ABSTRACT
The study of signals and systems can be carried out in terms of either a time-domain or a transform-domain formulation. The transform-domain approach to signals and systems is based on the transformation of functions using the Fourier, Laplace, and z-transforms. This chapter deals with the Fourier transform (FT), which can be viewed as a generalization of the Fourier series representation of a periodic function. The FT and Fourier series are named after Jean Baptiste Joseph Fourier, who first proposed in a 1807 paper that a series of sinusoidal harmonics could be used to represent the temperature distribution in a body. One of the major applications of the Laplace transform is in solving linear differential equations. The discrete-time counterpart to the solution of differential equations using the Laplace transform is the solution of difference equations using the z-transform. The chapter considers the first-order linear constant-coefficient difference equation.
