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 nois e is minimised. Our approach is based on the assumption that, at a sufficie ntly wide neighborhood of every time instant, the signal of interest is smo oth enough to be approximated by a low-order polynomial. The optimal soluti on is based on the least-squares method. Signal reconstruction is implement ed with a time-varying FIR filter whose coefficients are obtained in closed form via polynomial expansion. Furthermore, we show how the solution to th e general nonuniform sampling case can be much simplified when the sampling grid does not depart much from the uniform grid. We consider two special c ases in this form: jittered and additive random sampling with small varianc e of the sample period. The new schemes are illustrated with examples. (C) 2000 Elsevier Science B.V. All rights reserved.