通过逆解声学锥形管方程,高精度重建耳道截面面积分布。
Eardrum sound pressure prediction from ear canal reflectance based on the inverse solution of Webster's horn equation
- 基于时域反射率反演求解韦伯斯特声学锥方程,实现耳道截面函数估计。
- 在3.5 MHz高频下实现0.1 mm空间分辨率,显著提升重建精度。
- 适用于个性化助听器声学补偿,尤其适合高频响应要求高的场景。
为实现个性化入耳式助听系统中的均衡算法,需建立个体化耳道模型。在一维方法中,关键在于估算耳道的截面面积函数。本文通过有限差分法对时域反射率进行反演,求解韦伯斯特声学锥方程,有效且可重复地计算出个体耳道截面函数。研究进一步优化了数值逼近的终止条件,在典型耳道测量中高频信息缺失的背景下,通过将模拟输入阻抗外推至3.5 MHz(对应0.1 mm空间分辨率),提升了反演精度。同时,根据输入阻抗的带限最高频率动态调整低通滤波器截止频率,确立了在近似耳道长度处终止面积函数的鲁棒判据。最终,使用该一维电声模型结合所获面积函数,成功复现了三维模拟与实测的耳道传输阻抗,验证了模型的有效性。
原文摘要 · Abstract (English)
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 cut-off 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.
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