Time sampling and reconstruction in weighted reproducing kernel subspaces

This paper mainly studies the time sampling and reconstruction of signals in weighted reproducing kernel subspaces of Lνp. Firstly, a class of examples for weighted reproducing kernel subspaces are given. Then, using samples produced by a crossing time encoding machine or an Integrate-and-Fire time encoding machine satisfying some density constraints, iterative approximation algorithms are established for perfect recovery of signals in weighted reproducing kernel subspaces. Finally, an Integrate-and-Fire sampling scheme is discussed and an approximate reconstruction procedure is proposed for signals in weighted reproducing kernel subspaces. Moreover, we give detailed analysis for the approximate reconstruction method in the setting of shift-invariant subspaces.