Signal Processing and Integrated Circuits

Chapter 5

Design of Digital Filters

5.1 Introduction

The design techniques of digital filters are discussed in detail. At first, emphasis is laid on the conceptual organization and analytical methods of design. Then the chapter concludes with the details of how to use MATLAB® as a computer-aided design tool. Numerous examples are given throughout the chapter of both analytical and computer-aided design methods.

5.2 General Considerations

As in the case of analog filters studied in Chapter 3, the design of digital filters in the frequency domain can be accomplished according to the following procedure:

a. The specifications on the filter characteristics are used to obtain a description of the filter in terms of a stable transfer function. This is the approximation problem.

b. Once the transfer function of the filter has been determined, it can be realized using the techniques of Chapter 4. This is the synthesis or realization problem whose solution requires only knowledge of the coefficients of the transfer function.

The transfer function of a general IIR filters is of the form

5.1

and the special case of an FIR filter transfer function is obtained by putting B_N(z⁻¹) = 1 so that an FIR digital transfer function is a polynomial of the form

5.2

The frequency response of the filter is ...