Shape-preserving average frequency response curves using rational polynomials: A case study on human stapes vibration measurements

Abstract

The vibration of the human middle ear shows sharp variations in the amplitude and phase over the audible frequency range. Measurements often differ between subjects, and it is difficult to determine the average response of the human middle ear. However, such an average response curve is of great value in detecting pathological ears. Simply averaging the amplitude and phase for each frequency results in a “washed-out” view due to differences in the locations of the maxima and minima of the curves. Therefore, a method is required to consider each individual curve's shape in the average.This paper discusses a novel method based on frequency-response transfer functions. Each of the individual measurements is fitted with a rational polynomial. The average frequency response is determined by a weighted averaging of the individual curves' numerator and denominator polynomial coefficients. Such an average preserves the shape of the individual curves. The method is applied to vibrational data of the human stapes. As expected from the literature, two resonance frequencies at 1.14 ± 0.13 kHz and 3.61 ± 0.43 kHz were found. A comparison with other methods is made to discuss the method's advantages and disadvantages.