1. Signals: Analog, Discrete, and Digital

  1. Ronald L. Allen1 and
  2. Duncan W. Mills2

Published Online: 14 MAY 2004

DOI: 10.1002/047166037X.ch1

Signal Analysis: Time, Frequency, Scale, and Structure

Signal Analysis: Time, Frequency, Scale, and Structure

How to Cite

Allen, R. L. and Mills, D. W. (2003) Signals: Analog, Discrete, and Digital, in Signal Analysis: Time, Frequency, Scale, and Structure, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/047166037X.ch1

Author Information

  1. 1

    San José, California, USA

  2. 2

    Mountain View, California, USA

Publication History

  1. Published Online: 14 MAY 2004
  2. Published Print: 19 DEC 2003

ISBN Information

Print ISBN: 9780471234418

Online ISBN: 9780471660378



  • analog;
  • discrete;
  • digital;
  • signals;
  • sampling;
  • interpolation;
  • periodic signals;
  • special signal classes;
  • complex numbers;
  • random signals;
  • noise


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.