Comparison of energy-preserving and all-round Ambisonic decoders Franz Zotter Matthias Frank Hannes Pomberger.

Comparison of energy-preserving and all-round

Ambisonic decoders

Franz Zotter

Matthias Frank

Hannes Pomberger

Vector Base Amplitude Panning selects a loudspeaker pair (base) to vector pan with all-positive gains (pairs ≤90°)

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… for irregular layouts it still does the job easy (throw-away loudspeaker retains some outside signal)

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Performance measures: width slightly fluctuates

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Level and width estimators for VBAP on irregular layout

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Ambisonic panning is a little bit different: it assumes avirtual panning function (here horizontal-only)

red>0, blue<0: infinite resolution.infty-infty

infinite order enc

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Ambisonic panning is a little bit different: it assumes avirtual panning function (here horizontal-only)

red>0, blue<0: infinite resolution.infty-infty

infinite order

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Ambisonic panning is a little bit different: it assumes avirtual panning function (here horizontal-only)

red>0, blue<0: infinite resolution.infty

finite order

Now we should be able to sample:

circular/spherical polynomial discretization rules exist.

-infty

Optimally Sampled Ambisonics with max-rE

Always easy if we have optimal layout…

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What is an optimal layout?

• 2D examples: regular polygon setups,

• N=3, L=6

• N=3, L=7

• N=3, L=8

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What is an optimal layout?

• 2D examples: regular polygon setups,

• N=3, L=6

• N=3, L=7

• N=3, L=8

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What is an optimal layout?

• 2D examples: regular polygon setups,

• N=3, L=6

• N=3, L=7

• N=3, L=8

Perfect width, loudness, direction measures:

Circular/Sphericalt-designs with t ≥ 2N+1

Circular t-designs:regular polygons oft+1 nodes: easy

Spherical t-designs allow to express integrals as sums

• without additional weighting or matrix inversions:

• integral-mean over any order t spherical polynomial is equivalent to summation across nodes of the t-design.

• Applicable to measures of E if t ≥ 2N, and of rE if t ≥ 2N+1 given the order N

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t-designs: t = 3 (octahedron, N=1), 5 (icosahedron, N=2), 7 (N=3), 9 (N=4).

What about non-uniform arrangements?

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Performance measures for the simplest decoder: sampling

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• With max rE weights

Performance measures for the simplest decoder: sampling

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• With max rE weights

(left) in comparison to VBAP (right)

More elaborate: Mode matching decoder (??)

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Performance measures for mode-matching decoder: unstable

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• With max rE weights

• Nicer, but gains reach a lot of dB outside panning range…

Is Ambisonic Decoding too complicated?

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What we consider a break through…

Energy preserving Ambisonic Decoding:

[Franz Zotter, Hannes Pomberger, Markus Noisternig: „Energy-Preserving Ambisonic Decoding“, Journal: acta acustica, Jan. 2011.][Hannes Pomberger, Franz Zotter: „Ambisonic Panning with constant energy constraint“, Conf: DAGA, 2012.]

All-Round Ambisonic Decoding:

[Franz Zotter, Matthias Frank, Alois Sontacchi: „Virtual t-design Ambisonics Rig Using VBAP“,Conf: EAA Euroregio, Ljubljana, 2010]

[Franz Zotter, Matthias Frank, „All-Round Ambisonic Panning and Decoding“:Journal: AES, Oct. 2012]

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1st Step: Slepian functions for target angles (semi-circle)

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• These would be all:

1st Step: Slepian functions for target angles (semi-circle)

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• Reduced to smaller number (those dominant on lower semicircle discarded)

• Loudspeakers are then encoded in a the reduced set of functions

2nd Step: energy-preserving decoding:

Ambisonic Sound Field Recording and Reproduction 23

• Instead of

• Use closest row-orthogonal matrix for decoding:

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Virtual decoding to large optimal layout

• Decoder is the transpose (optimal virtual layout)

• Playback of optimal layout to real loudspeakers: VBAP

• Ambisonic order can now be freely selected!N -> infty yields VBAP.

• Number of virtual loudspeakers should be large

Ambisonic Sound Field Recording and Reproduction 25

Energy-preserving decoder vs. AllRAD

Ambisonic Sound Field Recording and Reproduction 26

Performance measures energy-preseving vs AllRAD

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• With max rE weights

• Energy-preserving: perfect amplitude, All-RAD: better localization measures, easier calculation

Concluding: flexible versus robust

• AllRAD is very flexible and always easy to calculate but not as smoothin loudness. Order is variable, but anoptimally smooth one exists.

• Energy-preserving is mathematicallymore challengeing but useful forhigh-quality decoding (in terms ofamplitude).

• Important for audio material that is recorded or produced in Ambisonics.

Ambisonic Sound Field Recording and Reproduction 28

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Thanks!

Advancements of Ambisonics

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VBAP and Ambisonics compared

Triplet-wise panning (VBAP)+ constant loudness+ arbitrary layout-- varying spread

Ambisonic Panning~+ constant loudness+ arbitrary layout~+ invariant spread

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Virtual t-design Ambisonics using VBAP: modified

Fig. 7: Energy measure [dB], and spread measure [°] as a function of the virtual source direction. [Frank, Zotter 201*]

N = 1

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Virtual t-design Ambisonics using VBAP: modified

Fig. 7: Energy measure [dB], and spread measure [°] as a function of the virtual source direction. [Frank, Zotter 201*]

N = 3

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Virtual t-design Ambisonics using VBAP: modified

Fig. 7: Energy measure [dB], and spread measure [°] as a function of the virtual source direction. [Frank, Zotter 201*]

N = 5

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Virtual t-design Ambisonics using VBAP: modified

N = 7

Fig. 7: Energy measure [dB], and spread measure [°] as a function of the virtual source direction. [Frank, Zotter 201*]

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Virtual t-design Ambisonics using VBAP: modified

N = 9

Fig. 7: Energy measure [dB], and spread measure [°] as a function of the virtual source direction. [Frank, Zotter 201*]

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Energy-preserving decoder

All-round Ambisonic decoder