Simulating the open-loop transfer function as a means for understanding acoustic feedback in hearing aids

Suppressing unstable acoustic feedback in hearing aids will first require knowledge of the open-loop transfer functions of such systems. Reported herein is a mathematical technique for simulating the open-loop transfer function of an in situ eyeglass-type hearing aid. In particular, a computer program was developed that characterized the hearing aid as a serial connection of two-port blocks, each representing one individual component of a hearing aid. Included, for example, were two-port blocks representing the microphone, amplifier, receiver, sound tubes leading to the eardrum (including the ear canal itself), earmold vent, and external pathway from the vent outlet back to the microphone. The computer program was validated by replicating laboratory data derived from an experiment involving a nonstandard manikin fitted with a nonstandard artificial ear. Next, the open-loop transfer function of an eyeglass-type hearing aid in situ on the manikin was simulated via the computer program. Unfortunately, those computer-generated data were not replicated in the laboratory due to the difficulty encountered in actually measuring the open-loop transfer function. Nevertheless, investigators were able to utilize those data to predict, within +/- 25 Hz, the "squeal" frequency of unstable acoustic feedback.     

A technique for simulating the amplifier-to-eardrum transfer function of an in situ hearing aid

There are numerous articles wherein mathematical models of various parts of an in situ hearing aid have been reported. Such parts include, for example, the microphone, receiver, cylindrical tubes carrying sound to the eardrum and out through the earmold vent, and the external path from the vent back to the microphone. This article extends these earlier works to include the hearing-aid amplifier. In particular, a mathematical technique for characterizing the amplifier in combination with the receiver is reported. Cascade parameters of a two-port model of one particular amplifier/receiver combination are obtained by this method. The cascade-parameter data and the method of obtaining this data are verified by two different experimental procedures. One procedure involves both computing and measuring the input driving-point impedance of the amplifier/receiver combination. In the second procedure, the amplifier-to-eardrum transfer function of a hearing aid incorporating this same amplifier/receiver combination and mounted on an artificial ear is both computed and measured. Experimental and computed values of this transfer function for three different earmold geometries are in reasonably close agreement. The amplifier/receiver model reported herein will be used in future studies of acoustic feedback in hearing aids.     

System identification of feedback in hearing aids.

The feedback problems of behind the ear (BTE), in the ear (ITE), and in the ear canal (ITEC) hearing aid categories have been investigated. All possible feedback paths (acoustical via vent, via tubing wall, mechanical, etc.) were converted to a single transfer function from the ear canal to the hearing aid microphone, here called the acoustic feedback equivalent (AFE). The attenuation of the AFE represents the maximum gain that can be used without the hearing aid starting to howl. Magnitude and phase responses of the AFE were identified on ten human subjects and on a Knowles ear manikin (KEMAR). The acoustic feedback via vent and leak between earmould and ear canal dominated the AFE. The transfer function from a reference point under the ear to the position of microphone of the different hearing aid categories was identified and used together with the AFE to calculate the maximum real ear aided gain (REAG) for the hearing aid categories. A model of the AFE, consisting of a fourth-order filter together with a delay, showed good agreement with the measured data.     

A computer simulation of hearing aid response and the effects of ear canal size

The response of a hearing aid is affected by many factors which include the head and outer ear, the microphone, amplifier, and receiver used in the hearing aid, the properties of the ear canal and the eardrum, and acoustic feedback through the vent. This article presents a computer simulation of an in-the-ear (ITE) hearing aid that includes all of the above factors. The simulation predicts the pressure at the eardrum for a frontal free-field sound source. The computer model was then used to determine the effects on the hearing aid response due to variations in the size of the ear canal. The simulation indicates that, for an unvented hearing aid, changes in the size of the ear canal shift the overall sound-pressure level at the eardrum but have only small effects on the shape of the frequency response. The situation is more complicated when a vent is present, however, since changes in the size of the ear canal that cause apparently small perturbations in the acoustic feedback signal may, nonetheless, have large effects on the overall system response.     

Variations in the feedback of hearing aids

Variations in the loop response of hearing aids caused by jaw movements, variations in acoustics outside the ear, and variations of vent size have been identified. Behind The Ear (BTE) and In The Ear Canal (ITEC) hearing aids were considered. The largest variations among the variations of the acoustics outside the ear, except when the hearing aid was partly removed, were found with the ITEC when a telephone set was placed by the ear. The variations of the loop response caused by changes in vent size were compared with the variations of a theoretical model of the feedback path. The theoretical model was also used to compare the feedback of different designs of the vent that gives the same acoustic impedance at low frequencies. The calculated feedback was less with the short vents (12 mm) than the long vents (24 mm).     

