Log spectral estimation for stationary and nonstationary processes

This research is concerned with two log spectral estimators in the context of both stationary and nonstationary signals. They differ because in one smoothing is realized before the logarithmic transformation, while the other is smoothed in the logarithimc domain. It is shown that for stationary signals the two estimators are similar, differing in expected value by only a universal constant. The first estimator, however, is smoother. For nonstationary signals, the estimators are biased by different amounts dependent upon the nonstationarity. The difference between the estimators is shown to be a sensitive test for nonstationarity. The estimators are used in the analysis and implementation of two solutions to the problem of blind deconvolution. It is found that the methods are equivalent for stationary signals, bu differ markedly for nonstationary signals in the presence of stationary background noise. Recommendations are made for the practical digital implementation of the practical digital implementation of the log spectral estimators.