An introduction to the mathematics of ambisonics


Fazi, Filippo Maria (2012) An introduction to the mathematics of ambisonics At 25th AES UK Conference: Spatial Audio in Today’s 3D World in association with the 4th International Symposium on Ambisonics and Spherical Acoustics, United Kingdom. 25 - 27 Mar 2012.

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Description/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.

Item Type: Conference or Workshop Item (Other)
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, United Kingdom, 2012-03-25 - 2012-03-27
Related URLs:
Subjects: Q Science > QC Physics
Organisations: Acoustics Group
ePrint ID: 350757
Date :
Date Event
25 March 2012Published
Date Deposited: 09 Apr 2013 10:49
Last Modified: 17 Apr 2017 15:45
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/350757

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