1. Project-Final Presentation Blind Dereverberation Algorithm for Speech Signals Based on Multi-channel Linear Prediction Supervisor: Alexander Bertrand Authors: Dusko Karaklajic Kong Fanxiao Dec.2008

2. Review of Previous Our Goals :  To solve the reverberation problem  Automatic Speech Recognition (ASR) problem  Room transfer function?  Title “Blind” –why?  Whitening of a signal?

3. Review of Previous Basic Principle  Input signal generation  AR (Auto Regressive) process  Prediction filters  Prediction error  Estimated AR process

4. Review of Previous Something about Mathematics  Transfer functions  Prediction Error  Size of the matrix H full row-rank matrix =>> (m+L)x2L and2L≥m+L  The AR polynomial

5. Review of Previous Why use multi-channel  Necessary and sufficient condition for existing of generalized inverse matrix

6. Basic Algorithm  Input signal generation  Prediction error  From the same eigenvalue λ of matrix C & Q Here C is the companion matrix and

7. Basic Algorithm  Calculate Q with the signal received at the microphone  The first column of the matrix Q give us the prediction filter coefficients as matrix  Calculate the prediction error

8. Basic Algorithm  Calculate the characteristic polynomial of Q to estimated AR  Recover the input signal by filtering the prediction error with the estimated AR parameters We can prove λ(Q)=λ(C) λ is the eigenvalue

9. Simulation Environment  Room Transfer functions  Simulation conditions Length of impulse response 50 taps Number of input signal samples 45,000 Length of generating AR process 21 taps Sampling frequency 16 kHz Length of prediction filters 50 taps Length of estimated AR process 101 taps

10. Simulation Room Transfer Function  Reflection coefficient of the walls 0.8  Different positions of microphones->different impulse response  Length of the impulse response?

11. Simulation Speech Simulation  AR process  Sound “U” is used for the estimation of AR parameters

12. Simulation Speech Simulation

13. Simulation Intermediate Results  “reverberated “ signal  Red-spectrum of the microphone signal  Blue-spectrum of the input speech signal

14. Simulation Final Result  whitening of the signal-output white noise  estimated AR coefficients

15. Simulation Final Result  Good “blind” AR parameter estimation!  Dereverberated signal

16. Simulation Statistics Results: SDR Before =3.22 SDR After =51.48

17. Simulation For Real speech signal

18. Simulation Intermediate result  “reverberated ” signal  Red-spectrum of the microphone signal  Blue-spectrum of the input speech signal

19. Simulation Final result  Good “blind” AR parameter estimation!  Dereverberated signal

20. Simulation Statistics Results: SDR Before =3.97 SDR After =20.33

21. Conclusions  Expected results vs. practical results  non-whitened output signal  Limitations?  Length of impulse response vs. Q matrix length vs. computational time  Simulated vs. Real Speech Signal  Noise free environment- not realistic