A mathematical theory of comodulation

Abstract

Amplitude comodulation is the phenomenon that for many types of sound sources, all of the individual frequency components emitted will be amplitude modulated in a related manner, i.e., they will all start/stop and rise/fall together. It is known from various psychophysical studies that comodulation plays an important role in perceptual grouping of sound components. In this work, amplitude comodulation is examined for possible use as a basis for auditory source separation. A derivation is presented of the equations governing a comodulated system for the case of constant frequency sources. A theorem is proved giving necessary and sufficient conditions for uniquely decomposing a sound mixture into its constituent sources. A by-product of these conditions is an understanding of the importance of common onsets and offsets in source separation. An algorithm is presented for computing the unique solution in those cases where one exists. Finally, possible future extensions to the case of frequency varying sources are discussed. [Work supported by NIH Training Grant No. 5T32 DC00038.]