Joint Signal Sampling and Detection

In this paper, we examine the joint signal sampling and detection problem when noisy samples of a signal are collected in the sequential fashion. In such a scheme, at the each observation time point we wish to make a decision that the observed data record represents a signal of the assumed target form. Moreover, we are able simultaneously to recover a signal when it departs from the target class. For such a joint signal detection and recovery setup, we introduce a novel algorithm relying on the smooth correction of linear sampling schemes. Given a finite frame of noisy samples of the signal we design a detector being able to test a departure from a target signal as quickly as possible. Our detector is represented as a continuous time normalized partial-sum stochastic process, for which we obtain a functional central limit theorem under weak assumptions on the correlation structure of the noise. The established limit theorems allow us to design monitoring algorithms with the desirable level of the probability of false alarm and able to detect a change with probability approaching one.