Transverse pressure distributions in a simple model ear canal occluded by a hearing aid test fixture

The sound field in a model ear canal with a hearing aid test fixture has been investigated experimentally and theoretically. Large transverse variations of sound pressure level, as much as 20 dB at 8 kHz, were found across the inner face of the hearing aid. Variations are greatest near the outlet port of the receiver and the vent port. Deeper into the canal, the transverse variations are less significant and, at depths greater than 4 mm, only a longitudinal variation remains. The model canal was cylindrical, 7.5 mm diameter, and terminated with a Zwislocki coupler to represent absorption by the human middle ear. The outer end of the canal was driven by the receiver in the hearing aid test fixture, with the acoustic output entering the canal through a 1 mm port. The hearing aid was provided with a 20-mm-long vent, either 1 or 2 mm in diameter. The sound field inside the canal was measured using a specially designed 0.2-mm-diam probe microphone [Daigle and Stinson, J. Acoust. Soc. Am. 116, 2618 (2004)]. In parallel, calculations of the interior sound field were performed using a boundary element technique and found to agree well with measurements.     

计算二维声腔传递矩阵的正方形线声源模型

在比较现有二维矩形声腔的声源计算模型特点的基础上,提出了一种新的正方形线声源计算模型,用于计算基于模态级数叠加法的压力响应函数.分析表明,此模型不仅可以克服点声源模型的奇异性,而且在合理选择模型的几何尺寸的前提下能得到比面源模型更为均匀的压力分布,提高了传递函数计算的准确率.数值试验考察了此模型的实际应用效果,表明新的线声源数学模型较圆形线声源更为简便,可以提高计算效率. 关键词： 传递矩阵 正方形线声源模型 二维声腔 模态级数叠加法     

Room reverberation effects in hearing aid feedback cancellation

Room reverberation can affect feedback cancellation in hearing aids, with the strength of the effects depending on the acoustical conditions. These effects were studied using a behind the ear (BTE) hearing aid mounted on a dummy head and coupled to the ear canal via an open fitting. The hearing aid impulse response was measured for the dummy head placed at eight closely spaced locations in a typical office. The feedback cancellation in the hearing aid used a set of filter coefficients that were initialized for one location within the room, and then allowed to adapt to the feedback path measured at the same or to a different location. The maximum stable gain for the hearing aid was then estimated without feedback cancellation, for the initial set of feedback cancellation filter coefficients prior to adaptation, and for the feedback cancellation filter after adaptation. A low-order ARMA model combining a fixed set of poles with an adaptive FIR filter is shown to be effective in representing the feedback path exclusive of reverberation. Increasing the adaptive filter length has only a small benefit in improving the feedback cancellation performance due to the inability of the system to model the room reverberation. The mismatch between the modeled and actual feedback paths limits the headroom increase that can be achieved when using feedback cancellation, and varies with the location within the room.     

Effect of handset proximity on hearing aid feedback

The increased sensitivity of hearing aids to feedback as a telephone handset is brought near has been studied experimentally and numerically. For the measurements, three different hearing aids were modified so that the open-loop transfer function could be measured. They were mounted in the pinna of a mannikin and the change in open-loop transfer function determined as a function of handset proximity. Increases of over 20 dB were observed, most of this change occurring within the first 10 mm of separation between pinna and handset. Numerical calculations performed using a boundary element technique were in good agreement with the measurements.     

Role of spectral cues in median plane localization

The role of spectral cues in the sound source to ear transfer function in median plane sound localization is investigated in this paper. At first, transfer functions were measured and analyzed. Then, these transfer functions were used in experiments where sounds from a source on the median plane were simulated and presented to subjects through headphones. In these simulation experiments, the transfer functions were smoothed by ARMA models with different degrees of simplification to investigate the role of microscopic and macroscopic patterns in the transfer functions for median plane localization. The results of the study are summarized as follows: (1) For front-rear judgment, information derived from microscopic peaks and dips in the low-frequency region (below 2 kHz) and the macroscopic patterns in the high-frequency region seems to be utilized; (2) for judgment of elevation angle, major cues exist in the high-frequency region above 5 kHz. The information in macroscopic patterns is utilized instead of that in small peaks and dips.     

