Approximation of discontinuous signals by sampling Kantorovich series

In this paper, the behavior of the sampling Kantorovich operators has been studied, when discontinuous functions (signals) are considered in the above sampling series. Moreover, the rate of approximation for the family of the above operators is estimated, when uniformly continuous and bounded signals are considered. Finally, several examples of (duration-limited) kernels which satisfy the assumptions of the present theory have been provided, and also the problem of the linear prediction by sampling values from the past is analyzed.