STATISTICS ON EXPONENTIAL AVERAGING OF PERIODOGRAMS

The algorithm of exponential averaging applied to subsequent periodogr ams of a stochastic process is used to estimate the power spectral den sity (PSD), For an independent process, assuming the periodogram estim ates to be distributed according to a chi(2) distribution with two deg rees of freedom, the probability density function (PDF) of the PSD est imate is derived, a closed expression is obtained for tile moments of the distribution, Surprisingly, the proof of this expression features some new insights into the partitions and Euler's infinite product, Fo r large values of the time constant of the averaging process, examinat ion of the cumulant generating function shows that the PDP approximate s the Gaussian distribution, Although restrictions for the statistics are seemingly tight, simulation of a real process indicates a wider ap plicability of the theory.