An Alternative Ambisonics Formulation: Modal Source Strength Matching and the Effect of Spatial Aliasing Franz Zotter Hannes Pomberger Matthias Frank.

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Presentation transcript:

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

Classical Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation) http://iem.at/Members/zotter 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)

Classical Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation) http://iem.at/Members/zotter 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)

Classical Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation) http://iem.at/Members/zotter 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]

Classical Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation) http://iem.at/Members/zotter 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 ?

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] !

spherical base solutions of the wave-equation irradiation: radiation: http://iem.at/Members/zotter spherical base solutions of the wave-equation irradiation: radiation:

Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis) http://iem.at/Members/zotter Does radiation synthesis work similarly inwards ? Is a boundary condition the correct way of describing Ambisonics ?

Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis) http://iem.at/Members/zotter 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]

Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis) http://iem.at/Members/zotter 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)

Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis) http://iem.at/Members/zotter Infinite-order source distribution of one source

Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis) http://iem.at/Members/zotter Angular band-limitation: finite resolution source strength

Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis) http://iem.at/Members/zotter Angular band-limitation: finite resolution source strength r0 r

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

Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis) http://iem.at/Members/zotter Discretization spatial Aliasing r0 r0 r r

Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis) http://iem.at/Members/zotter Discretization spatial Aliasing truncation r0 r

Alternative Ambisonics Formulation (Large Spherical Loudspeaker Arrays for Irradiation Synthesis) http://iem.at/Members/zotter

http://iem.at/Members/zotter Distance Coding (Virutal Resizing of Playback Facility)

Questions? First Ambisonics Symposium 25th – 27th June 2009 http://iem.at/Members/zotter First Ambisonics Symposium 25th – 27th June 2009 http://ambisonics.iem.at/symposium2009