Nonuniform sampling and study of transient systems response

Nonuniform sampling where sampling intervals are chosen by various criteria of the noisy signal is investigated. In this context, the minimum-variance polynomial approximation is used to reconstruct the signal values at uniform spacings. The statistical characterisation of error in the reconstructed signal values, and use of that property in an approximate maximum likelihood estimator, lead to very accurate results related to the study of transient system-response in noise. In the special case of uniform sampling, it is explained why the performance of the proposed method, which first preprocesses data by polynomial approximation, is superior to the performances of the existing methods based on singular value decomposition. Simulation results are presented to substantiate the theory