Beyond Bandlimited Sampling: Nonlinearities, Smoothness and Sparsity

Understand

Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields.

• In this survey we present several extensions of the Shannon theorem, that have been developed primarily in the past two decades, which treat a wide class of input signals as well as nonideal sampling and nonlinear distortions.
• This framework is based on viewing sampling in a broader sense of projection onto appropriate subspaces, and then choosing the subspaces to yield interesting new possibilities.
• For example, our results can be used to uniformly sample non-bandlimited signals, and to perfectly compensate for nonlinear effects.