Modeling the dependence of the distortion product otoacoustic emission response on primary frequency ratio

When measured as a function of primary frequency ratio r=f(2)/f(1), using a constant f(2), distortion product otoacoustic emission (DPOAE) response demonstrates a bandpass shape, previously interpreted as the evidence for a cochlear second filter. In this study, an alternate, interference-based explanation, previously advanced in variants, is forwarded on the basis of experimental data along with numerical and analytical solutions of nonlinear and linear cochlear models. The decrease of the DPOAE response with increasing and decreasing ratios is explained by a diminishing overlap generation region and the onset of negative interference among wavelets of different phase, respectively. In this paper, the additional quantitative hypothesis is made that negative interference becomes the dominant effect when the spatial width of the generation (overlap) region exceeds half a wavelength of the DPOAE wavelets. Therefore, r is predicted to be optimal when this condition is matched. Additionally, the minimum on the low-ratio side of the DPOAE curve is predicted to occur as the overlap region width equals one wavelength. As the width of the overlap region depends on both tuning and ratio, while wavelength depends on tuning only, an experimental method for estimating tuning from either the width of the pass band or the optimal ratio of the DPOAE vs. ratio curve has been theoretically formulated and evaluated using numerical simulations. A linear model without the possibility of nonlinear suppression is shown to reasonably approximate data from human subjects at low ratios reinforcing the relevance of the proposed negative interference effect. The different dependence of the distortion and reflection DPOAE components on r as well as the nonmonotonic behavior of the distortion component observed at very low ratios are also in agreement with this interpretation.