Statistics of instabilities in a state space model of the human cochlea

A state space model of the human cochlea is used to test Zweig and Shera's [(1995) "The origin of periodicity in the spectrum of evoked otoacoustic emissions," J. Acoust. Soc. Am. 98(4), 2018-2047 ] multiple-reflection theory of spontaneous otoacoustic emission (SOAE) generation. The state space formulation is especially well suited to this task as the unstable frequencies of an active model can be rapidly and unambiguously determined. The cochlear model includes a human middle ear boundary and matches human enhancement, tuning, and traveling wave characteristics. Linear instabilities can arise across a wide bandwidth of frequencies in the model when the smooth spatial variation of basilar membrane impedance is perturbed, though it is believed that only unstable frequencies near the middle ear's range of greatest transmissibility are detected as SOAEs in the ear canal. The salient features of Zweig and Shera's theory are observed in this active model given several classes of perturbations in the distribution of feedback gain along the cochlea. Spatially random gain variations are used to approximate what may exist in human cochleae. The statistics of the unstable frequencies for random, spatially dense variations in gain are presented; the average spacings of adjacent unstable frequencies agree with the preferred minimum distance observed in human SOAE data.