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An Alternative Ambisonics Formulation:
Modal Source Strength Matching and the Effect of Spatial Aliasing
Franz ZotterHannes PombergerMatthias Frank
Institute of Electronic Music and AcousticsUniversity of Music and Performing Arts, Graz
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Classical Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation)
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)
Angular band-limitation
DiscretizationComparison (Decoding)
ls1 ls2
ls3ls4
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Classical Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation)
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)
Angular band-limitation
DiscretizationComparison (Decoding)
ls1 ls2
ls3ls4
http://iem.at/Members/zotter
![Page 4: An Alternative Ambisonics Formulation: Modal Source Strength Matching and the Effect of Spatial Aliasing Franz Zotter Hannes Pomberger Matthias Frank Institute](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649f4e5503460f94c6fe87/html5/thumbnails/4.jpg)
Classical Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation)
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]
Angular band-limitation
DiscretizationComparison (Decoding)
ls1 ls2
ls3ls4
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Classical Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation)
What is spatial aliasing and what is the sweet-spot ? Do loudspeakers create plane waves ? What about ill-posed frequencies in mode-matching ?
Angular band-limitation
DiscretizationComparison (Decoding)
ls1 ls2
ls3ls4
http://iem.at/Members/zotter
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Compact Spherical Loudspeaker Arrays for Radiation Synthesis
(or: Motivation for reformulation of Ambisonics ? )
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] !
[Zotter, Sontacchi, Höldrich: Modeling a Spherical Loudspeaker System as Multipole Source, DAGA 2007]
smoothing of sound radiation
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spherical base solutions of the wave-equation
irradiation: radiation:
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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 ?
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![Page 9: An Alternative Ambisonics Formulation: Modal Source Strength Matching and the Effect of Spatial Aliasing Franz Zotter Hannes Pomberger Matthias Frank Institute](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649f4e5503460f94c6fe87/html5/thumbnails/9.jpg)
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]
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![Page 10: An Alternative Ambisonics Formulation: Modal Source Strength Matching and the Effect of Spatial Aliasing Franz Zotter Hannes Pomberger Matthias Frank Institute](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649f4e5503460f94c6fe87/html5/thumbnails/10.jpg)
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)
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Alternative Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Infinite-order source distributionof one source
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Alternative Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Angular band-limitation: finite resolution source strength
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Alternative Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Angular band-limitation: finite resolution source strength
r
r0
http://iem.at/Members/zotter
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Alternative Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Angular band-limitation: finite resolution source strength
r
r0
12
34
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Alternative Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Discretizationspatial Aliasing
r
r0
r
r0
http://iem.at/Members/zotter
![Page 16: An Alternative Ambisonics Formulation: Modal Source Strength Matching and the Effect of Spatial Aliasing Franz Zotter Hannes Pomberger Matthias Frank Institute](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649f4e5503460f94c6fe87/html5/thumbnails/16.jpg)
Alternative Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
Discretizationspatial Aliasing
truncation
r
r0
http://iem.at/Members/zotter
![Page 17: An Alternative Ambisonics Formulation: Modal Source Strength Matching and the Effect of Spatial Aliasing Franz Zotter Hannes Pomberger Matthias Frank Institute](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649f4e5503460f94c6fe87/html5/thumbnails/17.jpg)
Alternative Ambisonics Formulation(Large Spherical Loudspeaker Arrays for Irradiation Synthesis)
http://iem.at/Members/zotter
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Distance Coding (Virutal Resizing of Playback Facility)
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Questions?http://iem.at/Members/zotter
First Ambisonics Symposium 25th – 27th June 2009http://ambisonics.iem.at/symposium2009