open-loop dereverberation of multichannel room impulse responses bowon lee, mark a....
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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
Audio Display for a Virtual Reality Theater (Beckman Cube)
Audio Demo (Plywood Cube)
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
Problem Formulation
Consider a Multichannel System:
L sound sources and M control points
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
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
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
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
^
^
Problem Formulation (Continued)
How to Estimate the Room Impulse Responses?
How to Find the Inverse Transfer Function H ?^
Estimation of the Room Impulse Responses: Image Source Method
Two-Dimensional Illustration
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
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
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
Computing the Inverse Transfer Function: Modeling Delay
Delay the inverse transfer function to
make it a delayed causal sequence
)(ˆ)(~ jDjj eHeeH
Computing the Inverse Transfer Function
Example in 1-D Case
Experiment: 2 X 2 (L = M = 2) Case
Starter Pistol as a
Sound Source :
Best
Approximation of a
Point Source
SPL of a Starter Pistol
Comparison of Measured and Simulated Room Impulse Responses (First 20 ms)
Comparison of Measured and Simulated Room Impulse Responses (After 100 ms)
One More Problem: Image Source Method is only Accurate for t < 100 ms
)(ˆ)(~ / tgetg t
One More Problem: Image Source Method is only Accurate for t < 100 ms
Solution: Apply a Tapering Window
Results: 12 dB Dereverberation
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