3rd International Symposium on Ambisonics & Spherical
Acoustics@Lexington, Kentucky, USA, 2nd June 2011

Evaluation of a new Ambisonic decoder forirregular loudspeaker arrays using interaural cues

J. Treviño1,2), T. Okamoto1,3), Y. Iwaya1,2) and Y. Suzuki1,2)
1) Research Institute of Electrical Communication, Tohoku University, Japan
2) Graduate School of Information Sciences, Tohoku University, Japan
3) Graduate School of Engineering, Tohoku University, Japan1

Motivation
Implementation of 3D audio need for systems that can convey
the illusion of being immersed in a different environment
Telepresence, communications, entertainment, etc.

Fast trend towards the adoption of 3D systems
Mainstream use of multichannel audio
Sound field reproduction systems can enhance the presentationof 3D multimedia content
Ambisonic encodings of sound fields are ideal for applications
where a specific loudspeaker distribution cannot be assumed
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Decoding of Ambisonic data

Decoding is usually based on the pseudo‑inverse of a matrixof spherical harmonic functions
Requires a uniform sampling of the sphere

Regular array

Irregular array

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Drawbacks of standard decoders
Numerical instability when using irregular arrays
The pseudo-inverse is not a continuous operation
Re-encoding matrices for irregular loudspeaker distributions tend to be illconditioned

Suboptimal solutions when there are more loudspeakers
than ambisonic channels
Decoding becomes an underdetermined problem
The pseudo-inverse picks the solution with minimum Euclidean norm (nota meaningful parameter for human listeners)

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A new approach to Ambisonic decoding
Can be used to decode ambisonic data for reproduction overirregular arrays
Decodes the ambisonic data in two stages:
Decodes the non-problematic ambisonic channelsStabilizes the reconstruction error by imposing a constraint on its radialderivative+C (k)

p(k)

B(k)
TG (k)+Tp(k) = [CM ixed−order + G (k)]B(k)5Proposed decoder for irregular arrays
Generalized mixed-order ambisonics
Decode the largest combination of channels that result in a wellconditioned re-encoding matrix

Stabilization of the reconstruction error
Find the decoding gains that minimize the gradient of the reconstruction
error� ��∂G = arg min��ψ˜k (r, θ, ϕ) − φk (r, θ, ϕ)G ∂r−���esYmn (θs , ϕs ) ��Gmn (k)|�r−�r|sm=0 n=−mN
��sm
�

−ik|�
r −�
rs |

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The new decoder as a regularization
schemeConstraining the radial derivative of the reconstruction error
can also lead to a regularized least-squares problem:���∂�� �(k, �r)� = �L · G − d� ≤ ρ� ∂r�Constant term: d ≡ ∇[ψ̃(k, �r) − φ(k, �r)] · r̂|�r| − |r�s | cos(�r, r�s )Difference operator: Ls (k) ≡|�r − r�s |�1+ ik|�r − r�s |�7Evaluation
Our previous research has focused on the physical accuracy
with which the sound field is re-created
Implementation of 3D audi need for systems that can convey
the illusion of being immersed in a different environment
Interaural level difference
Interaural phase difference

Interaural cues derived fromthe binaural rendering ofambisonic recordings
Three virtual loudspeaker arrays
SAMRAI’s dummy head HRTF measurements

Dummy head SAMURAI
Koken Co., Ltd.
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Measurement of HRTFs
Measurements were made using a spherical loudspeakerarray housed in an anechoic chamber
All azimuth angles from -175 deg. to 180 deg. in increments of 5 degrees
Available for elevation angles between -80 deg. and 90 deg. in incrementsof 10 degrees

Spherical loudspeaker array in Tohoku University

9Regular, 42-channel loudspeaker array

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Results for the regular, 42-channel
loudspeaker array (azimuth)

Varying azimuth angle (elevation: 0 deg.)11

Irregular, 42-channel loudspeaker array

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Results for the irregular, 42-channel
loudspeaker array (azimuth)

Varying azimuth angle (elevation: 0 deg.)13

Irregular, 157-channel loudspeaker array
The proposed decoder was tested through the computer
simulation of a 157-channel, irregular loudspeaker array

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Results for the irregular, 157-channel
loudspeaker array
Simulation of a 500 Hz plane wave incident at an azimuth of
30 degrees

IdealStandard
decoder

Proposed
decoder-1 Sound pressure (normalized) 115

Results for the irregular, 157-channel
loudspeaker array (azimuth)

Varying azimuth angle (elevation: 0 deg.)

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Results for the regular, 157-channel
loudspeaker array (elevation)

Varying elevation angle (azimuth: 0 deg.)

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Concluding remarks
Two drawbacks to standard ambisonic decoders
Numerical instability
Suboptimal solutions

Introduced a new ambisonic decoding method
Weaker regularity constraints than standard decoders

Better solutions for human listeners
Evaluation using a three virtual loudspeaker arrays
Improved reconstruction of interaural cues (ILD, IPD)
Reduced dependence on the specific distribution of the loudspeakers

18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

19Demonstration of 3D audio-visual display
Hit the drum in the gymnasium
Vision signals: Stereo video recording using FUJIFILM FINEPIX REAL 3D W1sound signals: calculating by simulation and decoding by 5th order HOA

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Implementation of sound field recording
system based on HOA
T. Okamoto et al., Proc. SOIM-GCOE 2010

HOA recording system using a 121 spherical microphone array
9th order decoding
Completely synchronous 121-audio recording system using Digital Electric
Condenser Microphone (Digital ECM) and FPGA board
Sampling frequency is 48 kHz
4th Delta-Sigma modulation is used for 1-bit signals

Controlled by LabVIEW (National Instruments) in Windows XP (SP3)21

Results for the regular, 42-channel
loudspeaker array (elevation)

Varying elevation angle (azimuth: 0 deg.)23

Results for the regular, 42-channel
loudspeaker array (elevation)

Varying elevation angle (azimuth: 0 deg.)24

Irregular, 157-channel loudspeaker array25

Results for the regular, 157-channel
loudspeaker array (elevation)

Varying elevation angle (azimuth: 0 deg.)

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