The diffraction of sound by an impedance sphere in the vicinity of a ground surface

The problem of sound diffraction by an absorbing sphere due to a monopole point source was investigated. The theoretical models were extended to consider the case of sound diffraction by an absorbing sphere with a locally reacting boundary or an extended reaction boundary placed above an outdoor ground surface of finite impedance. The separation of variables techniques and appropriate wave field expansions were used to derive the analytical solutions. By adopting an image method, the solutions could be formulated to account for the multiple scattering of sound between the sphere and its image near a flat acoustically hard or an impedance ground. The effect of ground on the reflected sound fields was incorporated in the theoretical model by employing an approximate analytical solution known as the Weyl-van der Pol formula. An approximation solution was suggested to determine the scattering coefficients from a set of linearly coupled complex equations for an absorbing sphere not too close to the ground. The approximate method substantially reduced the computational time for calculating the sound field. Preliminary measurements were conducted to characterize the acoustical properties of an absorbing sphere made of open cell polyurethane foam. Subsequent experiments were carried out to demonstrate the validity of the proposed theoretical models for various source/receiver configurations around the sphere above an acoustically hard ground and an impedance ground. Satisfactory comparative results were obtained between the theoretical predictions and experimental data. It was found that the theoretical predictions derived from the approximate solution agreed well with the results obtained by using the exact solutions.     

Modeling of the dolphin’s clicking sound source: The influence of the critical parameters

A physical and a mathematical models of the dolphin’s source of echolocation clicks have been recently proposed. The physical model includes a bottle of pressurized air connected to the atmosphere with an underwater rubber tube. A compressing rubber ring is placed on the underwater portion of the tube. The ring blocks the air jet passing through the tube from the bottle. This ring can be brought into self-oscillation by the air jet. In the simplest case, the ring displacement follows a repeated triangular waveform. Because the acoustic pressure gradient is proportional to the second time derivative of the displacement, clicks arise at the bends of the displacement waveform. The mathematical model describes the dipole oscillations of a sphere “frozen” in the ring and calculates the waveform and the sound pressure of the generated clicks. The critical parameters of the mathematical model are the radius of the sphere and the peak value and duration of the triangular displacement curve. This model allows one to solve both the forward (deriving the properties of acoustic clicks from the known source parameters) and the inverse (calculating the source parameters from the acoustic data) problems. Data from click records of Odontocetes were used to derive both the displacement waveforms and the size of the “frozen sphere” or a structure functionally similar to it. The mathematical model predicts a maximum source level of up to 235 dB re 1 μPa at 1-m range when using a 5-cm radius of the “frozen” sphere and a 4-mm maximal displacement. The predicted sound pressure level is similar to that of the clicks produced by Odontocetest.     

Harmonic and intermodulation performance of hearing aids under large sound pressure levels

A mathematical model for the input-output functions of the hearing aids is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output when the input is formed of multitone large sound pressure levels. The special case of two-tone equal-amplitude incident pressure level is considered in detail. The results show that the third-order intermodulation component is always higher than the third-harmonic component. The results also show that the input-output functions exhibiting peak clipping exhibit the worst harmonic and intermodulation performance for large sound pressure levels. The simple wide-dynamic range compression (WDRC) input-output function exhibits the best harmonic and intermodulation distortion performance under large sound pressure levels. These results are consistent with the previously reported observations and reveal that there is a correlation between intelligibility of high-level speech and the harmonic and intermodulation performance of the hearing aid under large sound pressure levels.     

Directional dependence of interaural envelope delays

Interaural envelope delays were measured in six human subjects as a function of the location of a movable sound source, bandpassed between 3 and 16 kHz. A total of 324 source locations were tested in horizontal and vertical increments of 10 degrees. A method is described for estimating the complex directional transfer function of the external ear, independent of the position of the recording microphone in the ear canal. To compute interaural envelope delays, directional transfer functions from the left and right ears were convolved with a critical-band filter, the envelopes were computed, and the envelopes were cross correlated. Interaural envelope delays, as well as interaural group delays, varied somewhat with the center frequency of the critical-band filter and with the vertical location of the sound source. Nevertheless, to a first approximation, envelope delays measured in the ear canals increased monotonically with increasing angle of incidence relative to the median plane, as they would for two microphones on the surface of a rigid sphere. The results are discussed in relation to the possible contribution of interaural envelope delays to sound localization behavior.     

Active cancellation of occlusion: an electronic vent for hearing aids and hearing protectors

The occlusion effect is commonly described as an unnatural and mostly annoying quality of the voice of a person wearing hearing aids or hearing protectors. As a result, it is often reported by hearing aid users as a deterrent to wearing hearing aids. This paper presents an investigation into active occlusion cancellation. Measured transducer responses combined with models of an active feedback scheme are first examined in order to predict the effectiveness of occlusion reduction. The simulations predict 18 dB of occlusion reduction in completely blocked ear canals. Simulations incorporating a 1 mm vent (providing passive occlusion reduction) predict a combined active and passive occlusion reduction of 20 dB. A prototype occlusion canceling system was constructed. Averaged across 12 listeners with normal hearing, it provided 15 dB of occlusion reduction. Ten of the subjects reported a more natural own voice quality and an appreciable increase in comfort with the cancellation active, and 11 out of the 12 preferred the active system over the passive system.     

