been shown by practitioners that the sampling rate must be at least twice the highest frequency. The theoretical basis for this sampling rate was found through the independent work of several scientists in the 1920s, including H. Nyquist Figure 5.1 Miner's voice sampling commutator as drawn in his patent application. Source: Ref. [2] 1 This Historical Note is based on a paper by Luke [1]. Broadband Telecommunications Technologies and Management working for Bell Laboratories in the US, R. Hartley also working at Bell Laboratories, and V. Kotelnikov working at the Moscow Power Engineering Institute, Russia. These researchers proved what the practitioners already knew, that a sampling rate of twice the highest frequency was sufficient for exact reproduction of a signal. With the formulation and publication of the sampling theorem, it was noted by mathemati- cians that J. Lagrange had formulated the principle of approximating a continuous signal with discrete samples as early as 1765. H. D. Luke, in his paper on the historical development of the Sampling Theorem [1], recounts the contributions made by different individuals and fields of knowledge/art. He concludes: "The numerous different names to which the sampling theorem is attributed in the literature - Shannon, Nyquist, Kotelnikov, Whittaker, to Someya - gave rise to discussion of its origins. However, this history also reveals a process which is often apparent in theoretical problems in tech- nology or physics: first the practicians put forward a rule of thumb, then the theoreticians develop the general solution, and finally someone discovers that the mathematicians have long since solved the mathematical problem which it contains, but in 'splendid isolation'" [1]. Figure 5.2 shows a telecommunications block diagram. A source generates information which is carried to a receiver. In binary digital communications, the source information needs to be converted to a series of 1's and O's which are then digitally modulated and send over a medium. This conversion proc