Elements of Signal Theory

Abstract

In picture processing, pictures are regarded as two-dimensional signals. This chapter introduces and explains the basic concepts of signal theory. The treatment of signals as mathematical functions is discussed in Sect.2.1, and signal space and related notions, including linear representation of signals, are introduced in Sect.2.2. Section 2.3 reviews the most common systems of basis functions used for the linear representation of signals, while Sect.2.4 deals with the integral representation of signals, with special emphasis on Fourier transform. Section 2.5 is devoted to ways of describing signal transformations as well as to concepts of linear and nonlinear transforms. The discrete representation of linear transformation corresponding to linear representation of a signal with respect to a discrete basis is described in Sect.2.6, while Sect.2.7 treats the representation of linear transforms corresponding to integral representation of signals. Finally, Sect.2.8 reviews examples of the most popular linear operators.