Explicit expressions for the second order statistics of cepstral components representing
clean and noisy signal waveforms are derived. The noise is assumed additive to the signal,
and the spectral components of each process are assumed statistically independent complex
Gaussian random variables. The key result developed here is an explicit expression for the
cross-covariance between the log-spectra of the clean and noisy signals. In the absence of
noise, this expression is used to show that the covariance matrix of cepstral components
representing a vector of N signal samples, approaches a fixed, signal independent,
diagonal matrix at a rate of 1/(N*N). In addition, the cross-covariance expression is
used to develop an explicit linear minimum mean square error estimator for the clean
cepstral components given noisy cepstral components. Recognition results
on the ten English digits using the fixed covariance and linear
estimator are presented.
* Joint work with Dr. Mazin Rahim of AT&T Labs.
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Yariv Ephraim received the D.Sc. in Electrical Enginering in 1984 from the
Technion-Israel Institute of Technology. He was a Research Scholar at
Stanford University from 1984 through 1985, and a Member of Technical
Staff at AT&T Bell Laboratories from 1985 until 1993. He has been with
George Mason University since 1991 where he currently is an Associate
Professor of Electrical and Computer Engineering. His current research
interests are statistical signal processing with applications to speech
signals and array processing. He was elected Fellow of the Institute of
Electrical and Electronic Engineers in 1994.