ABSTRACT
This chapter begins with the Fourier transform (FT), which can be viewed as a generalization of the Fourier series representation of a periodic function. It presents Applications and examples involving the Fourier, Laplace, and z-transforms. The FT and Fourier series are named after Jean Baptiste Joseph Fourier, who first proposed in an 1807 paper that a series of sinusoidal harmonics could be used to represent the temperature distribution in a body. The transform domain approach to signals and systems is based on the transformation of functions using the Fourier, Laplace, and z-transforms. The Laplace transform can be viewed as the FT with the addition of a real exponential factor to the integrand of the integral operation. There the presentation centers on the relationship between the pole locations of a rational transform and the frequency spectrum of the transformed function; the numerical computation of the FT; and the application of the Laplace and z-transforms to solving differential and difference equations.
