comparison of energy-preserving and all-round ambisonic decoders franz zotter matthias frank hannes...
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Comparison of energy-preserving and all-round
Ambisonic decoders
Franz Zotter
Matthias Frank
Hannes Pomberger
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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
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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
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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).
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What about non-uniform arrangements?
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Performance measures for the simplest decoder: sampling
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• With max rE weights
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Performance measures for the simplest decoder: sampling
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• With max rE weights
(left) in comparison to VBAP (right)
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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…
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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:
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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
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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
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Energy-preserving decoder vs. AllRAD
Ambisonic Sound Field Recording and Reproduction 26
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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
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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*]
9/13
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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*]
9/13
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Energy-preserving decoder
All-round Ambisonic decoder