Discrete-time spectral estimation of continuous-parameter processes -- A new consistent estimate

This paper presents a new estimation scheme for the spectral density function of a stationary time series from observations taken at discrete instants of time. The sampling instants are determined by a Poisson point process on the positive real line. Under weak smoothness conditions on the spectral density, asymptotic expressions for the bias and Variance are derived, and it is shown that the estimate is mean-square consistent for all positive values of the average sampling rate. The new estimate compares favorably with the classical continuous-time spectral estimates.