Reduction of Additive Noise in
the Digital Processing of Speech
Avner Halevy
AMSC 664
Final Presentation
May 2009
Dr. Radu Balan
Department of Mathematics
Center for Scientific Computation and Math. Modeling
1
Background and Goal
• Digital speech signals
• Clean signals are degraded by noise
– From environment
– From processing (recording, transmitting, etc.)
• Speech enhancement: reduce noise without
distorting original (clean) signal
Scope and Goal
•
•
•
•
Focus on additive white Gaussian noise
Improve quality and intelligibility
Use short time analysis (frames)
Explore two algorithms:
– Spectral Subtraction
– Iterative Wiener Filtering
• Test objectively using TIMIT
3
Spectral Subtraction
• Estimate the magnitude of the noise spectrum
when speech is absent
• Subtract the estimate from the magnitude of
the spectrum of the noisy signal
• Keep the noisy phase
• Inverse Fourier to obtain enhanced signal in
time domain
4
Spectral Subtraction
y ( n)  x ( n)  d ( n)
Y ( )  X ( )  D( )
Y ( )  Y ( ) e

i
y
( )
p 1/ p
p

ˆ
X ( w)   Y ( )  Dˆ ( ) 


Xˆ ( )  Xˆ ( ) e

i
y
( )
xˆ (n)  Inverse Fourier { Xˆ ( )}
5
Wiener Filter - Theory
y ( n)  x ( n)  d ( n)
xˆ (n) 

 h(k ) y(n  k ),    n  
k  
e(n)  x(n)  xˆ (n), minimize
Pxx ( )
H ( ) 
Pxx ( )  Pdd ( )

E e 2 ( n)

Pxx ( )
 ( )
H ( ) 
, where  ( ) 
1   ( )
Pdd ( )
6
Iterative Wiener - Theory
V ( z) 
g
1  k 1 ak z
p
k
all - pole model
p
x(n)   ak x(n  k )  gw(n) time domain
k 1
Pxx ( ) 
g2
1   kp1 ak e  jk
2
Estimate a, x iterativel y using two step linear procedure :
1. Find argmax p a | x  (using linear prediction )
a
2. Use estimate for a to find argmax p ( x | a ) (using WF)
x
7
Implementation, Validation, Testing
• Both algorithms were implemented in
MATLAB on a standard PC
• Implementation validated using zero noise,
stability ensured using small nonzero noise
• Testing based on TIMIT
• Main objective measure used: segmental SNR
Noisy
Clean
Testing
9
Comparison of SS and IW
10
Iterative Wiener
Spectral Subtraction
Comparison of SS and IW
11
Comparison of Results
12
Comparison of Results
Comparison of Results
Convergence of IW: Female, 1st sent.
Convergence of IW: Female, 2nd sent.
Convergence of IW: Male, 1st sent.
Summary of Iteration Results
Conclusions
• Objectively, IW produced better results
• Subjectively, both methods suffer from severe
artifacts (musical noise)
• Possible improvement by more sophisticated
noise estimation
Questions?
Bibliography
• [1] Deller, J., Hansen, J., and Proakis, J. (2000) Discrete Time Processing
of Speech Signals, New York, NY: Institute of Electrical and Electronics
Engineers
• [2] Quatieri, T. (2002) Discrete Time Speech Signal Processing, Upper
Saddle River, NJ: Prentice Hall
• [3] Loizou, P. (2007) Speech Enhancement: Theory and Practice, Boca
Raton, FL: Taylor & Francis Group
• [4] Rabiner, L., Schafer, R. (1978) Digital Processing of Speech Signals,
Englewood Cliffs, NJ: Prentice Hall
• [5] Vaseghi, S. (1996) Advanced Signal Processing and Digital Noise
Reduction, Stuttgart, Germany: B.G. Teubner
• [6] Lim, J. and Oppenheim, A.V. (1978) All-pole modeling of degraded
speech, IEEE Trans. Acoust. Speech Signal Process., 26(3), 197-200
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