Reproduction of a 3D Sound Field
Using an Array of Loudspeakers
David Excell – 3222940
Supervisor: Dr. Thushara Abhayapala
June 2003
A thesis submitted in part fulfilment of the degree of
Bachelor of Engineering (Honours) at
The Department of Engineering
Australian National University
This thesis contains no material which has been accepted for the award of any other
degree or diploma in any university. To the best of the author’s knowledge and belief,
it contains no material previously published or written by another person, except where
due reference is made in the text.
David Excell
18 June 2003
Abstract
In this thesis the fundamental problem in signal processing of controlling a sound field
within a region of space is studied. Using spherical and cylindrical harmonics, reproduc-
tion systems in both two and three dimensions have been designed. From the design of
the systems, equations are derived describing the performance of the system for arbitrary
sound fields. The equations are defined in terms of the number of loudspeakers, the size
of the listening area and the frequency content of the sound fields.
Results from numerical verification have been included within this thesis. The im-
plementation of the 2D system is also included in this thesis demonstrating the ability
of the designed system to reproduce ‘real’ sound fields. In the implementation process,
a synthesis system was developed allowing conventionally recorded sound samples to
be placed in 2D space forming a spatial sound field. In the process it is demonstrated
that the reproduction system does not solely use amplitude panning techniques but also
considers the phase and delay of the sound field components to recreate the sound field.
ii
Acknowledgements
Without support and encouragement from a number of people and organisations the
research presented in this thesis would not have been possible. I would like to especially
thank the following:
• Dr. Thushara Abhayapala for his excellent supervision, guiding my efforts into
producing a piece of re