Simultaneous estimation of sparse signals and systems at sub-Nyquist rates

The novelty of this paper is divided into two technical sections; first we propose a novel algorithm for system identification with known input sparse signal, based on the Finite Rate of Innovation sampling theory. Then we consider the problem of simultaneously estimating the input sparse signal and also the linear system and propose a novel iterative algorithm for that setup. We will show that, based on our numerical simulations, the solution to the second problem is normally convergent.