On the Properties of Some Systems that Distort Signals - II

Abstract

In this paper we study the recoverability of square-integrable bandlimited signals (with arbitrary frequency) bands) that are distorted by a freguency-selective time-variable nonlinear operator and subsequently are bandlimited to the original bands. The distortion operator characterizes a very general class of systems containing linear time-invariant elements and a single time-invariant nonlinear element. The subseguent bandlimiting of the system's output signals can be thought of as being due to transmission through a channel that performs filtering. Our principal result asserts that, under certain conditions that are satisfied by many realistic systems, it is possible to uniquely determine the bandlimited input to the system from a knowledge of the bandlimited version of the output, in spite of the intermediate distortion which generally produces signals thal are not bandlimited to the original frequency bands. We show that the input signal can be determined by a stable iteralion procedure in which the approximating functions converge to their limit at a rate that is at least geometric.