Error Spectrum Analysis of Time-Variant Reconstruction from Nonuniform Sampling

The time-variant method proposed by Marvasti and Plotkin et al provides a straightforward, noniterative way to reconstruct a signal from nonuniformly spaced samples. We study its output error spectrum through simulations using a nonuniform sampling scheme in which sample instants are randomly chosen within uniformly spaced sampling windows of equal duration. Theoretically, the method can perform ideal, error-free reconstruction only for a small class of sampling grids that are difficult to implement. Therefore, it is of interest to investigate the consequences of violating this sampling constraint. Proper knowledge on the spectral behaviour allows better system design and hence improved performance. We make conclusions on the effects of and constraints on signal and filter bandwidth as well as average input and output sample rates. We also discuss the digital implementation of the algorithm