Memoryless Nonlinearities

Abstract

We have seen that Fourier analysis is a powerful tool for describing and analyzing linear systems. A particularly important application has been that of sampling continuous time signals to produce discrete time signals and the quantifying of the conditions under which no information is lost by sampling. The purpose of this chapter is twofold. First, we demonstrate that Fourier analysis can also be a useful tool for analyzing simple nonlinear systems. The techniques used in this chapter are a relatively minor variation of techniques already seen, but this particular application of Fourier theory is often overlooked in the engineering literature. Although a standard component of courses is devoted to nonlinear systems, the relative scarcity of such courses and the lack of examples in engineering transform texts has led to a common belief of near mythological nature that Fourier methods are useful only in linear systems. Using an idea originally due to Rice [28] and popularized by Davenport and Root [15] as the “transform method,” we show how the behavior of memoryless nonlinear systems can be studied by applying the Fourier transform to the nonlinearity rather than to the signals themselves.