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

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

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

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

5. 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

6. 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

7. 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.

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

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

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

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

12. 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).

13. What about non-uniform arrangements?

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

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

16. More elaborate: Mode matching decoder (??)

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

18. Is Ambisonic Decoding too complicated?

19. 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]

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

22. 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

23. 2nd Step: energy-preserving decoding:
Instead of
Use closest row-orthogonal matrix for decoding:
Ambisonic Sound Field Recording and Reproduction

25. 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

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

27. Performance measures energy-preseving vs AllRAD
With max rE weights
Energy-preserving: perfect amplitude, All-RAD: better localization measures, easier calculation

28. 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

29. Thanks!
Advancements of Ambisonics

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

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*]
9/13

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*]
9/13

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*]
9/13

34. 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

35. 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

36. Energy-preserving decoder
All-round Ambisonic decoder