Sydney, Australia, 23, Aug., 2010

Blind directivity estimation of a sound source in a room
using a surrounding microphone array

Takuma Okamoto(1)(2), Yukio Iwaya(1)(3) and Yôiti Suzuki(1)(3)(1) Research Institute of Electrical Communication(2) Graduate School of Engineering(3) Graduate School of Information Sciences
Tohoku University, Japan1

Introduction: editable sound field system
Sensor network technologies innear future

Editable sound field system

multi-channel microphone array system
not only recording sound fieldbut also extracting sound field properties

Contribution of Editable soundfield system
Decomposing sound field properties
accurately from recording soundinformation
Rendering extracted sound properties
not only original sound field
but also modified sound field

1. Recording sound field
Signal Processing

Signal Processing

2. Decomposing sound field properties- sound source positions- original sound source- directivities of sound sources- early reflection- reverberation

3. Rendering extracted sound properties
not only original sound field [1][1] S. Ise 1999

but also modified sound field2

Design of recording sound field system
Surrounding 157 microphone array

T. Okamoto et al. 2007

157 microphones is installed on all four walls and the ceiling
All microphones are installed 30 cm inside from all four walls and the ceiling
They are separated from each other by 50 cm

Enable synchronous recording of 157 channels at the sampling frequencyof 48 kHz with the linear PCM audio format using 4 PCs and 14 units ofA/D controlled by PureData

B & K Type 4951

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Research Aim:
estimation of directivity of a sound source
in a reverberant environment
Directivity of sound source
Sound sources in actual environments have no omni-directional feature
but they do have directivity in radiation
human voice, instrumental sound and so on...

it is important to consider the directivity of a sound source according to alistening point when synthesizing a high-definition 3D sound field

Previous studies for estimating directivity of sound source
In almost researches, directivity was recorded only in anechoic enviromnente.g., R. Jacques et al. 2005, B. FG Katz et al. 2007 and M. noisternig et al. 2009

Nakadai et al. was estimated only front direction of the sound source in areverberant environment (2005)

Our research aim
Developing method for estimating and decomposing all-around directivityof a sound source in a reverberant environment along with information of
the estimated source position and the original sound signal
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Proposed 1: Definition of Directivity modelof a sound source in a room
SIMO (Single-Input Multiple-Output) model including directivity ofa sound sources(n) : Source signald(θi , n): each directivity of a direction θihRi (n): each reverberant componentr(θi ) : each distance between
the source and each microphone ixi (n) : each observed signal at
microphone ix(n) =∞�k=0s(n) ∗ d(θk , n) ∗ h(θk , n) = s(n) ∗∞�∞�

k=0{d(θk , n) ∗ h(θk , n)}x(n) = s(n) ∗ {d(θ0 , n) ∗ h(θ0 , n) +d(θk , n) ∗ h(θk , n)}
k=1
��
∞
�
1x(n) = s(n) ∗ d(θ0 , n) ·+ d(θ0 , n) ∗ h� (θ0 , n) +d(θk , n) ∗ h(θk , n)r(θ0 )
k=1==s(n) ∗ {hD (n) + hR (n)}s(n) ∗ h(n)5Proposed 2: Decomposition of room transfer function of
directivity and reverberant component
Relationship between directivity andreverberant component
If sound source is omni-directional feature
direct sound component is only first response

When sound source has a directivity
directivity component is first to several samples
responses
hDi (n)hRi (n)Decomposition of directivity and reverberant component
1. Estimating total impulse response
Blind identification or dereverberation method
2. hDi (n) can be extracted as the early response

from the first response to time t = 2d/c
cutting impulse response as the first t response3. Amplitude correction corresponding to eachdistance di (n) = ri hDi (n)each distance is estimated from estimated soundsource position

r6

Estimating room impulse response using
estimated sound source signal
Estimating room impulse response
Blind identification is difficult problem
Estimating room impulse response using estimated sound source andreceived signals
Sound source signal can be estimated by a dereveberation method
We proposed a dereverberation algorithm, White-LIMEĥi (n) = (E{ŝ(n)ŝT (n)})−1 E xi (n)s(n)xi (n − 1)s(n − 1)..
.
xi (n − M + 1)s(n − M + 1)






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Directivity measurement
in an anechoic chamber
Directivity measurement as impulse response
1-way loudspeaker (Micropure; AP5001)
Measurements were taken from 0 deg to 180 deg in horizontal direction
with a clockwise rotation by 15 deg in an anechoic chamber
Time Stretched Pulse (TSP) signal was used for measurement
The impulse responses for 13 directions were measured

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Room impulse response measurement
in a room
Measurement of room impulse response which includes both
directivity of a sound source and reverberant component
Sound signal and loudspeaker are the same as an anechoic measurement
Measurement was taken by using surround 157-microphone array9

Recording conditions
Two patterns of the arrangements of the loudspeaker
28 microphones (z = 1.0 m) in the room
The reverberation time of this room was about 0.15 s
The order of the room impulse responses was 7200

Pattern A

Pattern B
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Simulations
Calculating 157 received signals xi (n)Convolving the source signal s(n) to each measured impulse response hi (n)The source signal was a musical piece (2.7 s) from RWC music database
The measured impulse responses were downsampled 48 kHz to 44.1 kHzThe order of all responses was shortened from 7200 to 6615

Estimating impulse responses
The estimated source signal ŝ(n) was obtained using White-LIME
Each estimated impulse response ĥi (n) was calculated from each observed
signal xi (n) and the estimated source signal ŝ(n)The average of the score of the SDR of each original response ĥi (n) was 62.6 dB
The estimated responses can be inferred accuratelyDecomposing directivity from room impulse responses
The distance between each microphone and the wall was 30 cm
The clipping length of each estimated response was approximately
44,100 ×2 × 0.6/340 ≈ 78 taps
Amplitude correction was taken from estimated sound source position andeach microphones
11Results ofAmplitude-frequency characteristics

Measured impulse
response (A)Estimated directivity (A)Measured impulse
response (B)Estimated directivity (B)Original directivity

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Results of 2 kHz in the 1/3 octave-band03300303003306020270240303006060 [dB]4090

12020270240

60 [dB]

4090

120033021030300

60
20270240

60 [dB]

4090150180

Original directivity

210150180

Measured impulse
response (A)Estimated directivity (A)00120210150
180

330

330

30300

300

60
20270

240

60

60 [dB]

4090120
210

30150

20270

240

60 [dB]4090

120
210150180180Measured impulse
response (B)Estimated directivity (B)13Results of similarity analysis
Confirming the effectiveness of our proposed method
Similarity based on the nearest neighbor method
Pattern vector
SimilarityP (f ) = (xθ1 (f ), xθ2 (f ). · · · , xθN (f ))|P1 (f ) − P2 (f )|S(P1 (f ), P2 (f )) = 1.0 −|P1 (f )|Pattern A

Pattern B

Our proposed method can estimate directivity patterns that closely
resemble real ones up to around 16 kHz

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Concluding remarks
Conclusions
Estimating directivity of a sound source in a reverberant environment
Using information of the estimated source position and the original sound signal
Cutting estimated impulse responses based on the distance between eachmicrophone and nearest wall
The simulation results demonstrate the availability of our proposed method

Future works
Our method presents a problem in estimating the sound source directivity
when the walls and microphones are close to each other
Widening the applicability of our pro- posed method is development of a method
extracting the early part from an impulse response with overlapped reflections

Estimating directivity of a sound source not only 2-dimensional direction
but also 3-dimensional direction for 3D sound field analysis and synthesis

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