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Digital Signal Processing Using MATLAB for Students and Researchers by JOHN W. LEIS

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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 ...

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