Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Similar presentations


Presentation on theme: "An Alternative Ambisonics Formulation: Modal Source Strength Matching and the Effect of Spatial Aliasing Franz Zotter Hannes Pomberger Matthias Frank."— Presentation transcript:

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


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

Similar presentations


Ads by Google