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

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

4. 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) o directional encoding = pure amplitude panning Directional Coding Input parameters Outputs (Ambisonic signals) Input Signal Encoding vector 1st order (Horizontal B-Format)2nd order (Horizontal only)

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

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

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

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

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

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

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

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

13. Conclusions Recall of some HOA fundaments and properties o Powerful mathematical approach o Highly versatile 3D sound field representation New: positional coding completed by distance coding o Efficient digital Near Field Control filters o Take care of the special case of enclosed sources A New, Viable HOA format : NFC HOA o It enables all HOA nice features considering natural/realistic sound fields o It doesnt necessarily interest only systems with very numerous loudspeakers

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