A time-domain interpretation of the KL spectrum

An information theoretic spectrum minimizing the frequency-domain Kullback-Leibler (KL) information number has been proposed by B.S. Choi (IEEE Trans. Acoust., Speech, and Signal Processing, vol.38, p.717-21, 1990). Based on the KL spectrum, a method of modifying a spectrum estimate was suggested. Some numerical examples 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. It is shown that a Gaussian autoregressive process of order p 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. A rationale for the existence of the KL spectrum is given