Coherence Unbiasing For Hearing-aid Distortion Measurements

Abstract

Coherence is a measure of the degree to which the output of a system is linearly related to the system input. The signal-to-distortion ratio (S D R) , where the distortion term includes all non-linear effects and noise in the system, can be computed from the coherence. There is growing interest in using coherence to measure distortion in hearing aids and audio systems since the broadband test signal exercises intermodulation as well as harmonic distortion mechanisms in the system under test. The results of using coherence to measure distortion, however, may not be accurate due to biases in the coherence-estimation procedure. For hearing-aid measurements, where the coherence is greater than 0. 5 (S D R > 0 dB) across most of the frequency range, the major source of bias is the group delay of the system under test. The coherence is normally computed by dividing the input and output signals into segments, computing the auto-and cross-spectra for each segment, and averaging the spectra across segments. Delay in the output relative to the input, despite being a linear operation, will reduce the magnitude of the estimated cross-spectrum and thus the estimated coherence and SDR. The amount o f bias i n the coherence estimate depends on the amount of group delay as compared to the segment size. As an example, a simulated hearing-aid response is shown in Fig 1 and the associated group delay in Fig 2. The hearing aid has ideal linear gain up to the input-referred amplifier clipping level of 8 5 dB SPL. The effects of the group delay are visible in the SDR curves of Fig 3, which were computed from the coherence using speech-shaped noise as the excitation, segments of 2048 samples with Hanning windowing and a 50 percent overlap, and a total of 8192 samples at a 20-kHz sampling rate. The magnitude-squared coherence vas smoothed in the frequency domain using one-third octave bandwidths. The curve parameter in Fig 3 is the input signal level in dB SPL. The bias has reduced the SDR in the regions of high group delay, thus limiting the minimum amount of distortion that can be detected at the low input levels. At high input levels, on the other hand, the distortion causes a greater reduction in the SDR than the bias and accurate measurements are obtained. The bias effects can be reduced by using the unbiasing system shown .in Fig …