Uppsala universitet
Causal MMSE Filters for Personal Audio:
A Polynomial Matrix Approach.

Simon Widmark

PhD Thesis, Uppsala University, ISBN 978-91-513-0416-8,
Acta Universitatis Upsaliensis, Uppsala Dissertations from the Factulty of Science and Technology, October 2018, 285 pp.

Dissertation in Electrical Engineering with specialization in Automatic Control, publicly examined in Siegbahnsalen, Ångström Laboratory, Uppsala on Friday October 5, 2018 at 9.00.

Thesis Opponent: Professor Fredrik Gustafsson, Linköping University, Linköping, Sweden.

Abstract in DIVA database

Chapter 1 and references in Pdf

Paper copies of the thesis can be obtained from Signals and Systems Group, Uppsala University, Box 534, SE-75121 Uppsala, Sweden.

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 near 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 energy transmitted into the quiet region.

A design with constrained energy 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 (IIR)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.

Table of Contents:
  1. Introduction. In Pdf (with references)
  2. Weighted causal MMSE design for personal audio filters
  3. Causal IIR Wiener pre-compensator design subject to quadratic constraints
  4. Constraints with respect to contrast
  5. The FIR Toepliz solution to the constrained contrast problem
  6. Constrained methods for personal audio
  7. Robustness to modelling errors and constraints on pre-ringing
  8. A case study: Robust zone design in a car.
Related Work
AES 48th Conf. 2012: Acoustical zone reproduction for car interiors using a MIMO framework, on which Chapter 2 is partly based.

IEEE TASLP paper 2018 on causal IIR audio precompensator filters subject to quadratic constraints, on which Chapter 3 is based.

IEEE TASLP paper 2019 on causal MSE-optimal filters for personal audio subject to constrained contrast, on which Chapter 4 is based.

Licentiate thesis by Annea Barkefors, May 2014 on Linear Quadratic Gaussian controllers for feedforward active noise control.

PhD Thesis by Adrian Bahne, 2014, on multichannel audio signal processing: Room correction and sound perception.

PhD Thesis by Lars-Johan Brännmark, 2011, on robust sound field control for audio reproduction: A polynomial approach to discrete-time acoustic modeling and filter design.

| Research on audio signal processing | Polynomial methods for filtering and control | Entry in publ. list |
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