Component covariance analysis for periodically correlated random processes

The paper is dedicated to the component method for estimating the periodically correlated random processes (PCRP) mean and covariance functions, when number of harmonics is finite. This method is based on the decomposition of these time periodic functions into trigonometric polynomials and the estimation of their Fourier coefficients. Then the component estimates of the PCRP mean and covariance functions are constructed on the basis of the coefficient estimates. The properties of the PCRP mean and covariance functions component estimates are investigated, asymptotical unbiasedness and mean square consistency for these estimates, and the corresponding formulae for their biases and variances, which depend on the record length and number of Fourier coefficients, are expressed. Comparison for the component and coherent method estimates is carried out for the case of amplitude and phase modulated signals.