17_Intro_to_Discrete

17_Intro_to_Discrete - Chapter 17 Introduction to...

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653 Chapter 17 Introduction to Discrete-Time Signals and Systems Chapter Outline 17.1 INTRODUCTION TO DISCRETE-TIME SIGNALS .............................. 656 17.1.1 Introduction ................................................................................................................................ 656 17.1.2 Signal Definitions ................................................................................................................... 657 17.1.3 Examples of Discrete-Time Signals .............................................................................. 658 17.2 INTRODUCTION TO SAMPLING ....................................................... 660 17.2.1 Introduction ................................................................................................................................ 660 17.2.2 Definitions .................................................................................................................................. 660 17.2.3 Analog-to-Digital Converters ............................................................................................ 663 17.3 CODING AND QUANTIZATION .......................................................... 665 17.3.1 Introduction ................................................................................................................................ 665 17.3.2 Coding .......................................................................................................................................... 666 17.3.3 Quantization .............................................................................................................................. 668 17.3.4 Summary ..................................................................................................................................... 669 17.4 DIGITAL-TO-ANALOG CONVERTERS .............................................. 670 17.4.1 Introduction ................................................................................................................................ 670 17.4.2 Zero-Order Hold ....................................................................................................................... 670 17.4.3 Digital-to-Analog Conversion ........................................................................................... 671 17.5 INTRODUCTION TO DISCRETE-TIME SYSTEMS ............................ 673 17.5.1 Introduction ................................................................................................................................ 673 17.5.2 Definitions .................................................................................................................................. 674 17.5.3 Discrete-Time System Representations ....................................................................... 675 17.5.4 System Response to Standard Inputs ............................................................................ 676 17.6 INTRODUCTION TO DIGITAL FILTERS ........................................... 677 17.6.1 Digital Filters ........................................................................................................................... 677 17.6.2 Examples of Discrete-Time Systems ............................................................................ 679 17.7 HOMEWORK FOR CHAPTER 17 ....................................................... 681 Introduction to Chapters 17 to 23 In the previous chapters we have analyzed physical processes that evolve in real time. Our basic approach is to model the observed physical process with a mathematical function. This approach is systematically presented through the development of the following concepts: 1. The definition of a signal and a system. 2. Signal representations.
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654 Chapter 17 Introduction to Discrete-Time Signals and Systems 3. System representations, their interrelationships, and their properties. 4. The propagation of a signal through a system in the frequency domain. The signal representations we used to model these physical processes are functions that depend on a real variable. These signal models lead naturally to differential equations as system models. We also used the Fourier series and Fourier transform, and the Laplace transform, analysis tools that can be applied to real functions, for alternative signal and system representations. Beginning with this chapter we turn our attention to physical processes that can’t be observed at every instant of time. We can effectively observe them only at discrete instants of time. Some of these processes are naturally discrete, such as the operation of a computer, or economic processes. Other discrete-time processes are generated from continuous-time processes by sampling. The definition of a signal and a system still applies to these discrete-time processes, but the representation of a discrete-time signal must be a discrete-time function. This starting point launches us into a separate but parallel development of discrete-time signals and systems. In fact, the parallels are so strong that from an abstract mathematical viewpoint, the results can be said to be the same (with a few exceptions). Nonetheless, different analysis tools are required for discrete functions, and the interpretations of the results in physical terms are different. Therefore, a discussion of discrete-time theory is given in the coming chapters.
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