SOIM-GCOE 10, Sendai, 19 Oct., 2010

Implementation of higher order Ambisonics
recording array with 121 microphones

T. Okamoto(1)(2), Y. Iwaya(1)(3), S. Sakamto (1)(3) and Y. Suzuki(1)(3)(1) Research Institute of Electrical Communication(2) Graduate School of Engineering(3) Graduate School of Information Sciences
Tohoku University, Japan1

Introduction and research aim
Implementation of 3D sound field recording and reproduction
systemRealizing communications with high sense-of-presenceSound field recording and reproduction based onhigher order Ambisonics (HOA)
Highly sound field reproduction around a center of arraythan WFS (Wave Field Synthesis) and BoSC (Boundary Surface Control)

WFS or BoSC

We have already implemented 5th order Ambisonics reproduction
system using 157 loud-speaker array
High definition Ambisonics recording system is required

Today’s topics
Implementation of 3D sound field recording system
Overview of HOA
Designing 121 spherical microphone array
Implementation with 121 Digital Electric Condenser Microphones(ECMs) and FPGA board

Ambisonics
Relationship between
reproduction accuracy
and frequency

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Concept of HOA
Simple example of orthogonal expansion
Taylor expansion
f (x) =∞�f (n) (a)n=0n!

f � (a)f �� (a)f (n) (a)2(x − a) = f (a) +(x − a) +(x − a) + · · · +(x − a)n + · · ·1!
2!
n!
nOrthogonal expansion of sound field information based on
spherical harmonics in HOA
p(kr, θ, φ) =+∞�m=0

im jm (kr)m�n nBmYm (θ, φ)n=−mnSound information is decomposed to expansion coefficients Bm
using
spherical harmonics Ymn (θ, φ) of each direction (θ, φ)Using more higher order m , more accurate sound field is reproduced
0 0�
P(cosϕ)ifn=0,N√m m(2m + 1) (m − |n|)!
nn nYmn (θ, ϕ) =2Nm Pm (cos ϕ) cos nθ if n > 0, Nm =√
4π(m + |n|)!
n −n
2Nm Pm (cos ϕ) sin nθ if n < 0,3

Sound field recording and reproduction
based on HOA system
Aspects of HOA system
Using more higher order m , moreaccurate sound field is reproduced
2More than (m + 1) channels areneeded to encode or decode order mRecording system and reproduction
system are independent each othernBm
HOAmAmbisonics

01234-4-3-2-101234n4

Implementation of 3D audio-visual display
T. Okamoto et al., Proc. IEEE IC-NIDC 2010

Combining HOA system with 3D projection display
Audio system: Completely synchronous 157-loudspeaker array system
Visual system: Stereo shutter technique with acoustic transparent screen
5th order decoding, which is highest order in the world, was realized

5Implementation of HOA recording systemwith more than 100 microphones
Current HOA recording system
Up to 64 channels with up to 6th order encoding
These systems use analog microphones and A/Ds

S. Moreau et al. (32 ch)@Orange Labs

D. N. Zotkin et al. (64 ch)@University of Maryland

A. Parthy et al. (64 ch)@University of Sydney

Our research aim
Implementation of HOA recording system with more than 100 microphones
More than 100 ch system cannot realize when using analog microphones and A/Ds
• Problems: Size of array must be large! Interconnection lines must be huge!
Digital Electric Condenser microphones (ECMs) and FPGA board are introduced6Designing 121 spherical microphone arrayArrangement of microphones
In HOA system, regular arrangement (equal density) is important
Nearly equal density arrangement
is calculated from regular icosahedronbased on polyhedral subdivision→→
methodTotal vertex number is 122
2020 → 42

Radius of sphere3.5 cm+ 80

7 cm

Designed from size of Digital ECMs, interconnectionlines and control board in the sphere1 channel at the bottom is used for interconnection output
Spatial aliasing frequency: 8.9 kHz

Designing of spherical arrangementwith 121 channels

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Spec of 121 spherical microphone array
Estimation of encoding order
In 121 ch system, up to 10th ordercan be calculated (10 + 1)2 = 121
Condition number of encoding matrix
Maximum eigenvalue / minimum eigenvalue

If condition number is less than 20 dB,
stable encoding can be realized
M. Noisternig et al. 2010

Radial functions

Up to 9th order encoding→ highest order in the world

Relationship between radial function ofrigid sphere and encoding order

Wm (kR) = i−m+1 (kR)2 h−�m (kR)
h−�m (kR) : Hankel function
In higher encoding order, sound informationin higher frequency components are much8Implementation using 121 Digital ECMs
and FPGA
121 ch recording system
Controlled by LabVIEW (National Instruments) in Windows XP (SP3)Completely synchronous 121-audio recording system using Digital ElectricCondenser Microphone (Digital ECM) and FPGA board
Sampling frequency is 48 kHz
4th Delta-Sigma modulation is used for 1-bit signals

9Concluding remarks
Conclusions
Implementation of 3D sound field recording system based on HOA
9th order encoding, which is highest order in the world, was realized
Completely synchronous 121-audio recording system using Digital Electric Condenser
Microphone (Digital ECM) and FPGA boardFuture works
System calibration
Acoustical measurement inanechoic chamber using
spherical loudspeaker array

Performance evaluation
Recording sound field in
actual environment andreproducing in our
157-loudspeaker array
Spherical loudspeaker array in R.I.E.C

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Acknowledgements
Mr. Y. Shigeno (HOSIDEN)
for contribution of Digital ECMs

Mr. J. Trevino (in our lab., MC2)
for making the animation movie of rotative
121 spherical microphone array

Mr. J. Matsunaga (in our lab., MC1)for cooperation to take acousticalmeasurements for system calibration

Mr. Y. Sato (in our lab., MC1)for cooperation to record several movies

GCOE program (CERIES)
Kakenhi (no.19001004) from the JSPS

11Signal format at each device
1. 121 Digital ECMs
48 kHz x 64 = 3.072 MHz, 4th ΔΣ modulation, 16 bit

2. Control substrate
Transforming time-division serial datausing Ser/Des communication
3 pairs of Ser/Des transmission
3.072 MHz × 48 = 147.457 bps (1 pair)

3. Data transfer cable
3 pairs of Ser/Des transmission = 442.368 bps

4. Control board
Decomposing time-division serial data tomultipoint parallel data
Input signals to FPGA boardSampling frequency: 3.072 MHz, 1 bit

5. FPGA board
Transforming signals using Cascaded Integrator
Comb (CIC) filter
Sampling frequency: 48 kHz, 16 bit

6. Control PC
Recording 48 kHz x 121 ch data to HDD※SerDes
SERializer/DESerializer
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