Causal MMSE Filters for Personal Audio : A Polynomial Matrix Approach

Sammanfattning: This thesis is devoted to the study of synthesis of causal filters for generating personal sound zones. Personal sound zones, personal audio or personal sound is the theory and practice of steering sound in such a way that it is amplified in one region and suppressed in another. In lower frequencies, this is accomplished by designing filters that control the complex pattern of constructive and destructive interference that a set of sound sources gives rise to. There are many ways of designing such filters and the field of personal audio has been rather active in the last few decades. As the algorithms approach actual production line implementation, the aspects of realisability gain in importance. It has been noted in the literature that filters that are causal by design solve many of the problems associated with implementability and may increase the subjective sound quality in the bright zone. However, the problem of synthesis of causal filters for personal audio has received less attention than that of non-causal filters. In this thesis, synthesis of causal filters for personal audio with emphasis on implementability is explored. Several different approaches, with varying formulations of the personal audio problem, are investigated and discussed. The majority of these designs are also implemented and tested in real systems.Practical designs that are studied include a weighted sound field synthesis design, drawing from the previous sound field synthesis literature, and a design with a constraint on the acoustic power transmitted into the quiet region. A design with constrained power difference between the quiet and the non-quiet (bright) region is also proposed and investigated. As an auxiliary result, a method for incorporating quadratic power constraints in the rational matrix filter approach to synthesis of Infinite Impulse Response Wiener filters is proposed. An expansion to include robustness to uncertainties in the systems under investigation is also investigated. General guidelines for the use of the different proposed methods are sought, but the problems are very complex. Over all, a user-centric approach is developed, where emphasis is placed on practical design and analysis of the optimization problems at hand.