Fast convergence reconstruction formulas for periodic nonuniform sampling of order 2

This paper studies the reconstruction of a random band-limited process from a nonuniform periodic sampling of order 2. This sampling scheme uses two interleaved sample sequences at the same rate chosen according to the Landau criterion. The associated exact reconstruction formula is composed of two series with cardinal sine functions as general terms. In practical applications, the signal is observed on a finite window. The exact reconstruction formula is then approached by truncation of the series. The series rate of convergence has thus a strong influence on the reconstruction performance in practice. Unfortunately, the cardinal sine functions lead to a slow convergence. In the case of an over-sampled process, we propose interpolation formulas derived from raised cosine filters. We show, through theoretical analysis and numerical simulations, that the regularity of these functions leads to a higher series convergence rate and thus improves the reconstruction performance even for a low over-sampling rate.