Sampling and reconstruction in sparse atomic spaces

This paper provides a quantitative notion of the sparsity for infinite dimensional atomic spaces, which play an important role in many signal processing applications. This notion of sparsity is defined as the ratio of the number of redundant samples (not necessary to recover any signal in the atomic space) to the number of all available samples of a particular canonical sampling system. It is shown that the so defined sparsity can be expressed in terms of the support of the spectral density of the sequence which generates the atomic space.