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After studying this chapter you will be able to
define discrete-time and continuous-time signals;
measure the “size” of a discrete-time signal using norms;
use the z-transform to convert discrete-time signals to the complex z-plane;
use the discrete-time Fourier transform to convert discrete-time signals to the frequency domain;
describe the properties of the z-transform and the discrete-time Fourier transform;
define a discrete-time state-space system;
determine properties of discrete-time systems such as stability, controllability, observability, time invariance, and linearity;
approximate a nonlinear system in the neighborhood of a certain operating point by a linear time-invariant system;
check stability, controllability, and observability for linear time-invariant systems;
represent linear time-invariant systems in different ways; and
deal with interactions between linear time-invariant systems.
Introduction
This chapter deals with two important topics: signals and systems. A signal is basically a value that changes over time. For example, the outside temperature as a function of the time of the day is a signal. More specifically, this is a continuous-time signal; the signal value is defined at every time instant. If we are interested in measuring the outside temperature, we will seldom do this continuously. A more practical approach is to measure the temperature only at certain time instants, for example every minute. The signal that is obtained in that way is a sequence of numbers; its values correspond to certain time instants. Such an ordered sequence is called a discrete-time signal.