# Comparison of energy-preserving and all-round Ambisonic decoders

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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°)

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

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

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

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

Ambisonic panning is a little bit different: it assumes a virtual panning function (here horizontal-only) finite order red>0, blue<0: infinite resolution. infty -infty Now we should be able to sample: circular/spherical polynomial discretization rules exist.

Optimally Sampled Ambisonics with max-rE
Always easy if we have optimal layout…

What is an optimal layout?
2D examples: regular polygon setups, N=3, L=6 N=3, L=7 N=3, L=8

What is an optimal layout?
2D examples: regular polygon setups, N=3, L=6 N=3, L=7 N=3, L=8

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

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

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

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

More elaborate: Mode matching decoder (??)

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

Is Ambisonic Decoding too complicated?

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]

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

1st Step: Slepian functions for target angles (semi-circle)
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:
Instead of Use closest row-orthogonal matrix for decoding: Ambisonic Sound Field Recording and Reproduction

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

Ambisonic Sound Field Recording and Reproduction

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 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 Reproduction

VBAP and Ambisonics compared
Triplet-wise panning (VBAP) + constant loudness + arbitrary layout -- varying spread Ambisonic Panning ~+ constant loudness + arbitrary layout ~+ invariant spread

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*] 9/13

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*] 9/13

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*] 9/13

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*] 9/13

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*] 9/13

Energy-preserving decoder
All-round Ambisonic decoder