the localization of sound sources in space. In addition, binaural hearing also significantly improves the detection of signals in noise. Humans can detect interaurally anti-phasic tones in masking noise at sound levels 15 dB below the detection threshold of the equivalent in-phase tones. Intermediate thresholds result from detecting tones in noise with an interaural time difference (ITD). The dependence on ITD has so far been most accurately accounted for by models using an array of internal delays, altering, and ideally compensating for the noise ITD. The array of internal delays, or an equivalent mechanism, however, has not been found in mammals. Alternative coding principles that do not include an array of delays can also explain many aspects of sound localization but have failed to account for some of the available data on binaural detection. By employing the complex-valued correlation coefficient, we show that a minimum assumption model can explain the outcome of a wide range of binaural detection experiments. The proposed mechanism requires fewer degrees of freedom when compared to models with an array of delays while arguably improving compatibility with mammalian physiology. Intriguingly, the 2-dimensional acoustic feature space of variance normalized complex correlation coefficients is at the same time a perceptually uniform space for binaural detection.
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