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

TL;DR

This paper presents a method to recover bilevel causal signals with finite rate of innovation from uniform samples using positive sampling kernels, ensuring stability even with noise.

Contribution

Introduces a novel recovery method for bilevel signals with finite rate of innovation using positive kernels and analyzes its stability under noise.

Findings

Successful recovery of bilevel signals from uniform samples.

Recovery method remains stable in the presence of bounded noise.

Applicable when sampling rate meets or exceeds the signal's maximal local rate of innovation.

Abstract

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 $x*h(nT), n\ge 1$, where the sampling kernel $h$ is causal and positive on $(0, T)$, and the sampling rate $\tau:=1/T$ 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.