1. An Alternative Ambisonics Formulation: Modal Source Strength Matching and the Effect of Spatial Aliasing
Franz Zotter Hannes Pomberger Matthias Frank
Institute of Electronic Music and Acoustics
University of Music and Performing Arts, Graz

2. Classical Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation)
Angular band-limitation
Discretization
Comparison (Decoding)
ls4
ls3
ls2
ls1
Superposition of a weighted continuum of plane wave directions at one point is capable of reproducing any incident field
Angular band-limitation by representing plane-wave directions (delta functions) in spherical harmonics truncating order
Discretization of plane-wave directions by loudspeaker positions
Mode-matching of a variable (finite-order) desired field with band- limited finite-order discrete loudspeaker fields (Decoder)

3. Classical Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation)
Angular band-limitation
Discretization
Comparison (Decoding)
ls4
ls3
ls2
ls1
Superposition of a weighted continuum of plane wave directions at one point is capable of reproducing any incident field
Angular band-limitation by representing plane-wave directions (delta functions) in spherical harmonics truncating order
Discretization of plane-wave directions by loudspeaker positions
Mode-matching of a variable (finite-order) desired field with band- limited finite-order discrete loudspeaker fields (Decoder)

4. Classical Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation)
Angular band-limitation
Discretization
Comparison (Decoding)
ls4
ls3
ls2
ls1
Teaching problems:
Non-temporal spectral representation in spherical harmonics
How to imagine sound pressure of plane-wave directions encoded into spherical harmonics ?
Decoding and angular band-limitation
[thanks to Markus Noisternig for his teaching experience]

5. Classical Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation)
Angular band-limitation
Discretization
Comparison (Decoding)
ls4
ls3
ls2
ls1
What is spatial aliasing and what is the sweet-spot ?
Do loudspeakers create plane waves ?
What about ill-posed frequencies in mode-matching ?

6. smoothing of sound radiation
Compact Spherical Loudspeaker Arrays for Radiation Synthesis (or: Motivation for reformulation of Ambisonics ? )
[Zotter, Sontacchi, Höldrich: Modeling a Spherical Loudspeaker System as Multipole Source, DAGA 2007]
smoothing of sound radiation
Boundary condition of sound particle velocity (surface) is capable of reproducing any radiating field
Angular band-limitation by encoding loudspeaker apertures into finite-order spherical harmonics series
Discretization of the boundary by loudspeakers
Mode-matching of a variable finite-order desired pattern at the surface with band- limited finite-order loudspeaker fields (Decoder)
Radial focusing of radiation pattern feasible (SH: base-solutions of wave-equation)
High orders are suppressed in radiation [Zotter07], the model is accurate [Meyer00, Pollow07] !

7. spherical base solutions of the wave-equation irradiation: radiation:
spherical base solutions of the wave-equation
irradiation: radiation:

8. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Does radiation synthesis work similarly inwards ?
Is a boundary condition the correct way of describing Ambisonics ?

9. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Does radiation synthesis work similarly inwards ?
Is a boundary condition the correct way of describing Ambisonics ?
What about spherically distributed point sources ? - no obstacle/reflection - fair model of loudspeakers there are existing models ! [J. Ahrens, S. Spors, AES 2008; simple-source approach] [F. Fazi et al, AES 2008; single-layer potential]

10. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
spherically distributed point sources
phi … source strength distribution
Continuous source strength is capable of reproducing any irradiating field (unlike boundary condition: radiation only !)
Discretization of sphere by loudspeaker placement
Angular band-limitation by encoding the discretized source strength (delta- function) into spherical harmonics
Modal source-strength matching of the loudspeaker fields with variable desired field (Decoder)
Radial focusing of reproduced source strength feasible (SH: base-solutions of wave-equation)

11. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Infinite-order source distribution of one source

12. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Angular band-limitation: finite resolution source strength

13. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Angular band-limitation: finite resolution source strength r0 r

14. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Angular band-limitation: finite resolution source strength r0 r 1 2 3 4

15. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Discretization
spatial Aliasing r0 r0 r r

16. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Discretization
spatial Aliasing
truncation r0 r

17. Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis)

18.
Distance Coding (Virutal Resizing of Playback Facility)

19. Questions? First Ambisonics Symposium 25th – 27th June 2009
First Ambisonics Symposium 25th – 27th June 2009