Extrapolation of bandlimited signals from finite samples via moments

Techniques are developed for extrapolation of bandlimited signals from a finite number of samples. This arises in such applications as radar, power spectral density functions, and spatial temporal mode estimation in arrays of sensors. The techniques are based on the use of prolate spherical functions, certain results from interpolation via the classical moments, and approximation theory. The results also yield solutions to the trigonometric moment problem. A more direct extrapolation approach is given in terms of both trigonometric and classical moments, which does not require interpolation but which requires approximation of the Fourier transforms of prolate spherical functions.<>