Robust Sound Field Control for Audio Reproduction
A polynomial approach to discrete-time acoustic
modeling and filter design.
PhD Thesis, Uppsala University,
January 2011, 286 pp.
Dissertation in Engineering Science with specialization
in Signal Processing, publicly examined
in Polhemssalen, Ångström Laboratory,
Uppsala on Friday February 11, 2011 at 13.15.
Thesis Opponent: Prof. Rodney Kennedy, Australian National University,
Paper copies of the thesis
can be obtained from Ylva Johansson,
Signals and Systems Group, Uppsala University,
Box 534, SE-75121 Uppsala, Sweden.
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
filter design is developed.
The work on modeling is centered around
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
is selected as a physically motivated channel model. As a means for
channel uncertainties, a probabilistic design model is proposed. 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.
are accounted for by applying the probabilistic uncertainty model to the
The work on filter design can be categorized into single- and
The single-channel problem concerns the improvement of the impulse and
of a single loudspeaker over a region in space, by means of a scalar
problem is posed in a SIMO (single-input multiple-output) feedforward
and is solved using polynomial methods. The solution offers several
useful insights and
results. In particular, new results are derived regarding the adverse
associated with mixed phase filters. Based on the new results, a refined
method is proposed that is practically free from pre-ringing artifacts.
In the multichannel
problem, a desired spatio-temporal sound field is approximated by the
joint use of several
loudspeakers. This problem is initially formulated and solved by
feedforward control over
a continuous spatial domain, assuming full knowledge of the spatial
field. To obtain a
practically feasible design, the control criterion is then spatially
discretized, resulting in
a standard MIMO (multiple-input multiple-output) linear quadratic
problem. Since information is generally lost in the discretization
process, a robust design
based on spatial interpolation and probabilistic error modeling is
designs are assessed in an automotive setting, using practical
measurements of a
nine-channel sound system in a car.
Acoustic signal processing, equalizers, error modeling,
feedforward control, interpolation, loudspeakers,
multivariable filters, polynomials, robustness,
Table of Contents:
- Sound field dimensionality and spatial interpolation
- Spatially robust single-channel compensation
- Multichannel compensation and sound field control
- Case study: An automotive sound system
- Concluding remarks
Audio research at Signals and Systems
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