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 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.

Soft-Constrained Spatially Selective Active Noise Control for Open-fitting Hearables

Recent advances in spatially selective active noise control (SSANC) using multiple microphones have enabled hearables to suppress undesired noise while preserving desired speech from a specific direction. Aiming to achieve minimal speech distortion, a hard constraint has been used in previous work in the optimization problem to compute the control filter. In this work, we propose a soft-constrained SSANC system that uses a frequency-independent parameter to trade off between speech distortion and noise reduction. We derive both time- and frequency-domain formulations, and show that conventional active noise control and hard-constrained SSANC represent two limiting cases of the proposed design. We evaluate the system through simulations using a pair of open-fitting hearables in an anechoic environment with one speech source and two noise sources. The simulation results validate the theoretical derivations and demonstrate that for a broad range of the trade-off parameter, the signal-to-noise ratio and the speech quality and intelligibility in terms of PESQ and ESTOI can be substantially improved compared to the hard-constrained design.

Using a one-dimensional finite-element approximation of Webster's horn equation to estimate individual ear canal acoustic transfer from input impedances

In many applications, knowledge of the sound pressure transfer to the eardrum is important. The transfer is highly influenced by the shape of the ear canal and its acoustic properties, such as the acoustic impedance at the eardrum. Invasive procedures to measure the sound pressure at the eardrum are usually elaborate or costly. In this work, we propose a numerical method to estimate the transfer impedance at the eardrum given only input impedance measurements at the ear canal entrance by using one-dimensional first-order finite elements and Nelder-Mead optimization algorithm. Estimations on the area function of the ear canal and the acoustic impedance at the eardrum are achieved. Results are validated through numerical simulations on ten different ear canal geometries and three different acoustic impedances at the eardrum using synthetically generated data from three-dimensional finite element simulations.

Optimization of a Fixed Virtual Sensing Feedback ANC Controller for In-Ear Headphones with Multiple Loudspeakers

In this paper we consider an in-ear headphone equipped with an inner microphone and multiple loudspeakers and we propose an optimization procedure with a convex objective function to derive a fixed multi-loudspeaker ANC controller aiming at minimizing the sound pressure at the ear drum. Based on the virtual microphone arrangement (VMA) technique and measured acoustic paths between the loudspeakers and the ear drum, the FIR filters of the ANC controller are jointly optimized to minimize the power spectral density at the ear drum, subject to design and stability constraints. For an in-ear headphone with two loudspeakers, the proposed multi-loudspeaker VMA controller is compared to two single-loudspeaker VMA controllers. Simulation results with diffuse noise show that the multi-loudspeaker VMA controller effectively improves the attenuation by up to about 10 dB for frequencies below 300 Hz when compared to both single-loudspeaker VMA controllers.

Sound Pressure Minimization at the Ear Drum for In-ear ANC Headphones using a Fixed Feedforward Remote Microphone Technique

In this paper we consider an in-ear headphone equipped with an external microphone and aim to minimize the sound pressure at the ear drum by means of a fixed feedforward ANC controller. Based on measured acoustic paths to predict the sound pressure generated by external sources and the headphone at the ear drum, the FIR filter coefficients of the ANC controller are optimized for different sound fields. Due to the acoustic feedback path between the loudspeaker and the microphone, a stability constraint based on the Nyquist stability criterion is introduced. Performance degradations due to reinsertions of the headphone and intra-subject variations are addressed by simultaneously optimizing the controller for several measurement repetitions of the acoustic paths. Simulations show that the controller optimized for an ipsilateral excitation produces an attenuation of at least -10 dB that extends approximately to +45{\deg} and -65{\deg} from the ipsilateral DoA. The controller optimized for a diffuse-field excitation achieves an attenuation of at least -10 dB over a wider range of DoAs on the ipsilateral side, namely +90{\deg} to -90{\deg}. Optimizing the controller for several measurement repetitions is shown to be effective against performance degradations due to reinsertions and intra-subject variations.