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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°) 2

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… for irregular layouts it still does the job easy (throw-away loudspeaker retains some outside signal) 3

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Performance measures: width slightly fluctuates 4 Level and width estimators for VBAP on irregular layout

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5 Ambisonic panning is a little bit different: it assumes a virtual panning function (here horizontal-only) red>0, blue<0: infinite resolution. infty -infty infinite order enc

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6 Ambisonic panning is a little bit different: it assumes a virtual panning function (here horizontal-only) red>0, blue<0: infinite resolution. infty -infty infinite order

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7 Ambisonic panning is a little bit different: it assumes a virtual 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… 8

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9 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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10 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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11 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/Spherical t -designs with t ≥ 2N+1 Circular t-designs: regular polygons of t+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 12 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? 13

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Performance measures for the simplest decoder: sampling 14 With max rE weights

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Performance measures for the simplest decoder: sampling 15 With max rE weights (left) in comparison to VBAP (right)

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More elaborate: Mode matching decoder (??) 16

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Performance measures for mode-matching decoder: unstable 17 With max rE weights Nicer, but gains reach a lot of dB outside panning range…

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Is Ambisonic Decoding too complicated? 18

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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 ] [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] 19

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1st Step: Slepian functions for target angles (semi-circle) 21 These would be all:

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1st Step: Slepian functions for target angles (semi-circle) 22 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 Reproduction23 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 Reproduction25

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Energy-preserving decoder vs. AllRAD Ambisonic Sound Field Recording and Reproduction26

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Performance measures energy-preseving vs AllRAD 27 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 smooth in loudness. Order is variable, but an optimally smooth one exists. Energy-preserving is mathematically more challengeing but useful for high-quality decoding (in terms of amplitude). Important for audio material that is recorded or produced in Ambisonics. Ambisonic Sound Field Recording and Reproduction28

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29 Thanks! Advancements of Ambisonics

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30 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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31 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 9/13

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32 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 9/13

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33 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 9/13

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34 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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35 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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36 Energy-preserving decoder All-round Ambisonic decoder

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