Estimation of the Spectrum of a Gaussian Stochastic Process on the Basis of a Realization of the Process with Omissions

The investigated problem is to formulate an estimate of the spectral density $f(\lambda)(|\lambda|\leqslant\pi)$ of a stationary Gaussian stochastic process $\xi_k$, $k=,\dots,-1,0,1,\dots$, on the basis of a realization of the process in which every sequence of $m$ observations is followed by $p$ omissions. An asymptotically (with unbounded growth of the volume of the realization) unbiased and consistent estimate is formulated for the value of the function $f(\lambda)$ at a point $\lambda_0$, where $|\lambda_0|\ne k\pi/(m+p)$, for the case $m>p\geqslant1$. The estimate of $f(\lambda_0)$ is given in a form suitable for computation by means of the rapid Fourier transformation method.