On Local Properties of Estimate of Spectral Function

Statistical estimates are set up for the spectral density $f(\lambda)$ with respect to a sample from a stationary sequence $X(t)$ at a specified point $\lambda$, which depends as little as possible on the behavior of $X(t)$ at all remaining frequencies. The asymptotic properties of the first two moments of these estimates are investigated and compared with the asymptotic properties of some other known estimates. The possibility of using the mixing properties of stationary sequence $X(t)$ for setting up unbiased consistent spectral density estimates is investigated. The problem of extracting useful signals from noise concentrated at nearby adjacent frequencies is solved in a general fashion.