Equivalent Circuits for the PNS3 Sampling Scheme

Periodic nonuniform sampling of order three (PNS3) is a sampling scheme composed of three periodic sequences with the same period. It is well-known that this sampling scheme can be useful to remove aliasing. Previous studies have provided conditions on the spectrum support for exact reconstruction in the case of functions. This paper deals more generally with the best mean-square interpolation for stationary processes with any known power spectrum, from PNS3 and possibly aliasing. We show that the best estimation is based upon particular linear filters, which depend on the gap between the sampling sequences. The mean-time error also depends on this gap. The errorless interpolation is a particular case. It requires the knowledge of the spectral support rather than the spectral true values.