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Brännmark, Lars-Johan (Uppsala University), “Robust Sound Field Control for Audio Reproduction: A Polynomial Approach to Discrete-Time Acoustic Modeling and Filter Design” Advisor: Prof. Ahlén, Anders(2011)
This thesis is concerned with the design and analysis of robust discrete-time filters for audio equalization and sound field control in real reverberant environments. Inspired by methods in polynomial control theory, a unified framework for acoustic modeling and filter design is developed.
The work on modeling is centered on three main themes: First, the acoustic channel between a loudspeaker and a point in space is studied in time, frequency and space, and a polynomial matrix fraction description with diagonal denominator is selected as a physically motivated channel model. Second, the concept of sound field dimensionality, based on the Karhunen-Loève expansion of the sound field, is explored and integrated into the polynomial systems context. Third, a method for spatial interpolation of acoustic transfer functions is proposed and evaluated. The work on filter design can be categorized into single- and multi-channel methods. The single-channel problem concerns the improvement of the impulse and frequency responses of a single loudspeaker over a region in space. In the multichannel problem, a desired spatio-temporal sound field is approximated by the joint use of several loudspeakers.
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