CHAPTER 3

SAMPLED SIGNALS AND DIGITAL PROCESSING

3.1 CHAPTER OBJECTIVES

On completion of this chapter, the reader should be able to

1. explain the concepts of sampling and reconstruction;

2. convert decimal numbers into unsigned binary, 2’s complement signed or floating-point formats, and convert binary numbers back to decimal;

3. explain quantization and signal-to-noise ratio (SNR);

4. be able to use difference equations and manipulate them for a given task;

5. be able to iterate difference equations and turn this into code for a digital signal processing (DSP) implementation; and

6. explain ideal reconstruction and derive the polynomial interpolation for a signal.

3.2 INTRODUCTION

Signals invariably come from the real world. To process signals via computer, it is necessary to have some systematic means to acquire the signal so as to capture all necessary information about the signal. This signal acquisition must take into account not only the physical characteristics of the signal but also the necessity of using a numerical representation of the signal at discrete instants in time.

3.3 PROCESSING SIGNALS USING COMPUTER ALGORITHMS

Most signals are analog in nature. Sound, for example, is a pressure variation over time. Images are composed of various light wavelengths at various intensities, over a two-dimensional plane. Many other signal types exist, such as radio frequency waves, bioelectric potentials, and so forth. The key element is to first convert the signal to an ...