CHAPTER 12 Applications of Discrete-Time Signals and Systems.................................
Nullius in verba
(Take nobody’s word for it).
Motto of the Royal Society,
Britain’s 350-year-old science fraternity12.1 Introduction
In this chapter we will present applications of the theory of discrete-time signals and systems to three
important areas: digital signal processing, digital control, and digital communications. The material
in this chapter is meant to be a more motivational than detailed presentation. We encourage our
readers to look for the details in excellent textbooks in these three areas [54, 22, 16].
Given the advances in digital technologies and computers, processing of signals is being done mostly
digitally. Early results in sampling, analog-to-digital conversion, and the fast computation of the
output of linear systems using the Fast Fourier Transform (FFT) made it possible for digital signal
processing to become a technical area on its own. (The first books in this area [63, 54] come from the
mid-1970s.) Although the origins of the FFT have been traced back to the German mathematician
Gauss in the early 1800s, the modern theory of the algorithm comes from the 1960s. It should be
understood that the FFT is not yet another transform, but an efficient algorithm to compute the
discrete Fourier transform (DFT), which we covered in Chapter 10.
Analog classic control systems can be implemented digitally using analog-to-digital and digital-to-
analog converters and computers to implement the control laws. The theory of sampled data shows
the connection between the Laplace and the Z-transform. The difficulty in the analysis of these
systems is the mixing of continuous- and discrete-time signals.
Digital communication systems provide a more efficient way to communicate information than
analog communication systems, but they are more demanding in terms of bandwidth. As
Signals and Systems Using MATLAB®. DOI: 10.1016/B978-0-12-374716-7.00016-8
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