Laplace Transform

Abstract

The direct and inverse Laplace transforms are defined in this chapter. Laplace transform has played a very important role in electrical engineering in the study of electronic systems responses, causal by essence. It was oriented primarily for the treatment of causal signals, null for negative time. Historically, the one-sided form of the Laplace transform was used. The transfer function of an electrical circuit, written in the form of a rational fraction was decomposed into simple elements. For canonical form of input signals, it was possible to calculate the output signal in the Laplace domain as products of simpler functions. Simple rules treated the boundary conditions at time t=0. With the use of distributions which allow generalizing all functions, the Laplace transform is less dominant today. An important goal of this chapter is to provide an understanding of the domain of definition of the Laplace transform and its association with causality and stability of a system. The special case of a marginally stable system is also discussed.