ABSTRACT
Although the Laplace transform (LT) has several advantages over the Fourier transform (FT) in circuit analysis, the FT is fundamental to signal analysis. Being conceptually an extension of Fourier analysis to nonperiodic signals, it utilizes the same frequency-domain representation as phasor analysis. It shares many of the operational properties of the LT but has some unique and very useful properties that are explored in this chapter. The FT provides a powerful tool for working in the frequency domain. This has many important applications in signal processing, communications, and control systems. The usefulness of FT techniques has been greatly enhanced by digital computation, based on a rapid and efficient algorithm known as the fast Fourier transform that computes the discrete FT. This transform is an approximation to the FT that produces a finite set of discrete-frequency spectrum values from a finite set of discrete-time values. The chapter ends with Parseval's theorem, which is concerned with energy in the frequency domain.
