ABSTRACT
This chapter describes the Fourier transform operation for discrete signals, the discrete Fourier transform. Discrete signals are defined for only a discrete set of values of the independent variable. Square brackets around the independent variable are used to indicate a discrete signal. In practical applications, discrete signals are often used to represent continuous signals. Digital signals take on discrete values for both the dependent and the independent variables. The transforms which are used with digital signals are called number theoretic transforms. A periodic signal is one that repeats at regular intervals. The chapter describes some of the properties of periodic signals. One of the major reasons that the Fourier transform operation is of importance in Radiology today is the discovery of the fast Fourier transform algorithm. The fast Fourier transform algorithm has transformed a vast amount of image processing from being impractical to being very practical.
