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 °)

2

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

3

Performance measures: width slightly fluctuates

Level and width estimators for VBAP on irregular layout 4

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 5

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 6

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.

7

Optimally Sampled Ambisonics with max-rE

Always easy if we have optimal layout… 8

What is an optimal layout?

• • • • 2D examples: regular polygon setups,

N=3, L=6

N=3, L=7 N=3, L=8 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

Perfect width, loudness, direction measures: Circular/Spherical

t

-designs with

t

≥ 2N+1 Circular t-designs: regular polygons of t+1 nodes: easy 11

Spherical t-designs allow to express integrals as sums

• without additional weighting or matrix inversions: • • integral-mean over

any order t spherical polynomial

equivalent to summation across nodes of the

t

is -design. Applicable to measures of E if

t

≥ 2N , and of rE if given the order N

t

≥ 2N+1

t

-designs:

t

= 3 (octahedron, N=1), 5 (icosahedron, N=2), 7 (N=3), 9 (N=4).

12

What about non-uniform arrangements?

13

Performance measures for the simplest decoder:

• With max rE weights 14

Performance measures for the simplest decoder:

• With max rE weights (left) in comparison to VBAP (right) 15

More elaborate: Mode matching decoder (??)

16

Performance measures for mode-matching decoder:

• • With max rE weights Nicer, but gains reach a lot of dB outside panning range… 17

Is Ambisonic Decoding too complicated?

18

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] 19

20

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

• These would be all: 21

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 22

2nd Step: energy-preserving decoding:

• Instead of • Use closest row orthogonal matrix for decoding: Ambisonic Sound Field Recording and Reproduction 23

24

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

With max rE weights Energy-preserving: perfect amplitude, All-RAD: better localization measures, easier calculation 27

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 28

Advancements of Ambisonics

Thanks!

29

VBAP and Ambisonics compared

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

Virtual t-design Ambisonics using VBAP: modified

N = 1 Fig. 7: Energy measure [dB], and spread measure [ ° ] as a function of the virtual source direction. [Frank, Zotter 201*]

Virtual t-design Ambisonics using VBAP: modified

N = 3 Fig. 7: Energy measure [dB], and spread measure [ ° ] as a function of the virtual source direction. [Frank, Zotter 201*]

Virtual t-design Ambisonics using VBAP: modified

N = 5 Fig. 7: Energy measure [dB], and spread measure [ ° ] as a function of the virtual source direction. [Frank, Zotter 201*]

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*]

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*]

Energy-preserving decoder All-round Ambisonic decoder 36