Single-Channel Speech Enhancement in Both White and Colored Noise

Xin Lei

Xiao Li

Han Yan

June 5, 2002

Outline

Introduction Methodology

• Spectrum subtraction • Wiener filtering • Kalman filtering

Experiments & Results Conclusion

Introduction

Concepts: Speech enhancement

Introduction

Block processing

Introduction

Applications• Voice communication system• Speech recognition system

Keywords • White noise• Colored noise

Methodology

Spectrum subtractionWiener filteringKalman filtering

Method I: Spectrum Subtraction

Assume we know the psd of noise

( ) ( ) ( ) ( ) ( ) ( )y n x n v n Y X V 2 2 2 * *( ) ( ) ( ) ( ) ( ) ( ) ( )Y X V X V X V

2( ) [ ( ) ]vP E V

2 2 2 2ˆ ( ) ( ) ( ) ( ) ( )vX Y E V Y P

)(ˆ)(ˆ

)(arg)(ˆ)(ˆ

1

XFnx

YXX

Diagram forSpectrum Subtraction

FFTNoisy speech

y(n)

Phase

IFFT

Subtraction of

2

12

Enhanced speech

x(n)

)(wPv

Method II: Wiener Filtering

Wiener Filter H(w)][][][ nvnxny ][nx

)()()(, wPwHwP YYX

•Cross Power Spectral Density:

)()(, wPwP XYX

)()(

)(

)(

)()(

wPwP

wP

wP

wPwH

VX

X

Y

X

•Signal and Noise are independent:

Wiener Filtering (cont’d)

If ,)()( wPwP VX 0)( wH

If ,)()( wPwP VX 1)( wH

•Wiener filter minimizes mean square error:

2][ˆ][ nxnxE

•H(w) weights spectrum according to different frequencies:

Wiener Filter Diagram

estimateNoisy speech y(n)

Enhancement speech x(n)

)(wPv

estimate)(wPy

)(ˆ wPv

)(ˆ wPy

)(ˆ)(ˆ)(ˆ

)(wP

wPwPwH

y

vy

Wiener Filter

Method III: Kalman Filtering

AR model of speech Prediction Observation

Goal: MMSE estimation Basic idea:

Estimation = Prediction + Gain (Observation - Prediction)

][][][

][][][1

nvnxny

nwinxanxp

ik

],[ˆ 21 tttt yyyxEx

)ˆ(ˆˆ

ˆˆ

111111

1

ttT

tttttt

tttt

xCyKxx

xAx

Parameter Estimation

Need to know Assume prior knowledge of Estimate speech parameters using Yule-

Walker Equation.

To achieve MMSE

22 ,, vA 2v

2, A

0

0

1

]0[]1[][

]1[]0[]1[

][]1[]0[ 2

1

w

pa

a

rprpr

prrr

prrr

][][ nrnr y

Kalman Filtering of Colored Noise

Colored noise has the same state-space AR model as speech does.

Assume prior knowledge of noise model parameters Estimate speech model parameters using Yule-

Walker Equation. To achieve MMSE,

][][][

][][][;][][][11

nvnxny

nuinvbnvnwinxanxq

ii

p

ii

][][][ nrnrnr vy

Experiments & Results

Experiment SetupComparison of enhancement effects

Experiments Setup

Clean speech Noise simulation SNR: 0dB

Enhancement in White Noise

Enhancement in Colored Noise

Conclusion

Comparisons Three different methods of speech enhancement Nonparametric vs. parametric estimation White noise vs. colored noise

Future work Speech/noise detector Iterative algorithm for Wiener/Kalman filters Recursive algorithm to reduce computation

Thank You !