Transfer function and system characterisation

This chapter is about connections and relationships between the alter native descriptions of continuous time linear systems. We are interested in questions such as, "what can we learn about the system (i.e. how does it respond or behave) by examining the transfer function?" The starting point for this discussion is the definition of the poles and zeros of the transfer function. The relationship between the position of the poles and the frequency response is examined. Several graphical methods are used to illustrate these points. An exploration of the relationship between the position of the poles and the impulse response is conducted. This provides both links between the transfer function and the time-domain system description as well as insights into system stability. The speed of response of linear systems is considered through the use of the step response and its relationship to system bandwidth is explored.