Random Sampling and Reconstruction of Spectra

This paper deals with the problem of perfect reconstruction of the spectrum of a weakly stationary stochastic process x ( t ) from a set of random samples { x ( t n )}. A broad class of random sampling schemes, for which the sampling intervals are dependent, is constructed. It is shown that this class is “alias free≓ relative to various families of spectra. It is further shown that the alias free property of this class of sampling schemes is invariant under random deletion of samples.