Digital Communications: Fundamentals and Applications, 3rd Edition

Appendix E

s-Domain, z-Domain, and Digital Filtering

Robert W. StewartDepartment of Electronic and Electrical Engineering University of Strathclyde, Glasgow, Scotland, UK

In Appendix A, Equations (A.26) and (A.27) defined the Fourier and inverse Fourier transforms, respectively. Although the Fourier transform is useful for a steady-state frequency analysis of a system, it is not particularly useful for transient analysis; and for some functions, the Fourier integral does not in fact exist, whereas the Laplace transform, discussed in this appendix, does. Hence, to allow a more in-depth analysis of linear systems, we often choose to use the Laplace transform. In terms of Laplace- and Fourier-defining equations, it is straightforward to show that ...