A nearly-optimum signal in communication theory

The method presented in this paper enables us to obtain, starting from a physical point of view, a nearly-optimum signal for communication theory. The product of pulse duration and spectral width, referred to the positive frequency spectrum only, is 1.1814 … as compared with the minimum theoretical value 1.1802 … obtained by Hilberg and Rothe for the Weber signal. With respect to the Weber signal our proposed function offers the not-negligible advantage of analytical simplicity. Some possible applications are outlined.