Recovery of bilevel causal signals with finite rate of innovation using positive sampling kernels

摘要

Bilevel signal x with maximal local rate of innovation R is a continuous-time signal that takes only two values 0 and 1 and that there is at most one transition position in any time period of 1/R. In this note, we introduce a recovery method for bilevel causal signals x with maximal local rate of innovation R from their uniform samples x*h(nT), n ≥ 1, where the sampling kernel h is causal and positive on (0, T), and the sampling rate T:= 1/T is at (or above) the maximal local rate of innovation R. We also discuss stability of the bilevel signal recovery procedure in the presence of bounded noises.