Advances in sound field analysis and control based on cylindrical coordinates

Abstract

This Ph.D. thesis concerns advances in acoustic transducer array technology for improved sound field analysis and control performance. Four principal investigations are presented, which address specific performance limitations of microphone arrays and loudspeaker arrays. The basic model, on which these investigations are founded, is the general solution of the Helmholtz equation in cylindrical coordinates. The individual acoustical investigations draw on the analysis of the eigenvalues and eigenfunctions of the forward operator, providing information on the robustness of the inverse solutions against non-uniqueness, ill-conditioning and spatial aliasing. A circular microphone array design based on tangentially aligned pressure gradient sensors is studied. The theoretical analysis is complemented by a simulation study, comparing the new design to conventional arrays built from pressure sensors. It is shown that the proposed design can provide an improved performance at low frequencies, while performing worse at high frequencies due to spatial aliasing. The effects of the latter can be compensated if the Direction-of-Arrival (DOA) of the incoming waves is known. A novel DOA estimation method for sound fields measured with circular microphone arrays is proposed to address this. Using analytical expressions to model the sound fields of point sources and plane waves, it is studied for which sound fields the method is applicable and how robust it is against model imperfections. The estimation accuracy for different numbers of sources and different levels of background noise is investigated in a simulation study and the method is tested against real data, obtained through acoustic measurements. The estimation results achieved in simulations and with experimental data compare well. The general solution to the Helmholtz equation is then applied as a model for acoustic radiation in wedge-shaped spaces. This investigation aims to improve the performance of loudspeaker arrays in restricted propagation spaces, e.g. rooms. By introducing boundary conditions to the general model, different sets of basis functions are implemented in the solution and it is shown that the model enables Nearfield Acoustical Holography (NAH). Using the same propagation model, a technique for sound field control with arrays in wedge spaces is developed. The inverse problem is solved by means of a mode-matching approach, leading to an expression for the driving signals ased on a target beam pattern. Both simulations and experiments with a hemi-cylindrical loudspeaker array prototype confirm the applicability of the model for both NAH and beamforming with loudspeaker arrays in wedge spaces. Different beam patterns are considered and the model is tested through simulations and experiments. The implications of the findings, how they are linked and what future developments they may lead to is discussed.

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Identifiers

ORCID for Falk-Martin Hoffmann: orcid.org/0000-0003-2925-2124

ORCID for Filippo Fazi: orcid.org/0000-0003-4129-1433

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