Polynomial filtering approach to reconstruction and noise reduction of nonuniformly sampled signals

The use of polynomial filtering for reconstruction of nonuniformly sampled signals is considered. The goal is to reconstruct the signal of interest at arbitrarily chosen time instants so that the effect of the disturbing noise is minimised. Our approach is based on the assumption that, at a sufficiently wide neighborhood of every time instant, the signal of interest is smooth enough to be approximated by a low-order polynomial. The optimal solution is based on the least-squares method. Signal reconstruction is implemented with a time-varying FIR filter whose coefficients are obtained in closed form via polynomial expansion. Furthermore, we show how the solution to the general nonuniform sampling case can be much simplified when the sampling grid does not depart much from the uniform grid. We consider two special cases in this form: jittered and additive random sampling with small variance of the sample period. The new schemes are illustrated with examples. (C) 2000 Elsevier Science B.V. All rights reserved.