Active control of radiation from a piston set in a rigid sphere

Active control of the sound radiated from a piston set in a rigid sphere with a set of control point sources around is considered in this paper, where the scattering sound field of the control sound from the rigid sphere has been taken into account to minimize the total radiated sound power. Analytic results of the sound power are obtained and numerical simulations show that it is possible to reduce the radiation from a small piston set in a rigid sphere similar to the size of a human head up to a certain frequency. It is found that the introduction of the scattering object makes significant differences from the active control without scattering objects. This being the case, the scattering object makes the active noise control easier. To increase the global reduction of sound-power output, the optimal number and locations of the control sources and the optimal number and locations of error sensors are discussed. Finally, experiments with one control source and one error sensor around a head simulator have been carried out to verify the simulation results.     

Localization ability with bimodal hearing aids and bilateral cochlear implants

After successful cochlear implantation in one ear, some patients continue to use a hearing aid at the contralateral ear. They report an improved reception of speech, especially in noise, as well as a better perception of music when the hearing aid and cochlear implant are used in this bimodal combination. Some individuals in this bimodal patient group also report the impression of an improved localization ability. Similar experiences are reported by the group of bilateral cochlear implantees. In this study, a survey of 11 bimodally and 4 bilaterally equipped cochlear implant users was carried out to assess localization ability. Individuals in the bimodal implant group were all provided with the same type of hearing aid in the opposite ear, and subjects in the bilateral implant group used cochlear implants of the same manufacturer on each ear. Subjects adjusted the spot of a computer-controlled laser-pointer to the perceived direction of sound incidence in the frontal horizontal plane by rotating a trackball. Two subjects of the bimodal group who had substantial residual hearing showed localization ability in the bimodal configuration, whereas using each single device only the subject with better residual hearing was able to discriminate the side of sound origin. Five other subjects with more pronounced hearing loss displayed an ability for side discrimination through the use of bimodal aids, while four of them were already able to discriminate the side with a single device. Of the bilateral cochlear implant group one subject showed localization accuracy close to that of normal hearing subjects. This subject was also able to discriminate the side of sound origin using the first implanted device alone. The other three bilaterally equipped subjects showed limited localization ability using both devices. Among them one subject demonstrated a side-discrimination ability using only the first implanted device.     

Further studies on moving source solutions relevant to jet noise

This study expands further on an earlier study reported in this journal wherein the power spectrum and total power of a moving point source in a round, slug flow jet were calculated. In the present study three further aspects are reported on. Firstly the effect of non-axial lines of source convection is explored with the aid of a plane jet, line source model problem. Secondly, for centerline source convection in a round jet, the effect of a small (non-zero) shear layer thickness is studied. This procedure is first illustrated by an application to the classical problem of reflection of plane sound waves from a velocity discontinuity. Finally inferences regarding the peak angle in the radiation pattern are drawn from the study and shown to be in rough agreement with experimental data.     

Constrained adaptation for feedback cancellation in hearing aids.

In feedback cancellation in hearing aids, an adaptive filter is used to model the feedback path. The output of the adaptive filter is subtracted from the microphone signal to cancel the acoustic and mechanical feedback picked up by the microphone, thus allowing more gain in the hearing aid. In general, the feedback-cancellation filter adapts on the hearing-aid input signal, and signal cancellation and coloration artifacts can occur for a narrow-band input. In this paper, two procedures for LMS adaptation with a constraint on the magnitude of the adaptive weight vector are derived. The constraints greatly reduce the probability that the adaptive filter will cancel a narrow-band input. Simulation results are used to demonstrate the efficacy of the constrained adaptation.     

Applied topology optimization of vibro-acoustic hearing instrument models

Designing hearing instruments remains an acoustic challenge as users request small designs for comfortable wear and cosmetic appeal and at the same time require sufficient amplification from the device. First, to ensure proper amplification in the device, a critical design challenge in the hearing instrument is to minimize the feedback between the outputs (generated sound and vibrations) from the receiver looping back into the microphones. Secondly, the feedback signal is minimized using time consuming trial-and-error design procedures for physical prototypes and virtual models using finite element analysis. In the present work it is demonstrated that structural topology optimization of vibro-acoustic finite element models can be used to both sufficiently minimize the feedback signal and to reduce the time consuming trial-and-error design approach. The structural topology optimization of a vibro-acoustic finite element model is shown for an industrial full scale model hearing instrument.