Sampling of multiple signals with finite rate of innovation and sparse common support

Abstract

The authors focus on the minimum sampling rate and the exact recovery condition in the sampling of multiple signals with finite rate of innovation (FRI) and sparse common support (SCS). The authors first propose the subspace-based recovery method and analyse its relation with the annihilating filter; then the proposed method is used for sampling the multiple signals with FRI and SCS. It is observed that the minimum sampling rate for the exact recovery heavily depends on the signal structure described by the defined characteristic matrix, based on which a sufficient and necessary condition is also presented. The numerical simulations show that the proposed recovery method and the recovery condition are feasible for the sampling of multiple signals with FRI and SCS.