Gateways Into Electronics

1

LINEAR SYSTEMS

1-1 INTRODUCTION

The language of linear systems pervades electronics, but it is present in many other domains: it can describe the dynamics of a ship's rudder as well as it can describe an audio amplifier. For this reason we will use a context-free approach to linear systems, and in view of our current state of knowledge, we will choose examples from domains other than electronics.

In this chapter we will treat linear systems at a rather intuitive level in order to get to essential ideas without delay. Nonetheless, we will make our statements as precise and as general as possible, and we will also point out where the more formal treatment presented in Chapter 2 is required.

In the spirit just outlined, let us establish some essential terminology before proceeding to an example. As shown in block diagram form in Fig. 1-1, a linear system is characterized mathematically by a linear operator that generates a well-defined output or response x(t) when presented with an input or excitation y(t).^† We will write

For the moment we will think of the excitation and of the response as ordinary functions of the time, although we will eventually see that the full power and simplicity of the theory of linear systems can be achieved only in the context of a larger class of mathematical ...