Digital-Filter Implementation

Abstract

In this chapter we will delve more deeply into the practical task of using digital filters. We will discuss how to accurately and efficiently implement FIR and IIR filters. You may be asking yourself why this chapter is important. We already know what a digital filter is, and we have (or can find) a program to find the coefficients that satisfy design specifications. We can inexpensively acquire a DSP processor that is so fast that computational efficiency isn't a concern, and accuracy problems can be eliminated by using floating point processors. Aren't we ready to start programming without this chapter? Not quite. You should think of a DSP processor as being similar to a jet plane; when flown by a qualified pilot it can transport you very quickly to your desired destination, but small navigation errors bring you to unexpected places and even the slightest handling mistake may be fatal. This chapter is a crash course in digital filter piloting. In the first section of this chapter we discuss technicalities relating to computing convolutions in the time domain. The second section discusses the circular convolution and how it can be used to filter in the frequency domain; this is frequently the most efficient way to filter a signal. Hard real-time constraints often force us to filter in the time domain, and so we devote the rest of the chapter to more advanced time domain techniques. We will exploit the graphical techniques developed in Chapter 12 in order to manipulate filters. The basic building blocks we will derive are called structures, and we will study several FIR and IIR structures. More complex filters can be built by combining these basic structures. Changing sampling rate is an important application for which special filter structures known as polyphuse filters have been developed. Polyphase filters are more efficient for this application than general purpose structures. We also deal with the effect of finite precision on the accuracy of filter computation and on the stability of IIR filters. 569