ABSTRACT
This chapter focuses on time-invariant linear systems, looks at their properties, and shows how to describe a linear system in the time and frequency domains. Much of the literature on linear systems is written from an engineering viewpoint, and looks especially at such topics as control theory and digital communications, as well as the identification of input/output systems. An alternative, equivalent, way of describing a linear system in the time domain is by means of a function called the step response function. An alternative way of describing a time-invariant linear system is by means of a function, called the frequency response function, which is the Fourier transform of the impulse response function. A necessary and sufficient condition for a linear system to be stable is that the Laplace transform of the impulse response function should have no poles in the right half-plane or on the imaginary axis.
