project-final presentation blind dereverberation algorithm for speech signals based on multi-channel...
DESCRIPTION
Review of Previous Basic Principle Input signal generation AR (Auto Regressive) process Prediction filters Prediction error Estimated AR processTRANSCRIPT
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