Signals: Analog, Discrete, and Digital

This chapter introduces signals and the mathematical tools needed to work with them, and combines discussions of analog signals, discrete signals, digital signals and the methods to transition from one of these realms to another. All that it requires of the reader is a familiarity with calculus. There are a wide variety of examples. They illustrate basic signal concepts, filtering methods, and some easily understood techniques for signal interpretation. The first section introduces the terminology of signal processing, the conventional architecture of signal processing systems, and the notions of analog, discrete, and digital signals. It describes signals in terms of mathematical models - functions of a single real or integral variable. Next, we cover the two basic signal families: analog and discrete, respectively. Later, we discuss sampling and interpolation. Next we cover periodicity, and foremost among these signals is the class of sinusoids. The chapter concludes with a discussion of the mathematics that arises in the detailed study of signals. A summary, a list of references, and a problem set complete the chapter.