On the Properties of Some Systems that Distort Signals -- I

A signal transmission system is a realization of an operator that maps input signals in one domain into output signals in a second domain. When the system contains energy-storage devices as well as timevariable or nonlinear elements, the mapping is usually quite complicated. Very little in the way of a general theory is known concerning the mathematical properties of such mappings. Of course one of the important properties of a mapping is its invertability or lack of invertability. Some particularly interesting results relating to the existence of the inverse of a special mapping have been obtained by Beurling, Landau, Miranker, and Zanies. They consider the situation in which a square-integrable bandlimited signal is passed through a monotonic nonlinear device. Beurling showed, by means of a nonconstructive proof, f that a knowledge of the Fourier transform of the distorted signal on the interval where the transform of the input signal does not vanish is sufficient to uniquely determine the input f B e u r l i n g ' s proof is g i v e n in R e f s . 1 a n d 3. 2033