Eardrum sound pressure prediction from ear canal reflectance based on the inverse solution of Webster's horn equation

To derive ear canal transfer functions for individualized equalization algorithms of in-ear hearing systems, individual ear canal models are needed. In a one-dimensional approach, this requires the estimation of the individual area function of the ear canal. The area function can be effectively and reproducibly calculated as the inverse solution of Webster's horn equation by finite difference approximation of the time domain reflectance. Building upon previous research, the present study further investigates the termination of the approximation at an optimal spatial resolution, addressing the absence of higher frequencies in typical ear canal measurements and enhancing the accuracy of the inverse solution. Compared to the geometric reference, more precise area functions were achieved by extrapolating simulated input impedances of ear canal geometries up to a frequency of 3.5 MHz, corresponding to 0.1 mm spatial resolution. The low pass of the previous work was adopted but adjusted for its cutoff frequency, depending on the highest frequency of the band limited input impedance. Robust criteria for terminating the area function at the approximated ear canal length were found. Finally, three-dimensional simulated and measured ear canal transfer impedances were replicated well, employing the previously introduced and herein validated one-dimensional electro-acoustic model fed by the area functions.