spatial sound encoding including near field effect: introducing distance coding filters and a...
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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
What for a spatial sound encoding approach
Part I - Fundaments of HOA: common conception and limitationso A directional encoding technique (based on amplitude panning)
o Only able to handle plane waves, thus artificial sound fields
Part II - Recent improvementso 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)
Spherical Harmonic functions:
Spherical Bessel Functions:
1st & Higher Order Ambisonics fundaments:Intrinsic representation properties
Intrinsic quality of representationo Using components Bmn
up to a limited order (mM)o Angular resolution radial expansion % wave length
0 0 , 1
( ) ( ) ( , )mm mn mn
m n m
p r j j kr B Y
Spherical Harmonic Decomposition : Fourier-Bessel series
o Sound field represented by coefficients Bmn
o = Spherical Harmonic component “Ambisonic Signals”pressure field spatial derivatives of successive orders m
o Around a reference point = listener point of view
Plane wave:
M=1 M=2 M=3 M=4
First & Higher Order Ambisonics Fundaments:Directional encoding
. ( , )mn mnB S Y
Approximation of elementary wave fronts as plane waves (far sources) Spherical harmonic decomposition of a plane wave (conveying S)
directional encoding = pure amplitude panning
),(111 Y
),( mnY
),(111 Y
),(110 Y
),(1 mmY
),(1 mmY
),(10 mY
1),(10 Y
mnB
10mB
1mmB
1mmB
111B X
111B Y 1
10B Z
100B W
( , )
S
Directional Coding
Input parameters Outputs
(Ambisonic signals)
Input Signal
1 100 001 1
11 111 1
11 11
( , )
( , )
( , )B .
( , )mn mn
B Y
B Y
B YS
B Y
Encoding vector
1st order (Horizontal B-Format)2nd order (Horizontal only)
First & higher order ambisonics fundaments:Decoding and sound field reconstruction
With finite distance loudspeakerso Wave encoded as plane reconstructed as spherical!
o Sound image is “projected” over the loudspeaker array
1D pinv(C) C .(C.C )T T
Decoding Matrix
D
Ambisonic signals
B
Decoder’s 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 wavef=600Hz
1st order: 2nd order: 5th order: 10th order:
10th order:
( / )
0
( )!( )
( )! !
nmc
mn
m n jcF
m n n
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 mathematical encoding equation:
( / ). ( , ). ( )cmn mn mB S Y F
Near Field Effect:oIt affects phase and amplitude ratios between spatial derivatives of
orders
oIt models the wave front curvature % wave length
o“Infinite” bass-boost with slope as strong as the order is high
oUnstable integrating filters: resulting signals diverge (esp. for higher orders)
Slope = m x 6dB/oct
f=1000Hzf=200Hzf=100Hz
Consequence on currently adopted HOA encoding schemeoMathematically powerful but physically unviable when dealing with near field
sources
oUnable to represent natural or realistic sound fields !
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
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 representationo 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 Bmn
are affected by the loudspeakers Near-Field
Effect Fm(R/c)()
Near Field compensation
( / )
1
( )R cmF
Without Near FieldCompensation
Introducing Near FieldCompensation
Distance coding filters & viable representation
o Positional encoding = directional + distance coding
( / )NFC( /c,R/c)
( / )
( )( )
( )
cm
m R cm
FH
F
NFC( ) NFC( )NFC( )'/ // , '/ ( ).mn m mn
R c R cR c R cB H B
oIts supports natural/realistic sound fields
oIt merely requires a “classic” matrix decoding
oImplicit parameter = “reference distance” R = loudspeaker array radius
oCan further adapt to any other loudspeaker distance R’ using NFC filters
(correct the wave field curvature)
Practicable “Near Field Coding” (NFC) filterso Model loudspeaker NF compensation + virtual source NF effect
o … at the same time, from the encoding stageFinite amplification:m x 20 log10(R/)
o Amplification depending on % R
NFC( / ) NFC( /c,R/c). ( , ). ( )R c
mn mn mB S Y H
NFC( / )
( / )
1
( )
R c
mn mnR cm
B BF
“Near Field pre-Compensated” HOA format (NFC-HOA)
oComponents defined as:
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
0NFC( / , / )
0
( )!( )! !
( )( )!
( )! !
nm
nc R cm nm
n
m n jcm n n
Hm n jc
m n n R
Bilinear-tranform+ roots extraction
Frequency responses: Impulses responses:
“Inside” sources
“Outside” sources
)/,/(NFC cRcrmH
)/,/(NFC1
cRcrH),(111 Y
),( mnY
),(111 Y
),(110 Y
),(1 mmY
),(1 mmY
),(10 mY
1),(10 Y
),( r
mnB
10mB
1mmB
1mmB
XB
111
YB
111
ZB
110
100B W
),,( r
S
Distance Coding
Directional Coding
Input parameters Outputs
(NFC HOA)
Input Signal
Positional Encoding
11 2 1/ 2 2
NFC( / , / ) 1 2 111 2
1 11 2 21
1 ' ' 1 '( )
1 ' '1 '
mq qm
c R cm mq q
q
b z b z b zH z g
a z a za z
(for odd order m)
Computation of directional encoding gains Ymn(,)
o Efficient, recursive algorithm
o Virtually unlimited order
A complete positional coding scheme
Illustration of sound field reconstruction
Outside virtual source:oQuite efficient reconstruction
oBetter than Wave Field Synthesis
o[Daniel et al, AES114]
Becomes easier when virtual source gets closer to the real ones
Enclosed virtual source:oFull reconstruction physically impossible anyway
oLarge amount of energy at low frequencies
oStrong interference beyond the virtual source distance
oRight direction of propagation ( WFS)
Gaussian-modulated sine pulse(fc = 500 Hz)
Frequency domain: Time domain:
Other consequences and applications
HOA recording systems become practicableo …by introducing NF compensation at the stage of the mic signal processingo otherwise: equalization filters are unstable [Daniel et al, AES114] and natural
sound fields cannot be physically representedo 4th order microphone prototype: being experimented at FTR&D Labs
Accurate binaural synthesis of close sourceso “Virtual Ambisonics”
= head-centred ambisonics + binaural synthesis of virtual loudspeakersSupports 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 doesn’t support rotations once the encoding is done
Conclusions
Recall of some HOA fundaments and propertieso Powerful mathematical approach
o Highly versatile 3D sound field representation
New: positional coding completed by distance codingo Efficient digital Near Field Control filters
o Take care of the special case of enclosed sources
A New, Viable HOA format : NFC HOAo It enables all HOA nice features considering natural/realistic sound fields
o It doesn’t necessarily interest only systems with very numerous loudspeakers
Work in progress
Evaluation of holophonic sound imaging over 48 loudspeakerso Up to 15th order Ambisonics
o Comparison of HOA and WFS for outside and enclosed sources
o In the context of the CARROUSO project
Experimentation of a 4th order ambisonic microphoneo 32 capsules over a sphere
Specification of a generic HOA formato 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