A TIME-DOMAIN INTERPRETATION OF THE KL SPECTRUM

Recently an information theoretic spectrum minimizing the frequency-domain Kullback-Leibler information number has been proposed. Based on the KL spectrum a method of modifying a spectrum estimate has been sugested. Some numerical examples have illustrated that the KL spectrum estimate is superior to the initial estimate, i.e., the autocovariances obtained by the inverse Fourier transformation of the KL spectrum estimate are closer to the sample autocovariances of the given observations than those of the initial spectrum estimate. In this correspondence, it is shown that a Gaussian AR(p) process is the closest in the time-domain Kullback-Leibler sense to independently and identically distributed normal random variables subject to the first p + 1 autocovariance constraints. It gives a rationale to the existence of the KL spectrum.