Radial Filter Synthesis for Spherical Microphone Arrays
Bachelor Thesis of Schwachtgen, Denis
Over the past few decades, research began to focus increasingly on the use of spherical microphone arrays to study the spatial properties of acoustic wave fields. To estimate the plane wave incidence accurately, the unwanted effects generated by the spherical microphone array itself in the recorded sound pressure should be eliminated by radial filtering. To that end, the synthesis of adapted radial filters will form the core of this research. Radial filters will be derived from both a modeled and a measured spherical microphone array. A closer description of the directivity measurement required to determine the aforementioned measurement based radial filter will be given. Since the filtering of radial terms relies on a mathematical inversion, appropriate numerical inversion methods such as the Moore-Penrose inversion and the soft-limiting inversion will be introduced as well. The analytic radial filtering methods will also be further enhanced to be more adapted to the physical needs of the spherical microphone array. The study will then conclude by evaluating the reconstruction capabilities of the different radial filter variants and determine the most favorable one.