ABSTRACT
Fourier1 transforms are used to solve a wide variety of problems; this chapter will provide a brief introduction to the subject. Fourier series, which are similar in some ways to Fourier transforms, can be used to represent periodic functions. While no physical variable can be perfectly periodic-since nothing goes on forever-many systems are close enough to being periodic for the Fourier-series representation to be useful. Fourier series are also useful as a way of thinking about how certain devices work, or how certain processes behave. Optical instruments, including radiometers and radars, often have properties that depend on the Fourier transform of some physical quantity. We shall see, for instance, that the power pattern-the relative sensitivity to radiation coming from different directions —of an antenna is the Fourier transform of a quantity that is related to the size and shape of the antenna. In the study of integral equations, we shall see that there are special methods that are appropriate for solving integral equations that have the form of a Fourier transform.
