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5_Signal_Def - Chapter 5 Introduction to Signals Chapter...

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67 Chapter 5 Introduction to Signals Chapter Outline 5.1 DEFINITION OF A SIGNAL ................................................................... 68 5.1.1 Definitions ....................................................................................................................................... 68 5.1.2 Examples .......................................................................................................................................... 70 5.1.3 Interconnections of Signals ..................................................................................................... 72 5.2 TIME SCALING, TIME SHIFTING, AND LIMITS OF SIGNALS ............ 76 5.2.1 Introduction ..................................................................................................................................... 76 5.2.2 Time Scaling .................................................................................................................................. 76 5.2.3 Time Shift ........................................................................................................................................ 80 5.2.4 Limits of Signals .......................................................................................................................... 81 5.2.5 MATLAB Experiments .............................................................................................................. 83 5.3 SIGNALS DEFINED ON INTERVALS ..................................................... 84 5.3.1 Pulse Definition ............................................................................................................................ 84 5.3.2 General Signals ............................................................................................................................. 85 5.3.3 MATLAB Experiments .............................................................................................................. 89 5.4 DIGITAL WAVEFORMS ........................................................................ 90 5.4.1 Introduction ..................................................................................................................................... 90 5.4.2 Symbols ............................................................................................................................................ 90 5.4.3 Message Signals ........................................................................................................................... 92 5.4.4 Time Division Multiplexing .................................................................................................... 94 5.5 SIGNALS AS SUMS OF SINUSOIDS ....................................................... 95 5.6 CHAPTER SUMMARY ........................................................................... 98 5.6.1 Definitions ....................................................................................................................................... 98 5.6.2 Signal Models ................................................................................................................................ 98 5.7 HOMEWORK FOR CHAPTER 5 ............................................................. 99 In Chapter 1 we informally introduced the concept of a signal. It is the purpose of this chapter to formally introduce the definition of a signal. We will then give a number of examples of signals. We will also discuss several ways of combining two or more signals to form more complicated signals. This discussion marks the beginning of the discussion of the main topics in this text. As we discussed in Chapter 1, a signal is a function that is used to describe physical observations. In order to use the signal to enhance our understanding of the physical phenomenon we must develop a representation of the signal. That is to say, we must write an explicit expression for the function that can be analyzed. This chapter is devoted to introducing several elementary methods for developing a representation of the signal. These methods are primarily ad hoc, but they are
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68 Chapter 5 Introduction to Signals routinely used in system theory. First we discuss several mathematical techniques for systematically reshaping known functions to match observations. These techniques are pervasive in signal modeling. Then we discuss modeling signals by breaking the signal into time intervals and developing a representation on each time interval. This technique leads to a model of a digital waveform that is widely used in digital communications and in computers. Finally, we introduce the idea of modeling signals with sinusoids. This concept, which is fundamental to much of the analysis in this text, takes on its most subtle form in the Fourier series. This important topic is taken up in Chapter 7. Summary of Sections Section 5.1: The definition of a signal is introduced. Section 5.2: We discuss time scaling and time shifting as well as signals defined as limits Section 5.3: Signal modeling based on intervals is introduced. Section 5.4: We discuss digital waveforms. Section 5.5: We discuss signals that are sums of sinusoids. Section 5.6: Chapter summary section. Coverage of the Text This chapter requires primarily the material on functions in Chapter 2. The MATLAB files require elementary knowledge of matrices given in Chapter 4.
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