21_Discrete_Systems

# 21_Discrete_Systems - Chapter 21 Discrete-Time System...

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809 Chapter 21 Discrete-Time System Representations Chapter Outline 21.1 DISCRETE CONVOLUTION. .............................................................. 810 21.1.1 Introduction. ............................................................................................................................... 810 21.1.2 Definitions. ................................................................................................................................. 811 21.1.3 FIR Systems. ............................................................................................................................. 812 21.1.4 Other Forms of the Convolution Summation. ............................................................ 813 21.1.5 MATLAB Experiments. ....................................................................................................... 815 21.2 DIFFERENCE EQUATIONS AND TRANSFER FUNCTIONS. ............... 816 21.2.1 Introduction. 816 21.2.2 Difference Equations. ............................................................................................................ 816 21.2.3 Transfer Functions. ................................................................................................................. 818 21.2.4 MATLAB Experiments. 822 21.3 BLOCK DIAGRAMS AND NETWORK STRUCTURES. ....................... 824 21.3.1 Introduction. 824 21.3.2 Basic Building Blocks. ........................................................................................................ 825 21.3.3 Network Structures. ................................................................................................................ 828 21.4 DTFT TRANSFER FUNCTION. ........................................................... 833 21.5 DISCRETE STATE SPACE REPRESENTATIONS. .............................. 835 21.5.1 Introduction. 835 21.5.2 All-Delay Block Diagrams and State Space Equations. ...................................... 836 21.5.3 Solution to State Space Equations. ................................................................................ 840 21.5.4 MATLAB Experiments. 843 21.6 NETWORK INTERCONNECTION STRUCTURES. 844 21.6.1 Introduction. 844 21.6.2 Cascade Form and Parallel Form. .................................................................................. 844 21.6.3 MATLAB Experiments. 848 21.7 CHAPTER SUMMARY. ....................................................................... 849 21.8 HOMEWORK FOR CHAPTER 21. ...................................................... 849 In Chapter 17 we introduced five system representations: convolution summations, difference equations, transfer functions, state space representations, and the DTFT transfer function. In this chapter we will discuss each of these system representations in more detail. Each system representation is defined and several examples of these systems are given. The whole development of this chapter is entirely analogous to the discussion of continuous-time systems in Chapters 10 to 12. Our presentation accents the similarities between continuous and discrete system. There are several important

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810 Chapter 21 Discrete-Time System Representations differences between these two classes of systems, and these differences are pointed out as well. We also introduce block diagrams as another representation for transfer functions. Using block diagrams we show how difference equations correspond to all-delay block diagrams. These results are analogous to the canonical all-integrator block diagrams discussed in Chapter 11. The presentation of this material is slightly different, however. We adopt the viewpoint of digital filters, and develop the system structures within that framework. As with continuous systems, these discrete system representations are all closely related to each other. These relationships are developed in the next chapter. Summary of Sections Section 21.1: We discuss discrete convolution. Section 21.2: We discuss difference equations and transfer functions. Section 21.3: We introduce block diagrams for discrete systems. Section 21.4: We introduce the DTFT transfer function. Section 21.5: We develop state space representations from all-delay block diagrams. Section 21.6: We show how to decompose a system into a cascade and parallel interconnection structure. Section 21.7: Chapter summary section. Coverage of the Text The results in this chapter require only the definition of discrete-time signals and systems in Chapter 17 and z -transforms in Chapter 18. The development of the concepts for discrete-time systems parallels the development of continuous-time systems, and frequent references are made to Chapters 10 - 12; however, this material is not strictly required except for Section 21.6. Section 21.6 requires the
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## This note was uploaded on 09/10/2009 for the course ECE 60367 taught by Professor Meehan during the Spring '09 term at Virginia Tech.

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21_Discrete_Systems - Chapter 21 Discrete-Time System...

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