ABSTRACT
This chapter reviews several of the most important properties of the Fourier transform, and several of the most common Fourier transform pairs. The Fourier transform changes signals to a form that simplifies the description of the operation of linear, time invariant systems. The basis functions for the Fourier transform are the imaginary exponentials. The Fourier transform and the inverse Fourier transform provide a method of changing back and forth between the space and the spatial frequency domain representations of a signal. The two representations provide the same information. Vectors provide geometrical insight into operations on signals. Transformation of a signal from the time domain to the frequency domain is analogous to representing a vector in terms of a new set of basis vectors. The eigenfunctions or eigenvectors of a system are signals which are not changed in shape or in direction as they go through a system.
