Mathematical analysis of head-related transfer functions

  • Mathematische Analyse kopfbezogener Übertragungsfunktionen

Gerhard, Maike; Führ, Hartmut (Thesis advisor); Wagner, Hermann (Thesis advisor)

Aachen (2020)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2020


In this thesis we present three algorithms for the mathematical analysis of head-related transfer functions. All three algorithms can be implemented effectively. First we derive the algorithms from our mathematical model of signal transmission. Then the algorithms are tested in numerical experiments using realistic data. The first algorithm computes a measure of the acoustic similarity between two sound source positions. It provides two threshold values ​​for the signal-to-noise ratio, which are important for localization in noise. If the signal-to-noise ratio is above the higher threshold value, localization errors can be ruled out if the acoustic information is used optimally. If the signal-to-noise ratio is below the lower threshold value, it is possible that the acoustic information is misleading, that is, it causes incorrect localizations. The second algorithm is a new sound localization algorithm based on the principle of orthogonal projection. We show that the algorithm is essentially optimal, in the sense that it distinguishes positions as soon as the signal-to-noise ratio exceeds the higher threshold mentioned above. In addition to the direction of arrival, the algorithm computes an estimator of the emitted signal. A comparison of simulation results shows that the algorithm presented is superior to other common methods of sound localization in terms of localization accuracy. Furthermore it is extremely robust to changes in the frequency content and in the phase spectrum of the signal to be localized. The third algorithm is based on stochastic modeling of the discrimination between two sound source positions. It provides an upper bound for the probability of confusion between the two sound source positions. Our results indicate that this algorithm is suitable for predicting the outcome of localization experiments or the localization ability of subjects.


  • Department of Mathematics [110000]
  • Mathematics Teaching and Research Area [114320]