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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 !