Digital Signal Processing with Examples in MATLAB, 2nd Edition

11

Models of Analog Systems

11.1  Introduction

Digital models of analog filters and other continuous systems are useful in situations where we wish to duplicate or replace the continuous system with an “equivalent” discrete system. As suggested in Figure 11.1, the accuracy of the model is measured in terms of a discrete error, e_k, at regularly spaced sample points. The analog-to-digital converters (ADCs) in Figure 11.1 are assumed to produce impulse samples at synchronized points in time. In Chapter 9, we discussed the design of digital filters that minimize the mean-squared value of e_k. In this chapter, we wish to arrive at models that produce a small or vanishing value of e_k under specified input conditions.

A simple linear approximation ...