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# Chap_15 - Chapter 15 Signal and System Analysis in the...

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551 Chapter 15 Signal and System Analysis in the Frequency Domain Chapter Outline 15.1 INTRODUCTION TO SIGNAL AND SYSTEM INTERACTION ............ 553 15.1.1 An Example ............................................................................................................................... 553 15.1.2 Analysis in the Frequency Domain ................................................................................ 555 15.1.3 Periodic Input Signals .......................................................................................................... 557 15.1.4 Energy Input Signals ............................................................................................................. 559 15.1.5 Aperiodic Power Input Signals ......................................................................................... 559 15.1.6 Summary ..................................................................................................................................... 560 15.2 INTERPRETATION OF THE FREQUENCY RESPONSE THEOREM ..561 15.2.1 Introduction ................................................................................................................................ 561 15.2.2 Fourier Series Interpretation of the Frequency Response Theorem ............... 561 15.2.3 An Example ............................................................................................................................... 564 15.2.4 MATLAB Experiments ........................................................................................................ 567 15.3 PROPAGATION OF A PULSE TRAIN THROUGH A NETWORK ........ 568 15.3.1 Introduction ................................................................................................................................ 568 15.3.2 Case 1: Input Signal x 1 ( t ) ................................................................................................. 570 15.3.3 Case 2: Input Signal x 2 ( t ) ................................................................................................. 572 15.3.4 Comparison: Case 1 and Case 2 .................................................................................... 572 15.3.5 A Pulse Train ............................................................................................................................ 574 15.3.6 Summary of the Propagation of the Pulse Train ...................................................... 575 15.3.7 MATLAB Experiments ........................................................................................................ 576 15.4 PROPAGATION OF ENERGY SIGNALS THROUGH A SYSTEM ........ 579 15.4.1 Introduction ................................................................................................................................ 579 15.4.2 Propagation of a Pulse Through an RC Network ..................................................... 579 15.4.3 Summary of the Section ...................................................................................................... 584 15.4.4 MATLAB Experiments ........................................................................................................ 584 15.5 TRACKING FOR LINEAR MOTORS .................................................. 586 15.5.1 Introduction ................................................................................................................................ 586 15.5.2 The Motor ................................................................................................................................... 586 15.5.3 Performance of the Motor ................................................................................................... 588 15.5.4 MATLAB Experiments ........................................................................................................ 591 15.6 AMPLITUDE MODULATION AND FREQUENCY DIVISION MULTIPLEXING ................................................................................ 591 15.6.1 Introduction ................................................................................................................................ 591 15.6.2 Amplitude Modulation ......................................................................................................... 592

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552 Chapter 15 Signal and System Analysis in the Frequency Domain 15.6.3 Demodulation ............................................................................................................................ 593 15.6.4 Frequency Division Multiplexing .................................................................................... 594 15.7 CHAPTER SUMMARY ....................................................................... 596 15.8 HOMEWORK FOR CHAPTER 15 ....................................................... 597 Up to this point we have studied: signals in Chapter 8, and systems in Chapters 10 - 12. Then in Chapter 14 we introduced the frequency response theorem which gives us an explicit link between the system and the signal propagating through it. The frequency response theorem as stated in the last chapter allows for only a pure sinusoidal input signal. In this chapter we will extend the interpretations of the frequency response theorem in two ways. First, we will allow the input signal to be an infinite sum of sinusoids (a Fourier series). This straightforward application of the frequency response theorem extends the theorem to all periodic signals. Second, we extend the frequency response theorem to accommodate energy and power signals as input and output signals through the use of Fourier transforms. In Chapter 8 we have developed several signal representations: the Fourier series, the Fourier transform, amplitude and phase spectrums, energy spectral density, and the power spectral density. All of these signal representations have graphical representations. By combining these concepts with the frequency response function from the frequency response theorem, we obtain a graphical interpretation of how a signal propagates through a system. This chapter contains an extended example, a pulse train and a signal pulse propagating through a RC network, to illustrate fully the various graphical interpretations of the frequency response theorem using concepts from signal representations. The graphical interpretations are straightforward for Fourier series, but when extended to energy signals, they become a little blurred. By comparing the
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