A Prony-like method for non-uniform sampling

In this paper a Prony-like method for non-uniform sampling is proposed. The unknown parameters are estimated on the base of a new linear regression equation which uses filtered signals obtained directly from the measurements. The approach uses the derivative method in the frequency domain yielding exact formula in terms of multiple integrals of the signal, when placed in the time domain. These integrals are explicitly solved by projecting signal on some set of orthogonal basis functions or, more in general, by using a polynomial that fits data in the least-squares sense. The effectiveness of the proposed approach is shown by simulated experiments.