1. Open-Loop Dereverberation of Multichannel Room Impulse Responses Bowon Lee, Mark A. Hasegawa-Johnson, and Camille Goudeseune Department of Electrical and Computer Engineering Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign

2. Audio Display for a Virtual Reality Theater (Beckman Cube)

3. Audio Demo (Plywood Cube)

4. 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

5. Problem Formulation  Consider a Multichannel System: L sound sources and M control points

6. Problem Formulation (Continued)  Transfer function G from L sound sources to M control points

7. Problem Formulation (Continued)  Inverse transfer function H from M desired control points to L sound sources

8. Problem Formulation (Continued)  Multichannel System from M desired control points to M actual control points

9. 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 : ^ ^

10. Problem Formulation (Continued)  How to Estimate the Room Impulse Responses?  How to Find the Inverse Transfer Function H ? ^

11. Estimation of the Room Impulse Responses: Image Source Method  Two-Dimensional Illustration

12. Image Source Method (Continued)  : Reflection coefficient of the wall (uniform)  : Index of the image source location  : Distance between the image source and receiver  : Impulse arrival time

13. 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

14. Computing the Inverse Transfer Function: Regularization  Add a small constant β to the diagonal components before the inversion :

15. Computing the Inverse Transfer Function: Modeling Delay  Delay the inverse transfer function to make it a delayed causal sequence

16. Computing the Inverse Transfer Function Example in 1-D Case

17. Experiment: 2 X 2 (L = M = 2) Case  Starter Pistol as a Sound Source : Best Approximation of a Point Source

18. SPL of a Starter Pistol

19. Comparison of Measured and Simulated Room Impulse Responses (First 20 ms)

20. Comparison of Measured and Simulated Room Impulse Responses (After 100 ms)

21. One More Problem: Image Source Method is only Accurate for t < 100 ms

22.  Solution: Apply a Tapering Window

23. Results: 12 dB Dereverberation

24. Summary  Open-Loop Inversion of Room Impulse Responses  Estimation of Room Impulse Responses by Image Source Method  Measurement of Room Impulse Responses using a Starter Pistol  12 dB Dereverberation