Minimal L1-norm reconstruction function for oversampled signals: Applications to time-delay estimation

We consider the problem of the reconstruction of an oversampled band-limited signal and obtain an explicit expression for the reconstruction function with minimal -norm. It has good sparseness and localization properties that recommends its use in time-delay estimation but the result may be of interest in other domains. Compared to the standard sine cardinal reconstruction function, its rate of decrease is almost one order of magnitude higher.