A spectral estimation method by non-equinterval smoothing of log periodogram

We develop an automatic smoothing procedure for an estimate of the spectral density of a random process. The procedure is based on smoothing the periodogram with variable bandwidth and a spline interpolation. Effective varying bandwidth is obtained by approximating the log periodogram with a step function whose positions of level changes are determined using a dynamic programming technique. We show that the step function can be obtained by minimizing the cost function D ( C ||μ k ) for a given K . The number of partitions K also can be chosen by minimizing another cost function L(K) . Some numerical examples show that the resulting estimates are shown to be good representations of the true spectra.