Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A....
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![Page 1: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/1.jpg)
Open-Loop Dereverberation of Multichannel Room Impulse Responses
Bowon Lee, Mark A. Hasegawa-Johnson, andCamille Goudeseune
Department of Electrical and Computer EngineeringBeckman Institute for Advanced Science and Technology
University of Illinois at Urbana-Champaign
![Page 2: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/2.jpg)
Audio Display for a Virtual Reality Theater (Beckman Cube)
![Page 3: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/3.jpg)
Audio Demo (Plywood Cube)
![Page 4: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/4.jpg)
Introduction
Free-Field Audio Display
Sound Control at Multiple Points
Open-Loop Inversion of Room Impulse Responses
Image Source Method to Estimate Room Impulse
Responses
![Page 5: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/5.jpg)
Problem Formulation
Consider a Multichannel System:
L sound sources and M control points
![Page 6: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/6.jpg)
Problem Formulation (Continued)
)(
)(
)()(
)()(
)(ˆ
)(ˆ 1
1
1111
zV
zV
zGzG
zGzG
zX
zX
LMLM
L
M
GVX ˆ
Transfer function G from L sound
sources to M control points
![Page 7: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/7.jpg)
Problem Formulation (Continued)
)(
)(
)()(
)()(
)(
)( 1
1
1111
zX
zX
zGzH
zHzH
zV
zV
MLML
M
L
Inverse transfer function H from M desired
control points to L sound sources
HXV
![Page 8: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/8.jpg)
Problem Formulation (Continued)
Multichannel System from M desired control point
s to M actual control points
)(
)(
)()(
)()(
)()(
)()(
)(ˆ
)(ˆ 1
1
111
1
1111
zX
zX
zHzH
zHzH
zGzG
zGzG
zX
zX
MLML
M
MLM
L
M
GHXX ˆ
![Page 9: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/9.jpg)
Problem Formulation (Continued)
We do not know the transfer function G,
a matrix of exact room impulse responses
Create inverse H using the estimation of the
room impulse responses G instead of G :
XHGX ˆˆ
^
^
![Page 10: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/10.jpg)
Problem Formulation (Continued)
How to Estimate the Room Impulse Responses?
How to Find the Inverse Transfer Function H ?^
![Page 11: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/11.jpg)
Estimation of the Room Impulse Responses: Image Source Method
Two-Dimensional Illustration
![Page 12: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/12.jpg)
Image Source Method (Continued)
)()(||||||
lmnl m n lmn
nml
td
rtg
r
lmnd
lmn
),,( nml
: Reflection coefficient of the wall (uniform)
: Index of the image source location
: Distance between the image source and receiver
: Impulse arrival time
![Page 13: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/13.jpg)
Computing the Inverse Transfer Function
Room impulse responses are non-minimum
phase in most cases
Therefore, they are not exactly invertible
Solution: Use regularization and modeling
delay
![Page 14: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/14.jpg)
Computing the Inverse Transfer Function: Regularization
Add a small constant β to the diagonal compon
ents before the inversion :
TT GIGGH ˆ)ˆˆ(ˆ 1
![Page 15: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/15.jpg)
Computing the Inverse Transfer Function: Modeling Delay
Delay the inverse transfer function to
make it a delayed causal sequence
)(ˆ)(~ jDjj eHeeH
![Page 16: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/16.jpg)
Computing the Inverse Transfer Function
Example in 1-D Case
![Page 17: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/17.jpg)
Experiment: 2 X 2 (L = M = 2) Case
Starter Pistol as a
Sound Source :
Best
Approximation of a
Point Source
![Page 18: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/18.jpg)
SPL of a Starter Pistol
![Page 19: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/19.jpg)
Comparison of Measured and Simulated Room Impulse Responses (First 20 ms)
![Page 20: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/20.jpg)
Comparison of Measured and Simulated Room Impulse Responses (After 100 ms)
![Page 21: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/21.jpg)
One More Problem: Image Source Method is only Accurate for t < 100 ms
![Page 22: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/22.jpg)
)(ˆ)(~ / tgetg t
One More Problem: Image Source Method is only Accurate for t < 100 ms
Solution: Apply a Tapering Window
![Page 23: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/23.jpg)
Results: 12 dB Dereverberation
![Page 24: Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and.](https://reader035.fdocuments.us/reader035/viewer/2022070412/56649f0e5503460f94c22df1/html5/thumbnails/24.jpg)
Summary
Open-Loop Inversion of Room Impulse Responses
Estimation of Room Impulse Responses by Image So
urce Method
Measurement of Room Impulse Responses using a S
tarter Pistol
12 dB Dereverberation