Phase coherence of spontaneous otoacoustic emissions derived from a cochlear model

Spontaneous otoacoustic emissions (SOAEs) are commonly presented by averaging spectral magnitudes calculated in adjacent time segments of the recorded signal. To include the information carried by SOAE phase, Bergevin et al. [under preparation] proposed calculating the phase difference between adjacent time segments and then determine the vector strength to compute a measure of phase coherence. In stronger human SOAE peaks (magnitude >0 dB SPL), phase coherence plotted as a function of segment duration usually shows a maximum at around 100 ms, which shortens with increasing SOAE frequency above ∼2 kHz. Similar bell shaped dependencies coherence can be observed for simulated SOAEs from a nonlinear cochlear model composed of fluid-coupled oscillators, which simulate the transversal displacement of the basilar membrane (BM) [Vencovský et al. JASA, 2020]. The simulated BM displacement is amplified by feedback undamping force, which is transformed by a sigmoidal nonlinearity proportional to the second-order Boltzmann function. To evoke SOAEs, irregularities are added into the undamping feedback force and the model is driven by broad band noise applied into the eardrum (external noise) and into the undamping feedback force (internal noise). It appears that a combination of external and internal noise is needed to obtain the bell-shaped dependence of phase coherence on the segment duration similar to the one observed in human SOAEs. These results help guide how stochastic considerations must be included into active cochlear models.