Level-Crossings Sampling for Signal Recovery with Slepian Derivatives

We study the problem of the signal recovery for the class of stationary bandlimited Gaussian processes when the measured information is given in terms of signal level crossings. Level-crossing data collection is based on signal amplitude sampling with error-free timing information and it is a preferable sampling paradigm due to its low-power consumption. In this paper, we develop a reconstruction method that incorporates not only level-crossings samples but also the additional information on the signal derivative. The signal derivative, however, is not observed and we utilize the Slepian model for the process behavior after crossings the given level. The model consists of the linear regression function with the universal Rayleigh component that characterizes the signal slope and a non-stationary Gaussian noise process. The existing methods for signal recovery with derivatives assume that both the signal and its derivatives are observed and they form the observation set. Our approach yields the improved reconstruction accuracy and provides a new strategy for a general class of event-driven data analysis algorithms.