Mathematical theory of sampling analog signals revisited

This paper is an attempt to formulate a unique mathematical theory of the sampling operation of analog signals by connecting all of its scattered in the literature fragments into a one whole. We think that there exists a need for performing this, since many of the fragments mentioned appear to be inconsistent with each other, especially in the cases when they are misunderstood and misinterpreted. Our hope is that this paper will meet expectations of many people working in the area of digital signal processing to have an ordered mathematical theory that describes the signal sampling process.