THE ESTABLISHMENT OF SAMPLING AS A SCIENTIFIC PRINCIPLE -A STRIKING CASE OF MULTIPLE DISCOVERY
Paulo J. S. G. Ferreira, Rowland Higgins · 2011
During the period 1928–1949, several engineers contributed to the establishment of a sampling principle. They did this virtually independently of each other in the context of communications theory and practice. Five names stand out as being the main players in this drama: H. Nyquist, who laid the foundations for the minimal sampling rate; V. A. Kotel′nikov, C. E. Shannon, and I. Someya, whose treatment of the sampling principle was mathematical; and H. Raabe, who derived the minimal sampling rate and built hardware to reconstruct signals from samples taken at that rate. Their work is described below. As Shannon recognized, the mathematical set-ting already existed. In fact, it was part of a tradition that can now be traced back to Cauchy, but its significance for application was simply not realized until Shannon’s time. Our notation is described in context, or else com-pletely standard. For background and references to original work, see [1] and [3]. The Sampling Principle I. Signal functions having finite energy and frequency content confined to a bounded set