ABSTRACT
In the year 1765, J. L. Lagrange proposed a sampling theorem for bandlimited periodic functions by stating that the knowledge of functional values at 2n + 1 equidistant points within a period is sufficient to represent uniquely a periodic function by sine and cosine terms. Following P. L. Butzer and R. L. Stens, the history of today’s understanding of the sampling theory can be traced back to the interpolation theory using equidistant nodes published by the Belgian mathematician Charles–Jean Baron de la Vallee Poussin. He probably was the first person to consider sampling for not necessarily bandlimited functions already in 1908. As a consequence of the discovery of the several independent introductions of the sampling theorem, people started to refer to the theorem by including the names of the aforementioned authors, resulting in such phrases as the Whittaker-Kotel’nikov-Shannon sampling theorem. It should be noted that the classical proof of the Shannon sampling theorem as recapitulated is indeed rigorous.
