Signal Processing and Integrated Circuits

Chapter 3

Design of Analog Filters

3.1 Introduction

The general theory and techniques of analog continuous-time filter design [13, 14] are discussed. These design techniques are by now classical in the sense of being timeless. They are important in themselves and are also of direct relevance to the design of all types of filter, including those which are of the sampled-data type such as digital and switched capacitor filters. This is because the filtering operation is based on the same principles and, very often, analog continuous-time models are used as starting points for the design of other types. The heavy numerical calculations which used to be a distraction from the conceptual organization of the subject can now be easily performed by powerful software tools. Therefore the chapter contains a detailed guide and numerous examples of the use MATLAB® in the design of analog filters and analysing their responses. The chapter concludes with a very important application in telecommunications namely: that of the design of pulse shaping filters for data transmission.

3.2 Ideal Filters

Consider a system or network, as shown in Figure 3.1 whose input is f(t) and output is g(t). With the original explicit notation of the Fourier transform we write

3.1

and

The transfer function of the system ...