Linear Time Invariant Systems

Abstract

We assume the reader to have familiarity with linear time-invariant (LTI) systems. In this chapter we merely summarise the main results of this theory. We are going to call the quantities that are considered the input, the output and some characterization of the system signals. This should evoke a meaningful interpretation in most of the systems that we are going to discuss. Mathematically they are distributions. The meaning of time-invariant is very intuitive: suppose that we apply the input signal x(t) to a system represented by an operator $${\mathcal {H}}$$ and observe the signal $$ y(t) = {\mathcal {H}}[x(t)] $$ as its output.