CHAPTER 8
DISCRETE-TIME FILTERS
8.1 CHAPTER OBJECTIVES
On completion of this chapter, the reader should be able to
1. explain the basic types of filters and approaches to filter design;
2. design a finite impulse response (FIR) filter for a given frequency specification;
3. plot the frequency response of a filter;
4. be conversant with filter windows and where they are used; and
5. explain and implement fast filtering algorithms.
8.2 INTRODUCTION
This chapter introduces digital filters, which are able to remove (filter out) or enhance certain frequency components in a signal. Digital filters are a key technology in many audio processing applications and are fundamental to communications systems. The idea of a digital filter is to either reduce or increase the strength of a signal but only over specific frequency ranges. Digital filters are used in various applications, a few of which are
1. audio recording/playback/enhancement applications,
2. noise removal,
3. sub-band filtering for audio and image storage and/or transmission, and
4. narrow-band filtering for selecting a communications channel.
To give a concrete example, consider Figure 8.1, which shows a sample application—measuring the electrocardiogram (ECG) signals as derived from the beating of the human heart. Such a measurement has a great many clinical and diagnostic applications and is attractive because the signal can be measured at various points on a patient’s skin, thus monitoring the heart externally. The ...
