On signal representation from generalized samples: Minmax approximation with constraints

Signal representation plays a major role in many DSP applications. In this paper we consider the task of calculating representation coefficients of an analog signal, where the only available data is its samples based on practical non-ideal acquisition devices. We adopt a minmax approach and further incorporate regularity constrains on the original continuous-time signal. These constraints stem from the nature of applications where smooth signals serve as input data. The ensued solution is shown to consist of an orthogonal projection within a Sobolev space. Illustrating examples are given, utilizing this constrained minmax approach. Our conclusion is that this new approach to signal representation could improve presently available systems, especially in non-ideal situations.