Minimal Bounds on Nonlinearity in Auditory Processing

Abstract: Time-reversal symmetry breaking is a key feature of nearly all natural sounds, caused by the physics of sound production. While attention has been paid to the response of the auditory system to "natural stimuli," very few psychophysical tests have been performed. We conduct psychophysical measurements of time-frequency acuity for both "natural" notes (sharp attack, long decay) and time-reversed ones. Our results demonstrate significantly greater precision, arising from enhanced temporal acuity, for such "natural" sounds over both their time-reversed versions and theoretically optimal gaussian pulses, without a corresponding decrease in frequency acuity. These data rule out models of auditory processing that obey a modified "uncertainty principle" between temporal and frequency acuity and suggest the existence of statistical priors for naturalistic stimuli, in the form of sharp-attack, long-decay notes. We are additionally able to calculate a minimal theoretical bound on the order of the nonlinearity present in auditory processing. We find that only matching pursuit, spectral derivatives, and reassigned spectrograms are able to satisfy this criterion.