Fazi, Filippo Maria
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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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.
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