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

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?

Review of Previous

Basic Principle

Input signal generationAR (Auto Regressive) processPrediction filtersPrediction errorEstimated AR process

Review of Previous

Something about Mathematics

1,0 ,1 ,

0

( ) ( ) ...m

k mi i i i i m

k

H z h k z h h z h z

Transfer functions

Prediction Error

1 1( ) T Tn ne n x h x Hw

Size of the matrix H full row-rank matrix =>> (m+L)x2L and2L≥m+L

The AR polynomial1

1( ) 1 { ... }NNa z a z a z

Review of Previous

Why use multi-channel

1 2[ , ]H H H

2 21 1min {| ( ) | } min {| | }T T

n nE e n E x h x Hw

1 1 1 1( { } ) { }T T T Tn n n nw H E x x H H E x x h

Necessary and sufficient condition for existing of generalized inverse matrix

Basic Algorithm

Input signal generation

1T

n n nx C x e

1,0 ( )e h e n

1 1 1( { }) { }T Tn n n nQ E u u E u u

Prediction error

From the same eigenvalue λ of matrix C & Q

Here C is the companion matrix

and [ ( ),0...,0]Tne e n

Basic Algorithm

Calculate Q with the signal received at the microphone

1 1 1( { }) { }T Tn n n nQ E u u E u u

The first column of the matrix Q give us the prediction filter coefficients

11( )T Tw H HH Ch 1( )T TQ H HH CHas matrix

Calculate the prediction error

1 1( ) T Tn ne n x h x Hw

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

( , ) ( , )c Cf Q f C

Simulation

Environment Room Transfer functions

Simulation conditionsLength of impulse response 50 tapsNumber of input signal samples 45,000Length of generating AR process 21 tapsSampling frequency 16 kHzLength of prediction filters 50 tapsLength of estimated AR process 101 taps

Simulation

Room Transfer Function

Reflection coefficient of the walls 0.8 Different positions of microphones->different impulse response Length of the impulse response?

Simulation

Speech Simulation

AR process Sound “U” is used for the estimation of AR parameters

Simulation

Speech Simulation

Simulation

Intermediate Results

“reverberated “ signal Red-spectrum of the microphone signal Blue-spectrum of the input speech signal

Simulation

Final Result

whitening of the signal-output white noise estimated AR coefficients

Simulation

Final Result

Good “blind” AR parameter estimation! Dereverberated signal

Simulation

Statistics

Results:• SDRBefore =3.22• SDRAfter =51.48

Simulation

For Real speech signal

Simulation

Intermediate result

“reverberated ” signal Red-spectrum of the microphone signal Blue-spectrum of the input speech signal

Simulation

Final result

Good “blind” AR parameter estimation! Dereverberated signal

Simulation

Statistics

Results:• SDRBefore =3.97• SDRAfter =20.33

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