Jérôme Daniel, France Telecom R&D jerome. ! daniel ! @ ! francetelecom

1. Spatial Sound Encoding Including Near Field Effect:Introducing Distance Coding Filters and a Viable, New Ambisonic Format Jérôme Daniel, France Telecom R&D jerome.!daniel!@!francetelecom.com

2. What for a spatial sound encoding approach • First & Higher Order Ambisonics (HOA) • Models the acoustic reality of sound field • Homogeneous directional information • Scalable multi-channel 3D audio format • Flexibility (transformations & decoding) • Part I - Fundaments of HOA: common conception and limitations • A directional encoding technique (based on amplitude panning) • Only able to handle plane waves, thus artificial sound fields • Part II - Recent improvements • Distance coding filters able to handle near field sources • New encoding format that supports natural or realistic sound fields • True “holophonic” rendering (comparison with WFS) • Efficient DSP tools for positional encoding

3. Spherical Harmonic functions: Spherical Bessel Functions: Plane wave: M=1 M=2 M=3 M=4 1st & Higher Order Ambisonics fundaments:Intrinsic representation properties • Spherical Harmonic Decomposition : Fourier-Bessel series • Intrinsic quality of representation • Using components Bmns up to a limited order (mM) • Angular resolution  radial expansion % wave length • Sound field represented by coefficients Bmns • = Spherical Harmonic component  “Ambisonic Signals” • pressure field spatial derivatives of successive orders m • Around a reference point = listener point of view

4. Input parameters Outputs (Ambisonic signals) 1st order (Horizontal B-Format) 2nd order (Horizontal only) Input Signal Directional Coding Encoding vector First & Higher Order Ambisonics Fundaments:Directional encoding • Approximation of elementary wave fronts as plane waves (far sources) • Spherical harmonic decomposition of a plane wave (conveying S) •  directional encoding = pure amplitude panning

5. Ambisonic signals B Decoding Matrix D ~ Soundfield reconstructed by the array (assuming far loudspeakers) B = C.S ~ B = B The goal: • Expansion of the reconstruction area with increasing order 1st order: 2nd order: 5th order: 10th order: monochromatic plane wave f=600Hz 10th order: First & higher order ambisonics fundaments:Decoding and sound field reconstruction • Decoder’s task: to “recompose” ambisonic sound field • With finite distance loudspeakers • Wave encoded as plane  reconstructed as spherical! • Sound image is “projected” over the loudspeaker array Loudspeaker signals S = D.B

6. Directional encoding gain (like for plane waves) • Near field modelling transfer function: f=100Hz f=1000Hz f=200Hz What about finite distance sources ? • The case of a spherical wave (point source) • Incidence (q,d ), distance r, conveying S • Sph. Harm. Decomposition  ambisonic components •  mathematical encoding equation: Slope = m x 6dB/oct • Near Field Effect: • It affects phase and amplitude ratios between spatial derivatives of  orders • It models the wave front curvature % wave length • “Infinite” bass-boost with slope as strong as the order is high • Unstable integrating filters: resulting signals diverge (esp. for higher orders) • Consequence on currently adopted HOA encoding scheme • Mathematically powerful but physically unviable when dealing with near field sources • Unable to represent natural or realistic sound fields !

7. Summary: the past, common way of looking Ambisonics… • In spite of featuring very attractive properties… • Homogeneous directional representation • Independent from the rendering loudspeaker layout • Scalable, flexible • …the commonly accepted definition of HOA suffers from limitations: • Pure amplitude panning technique: only directional encoding • Plane wave model used for encoded virtual sources •  acoustically unrealistic • Unable to represent natural sound fields (at higher orders) • Neither virtual source encoding nor natural recording • Next: • The key to overcome these limitations • A viable, modified ambisonic format • Distance Coding (or Near Field Control) filters • Other consequences and applications

8. Near Field compensation Without Near Field Compensation Introducing Near Field Compensation Anticipating a reproduction requirement • Take into account the finite distance of loudspeakers • Near field compensation is required to correct the curvature of loudspeakers waves Ambisonic signals B Decoding Matrix D Reconstructed components Bmns are affected by the loudspeakers Near-Field Effect Fm(R/c)(w) • Towards a solution for natural sound field representation • Since compensation of loudspeaker near field is required… • …why not introducing it from the encoding stage?

9. Finite amplification: m x 20 log10(R/r) • Amplification depending on r % R • “Near Field pre-Compensated” HOA format (NFC-HOA) • Components defined as: Distance coding filters & viable representation • Practicable “Near Field Coding” (NFC) filters • Model loudspeaker NF compensation + virtual source NF effect • … at the same time, from the encoding stage • Positional encoding = directional + distance coding • Its supports natural/realistic sound fields • It merely requires a “classic” matrix decoding • Implicit parameter = “reference distance” R = loudspeaker array radius • Can further adapt to any other loudspeaker distance R’ using NFC filters • (correct the wave field curvature)

10. Input parameters Positional Encoding Outputs (NFC HOA) (for odd order m) Input Signal Bilinear-tranform + roots extraction Distance Coding Directional Coding Frequency responses: Impulses responses: “Inside” sources “Outside” sources Generic & efficient DSP tools for encoding • Design of digital NFC (distance coding) filters: • Parametric, minimal-cost IIR filters • Filter coefficients: functions of r, R, c, fs, and tabulated roots • Computation of directional encoding gains Ymns(q,d) • Efficient, recursive algorithm • Virtually unlimited order • A complete positional coding scheme

11. Illustration of sound field reconstruction Frequency domain: Time domain: Gaussian-modulated sine pulse (fc = 500 Hz) • Outside virtual source: • Quite efficient reconstruction • Better than Wave Field Synthesis • [Daniel et al, AES114] • Becomes easier when virtual source gets closer to the real ones • Enclosed virtual source: • Full reconstruction physically impossible anyway • Large amount of energy at low frequencies • Strong interference beyond the virtual source distance • Right direction of propagation ( WFS)

12. Other consequences and applications • HOA recording systems become practicable • …by introducing NF compensation at the stage of the mic signal processing • otherwise: equalization filters are unstable [Daniel et al, AES114] and natural sound fields cannot be physically represented • 4th order microphone prototype: being experimented at FTR&D Labs • Accurate binaural synthesis of close sources • “Virtual Ambisonics” • = head-centred ambisonics + binaural synthesis of virtual loudspeakers • Supports sound field rotations, thus head-tracking adaptation • “Ear-centred double virtual ambisonics” • Binaural B-format encoding scheme enriched by NF-Coding filters • More accurate than “head-centred virtual ambisonics” • … but doesn’t support rotations once the encoding is done

13. Conclusions • Recall of some HOA fundaments and properties • Powerful mathematical approach • Highly versatile 3D sound field representation • New: positional coding completed by distance coding • Efficient digital Near Field Control filters • Take care of the special case of enclosed sources • A New, Viable HOA format : NFC HOA • It enables all HOA nice features considering natural/realistic sound fields • It doesn’t necessarily interest only systems with very numerous loudspeakers

14. Work in progress • Evaluation of holophonic sound imaging over 48 loudspeakers • Up to 15th order Ambisonics • Comparison of HOA and WFS for outside and enclosed sources • In the context of the CARROUSO project • Experimentation of a 4th order ambisonic microphone • 32 capsules over a sphere • Specification of a generic HOA format • In MPEG-4 (for AudioBIFS V3) • => handle multi-channel audio streams as scalable 3D sound fields • As a extension of the Wave file format • Detailed propositions in the paper