Cross-correlation procedures for measuring noise and distortion in AGC hearing aids

The magnitude-squared coherence function (MSC) has been used to measure noise and distortion in linear and compression hearing aids. However, the MSC will overestimate the distortion in a linear time-varying system such as a compression amplifier. The reduction in coherence caused by varying the gain in an otherwise linear system can be substantial, and can lead to large errors in estimating the distortion present in a compression hearing aid. The effects of gain changes in a linear system can be reduced by measuring the normalized system input-output cross correlation, which emphasizes the variance in the system phase response and deemphasizes the system gain fluctuations. Estimates of the total noise and distortion produced using the MSC, phase variance, and notched-noise measurement techniques are compared for additive noise, clipping distortion, and compression amplification. The MSC is found to give the most accurate results for estimating the noise and distortion in a linear time-invariant system, and the notched noise measurements are the most accurate for a compression system. The phase variance is found to give reasonable measurements for a time-varying gain as long as the system variations are slow relative to the length of the analysis data segments.