Introduction

The transfer function is a convenient representation of a linear time-invariant dynamical system. Mathematically, the transfer function is a function of complex variables.

A transfer function is the ratio of the output of a system to the input of a system. If we have an input function of $X(s)$, and an output function $Y(s)$, we define the transfer function $H(s)$ to be:

$$H(s)=\frac{Y(s)}{X(s)}$$