An introduction to the mathematics of ambisonics
An introduction to the mathematics of ambisonics
This lecture is intended as a tutorial on some basic and more advanced mathematical concepts and tools that are used (or may be used) when dealing with Ambisonics and sound field representation.
The talk covers some elementary concepts like the Fourier series, both in its classical version (involving sine and cosines) and the spherical harmonic expansion. The concept of spaces of functions is then introduced and the analogy with the more familiar Cartesian spaces is discussed, including the representation of a function as a linear combination of the elements of an orthogonal basis. Finally, the more advanced topic of integral representation of sound fields is presented and the integral operators known as the Herglotz wave function and the single layer potential are introduced. Their relation with Ambisonics and spherical acoustics is explained.
Fazi, Filippo Maria
e5aefc08-ab45-47c1-ad69-c3f12d07d807
25 March 2012
Fazi, Filippo Maria
e5aefc08-ab45-47c1-ad69-c3f12d07d807
Fazi, Filippo Maria
(2012)
An introduction to the mathematics of ambisonics.
25th AES UK Conference: Spatial Audio in Today’s 3D World in association with the 4th International Symposium on Ambisonics and Spherical Acoustics, York, United Kingdom.
25 - 26 Mar 2012.
Record type:
Conference or Workshop Item
(Other)
Abstract
This lecture is intended as a tutorial on some basic and more advanced mathematical concepts and tools that are used (or may be used) when dealing with Ambisonics and sound field representation.
The talk covers some elementary concepts like the Fourier series, both in its classical version (involving sine and cosines) and the spherical harmonic expansion. The concept of spaces of functions is then introduced and the analogy with the more familiar Cartesian spaces is discussed, including the representation of a function as a linear combination of the elements of an orthogonal basis. Finally, the more advanced topic of integral representation of sound fields is presented and the integral operators known as the Herglotz wave function and the single layer potential are introduced. Their relation with Ambisonics and spherical acoustics is explained.
This record has no associated files available for download.
More information
Published date: 25 March 2012
Venue - Dates:
25th AES UK Conference: Spatial Audio in Today’s 3D World in association with the 4th International Symposium on Ambisonics and Spherical Acoustics, York, United Kingdom, 2012-03-25 - 2012-03-26
Organisations:
Acoustics Group
Identifiers
Local EPrints ID: 350757
URI: http://eprints.soton.ac.uk/id/eprint/350757
PURE UUID: 8de0be17-425c-41fa-be5b-d84e85451f21
Catalogue record
Date deposited: 09 Apr 2013 10:49
Last modified: 02 Sep 2023 01:41
Export record
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
