Fourier Transform Analysis

Abstract

In Chapter 3 we have discussed the frequency representation of a periodic signal. Fourier series expansions of periodic signals give us a basic understanding how to deal with signals in general. Since most signals we deal with are aperiodic energy signals, we will study these in terms of their Fourier transforms in this chapter. Fourier transforms can be derived from the Fourier series by considering the period of the periodic function going to infinity. Fourier transform theory is basic in the study of signal analysis, communication theory, and, in general, the design of systems. Fourier transforms are more general than Fourier series in some sense. Even periodic signals can be described using Fourier transforms. Most of the material in this chapter is standard (see Carlson, 1992, Lathi, 1983, Papoulis, 1962, Morrison, 1994, Ziemer and Tranter, 2002, Haykin and Van Veen, 1999, Simpson and Houts, 1971, Baher, 1990, Poularikis and Seely, 1991, Hsu, 1967, 1993, Roberts, 2004, and others).