On second order statistics and linear estimation of cepstral coefficients

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-2. 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.