4.1 Introduction

Imagine that you had constructed a very fast and flexible real-time DSP system, with a high resolution codec, a powerful processing core and a large amount of memory to store code and data. You might think that from now on, the new digital order of things should dictate that knowledge of continuous or analog systems would be an irrelevancy but this would be mistaken. DSP systems are widely employed to replicate or emulate the performance of analog circuits, because they can do so without incurring all the penalties associated with their continuous-time counterparts. But why do it in the first place? Surely designers only build analog filters with gradual roll-offs because they know that sharp transition zones come with the attendant risks of instability and phase distortion. In contrast, a DSP filter can be designed with a brick-wall response and unconditional stability, so why bother with the old equations? For several reasons. First, the circuit required might be so simple that a DSP solution would represent over-kill, and it would be nice to model its behaviour using a real-time DSP system to mimic its performance as the values of the various components are altered by re-programming the system. Second, many mechanical linear systems, such as damped mass spring arrangements, pendulums, ultrasonic transducers and so on, can be precisely represented in equivalent electrical form using suitable combinations of resistors, capacitors, inductors and occasionally gain-stages (amplifiers). Again therefore, to replicate in real-time the performance of mechanical systems, we...