23_Dis_Freq_Resp

23_Dis_Freq_Resp - Chapter 23 Frequency Domain Analysis of...

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895 Chapter 23 Frequency Domain Analysis of Discrete- Time Systems Chapter Outline 23.1 FREQUENCY RESPONSE THEOREM FOR DISCRETE SYSTEMS. ...897 23.1.1 Introduction. ............................................................................................................................... 897 23.1.2 The Frequency Response Theorem. ............................................................................... 898 23.1.3 The Frequency Response Function. 901 23.1.4 MATLAB Experiments. ....................................................................................................... 906 23.2 RELATIONSHIP TO CONTINUOUS-TIME SIGNALS. ........................ 908 23.2.1 Introduction. 908 23.2.2 Analysis. ...................................................................................................................................... 908 23.2.3 MATLAB Experiments. 911 23.3 CLASSIFICATION OF FREQUENCY RESPONSE FUNCTIONS. .......... 911 23.3.1 Introduction. 911 23.3.2 Bandwidth of a System. 912 23.3.3 Ideal Filters . .............................................................................................................................. 914 23.4 IIR FILTER DESIGN. ......................................................................... 916 23.4.1 Introduction. 916 23.4.2 Bilinear Transformation. ...................................................................................................... 918 23.4.3 Filter Design . ............................................................................................................................ 922 23.4.4 MATLAB Experiments. 922 23.5 LINEAR PHASE FIR FILTERS . .......................................................... 924 23.5.1 Introduction. 924 23.5.2 Linear Phase Filters . ............................................................................................................. 924 23.5.3 FIR Filters. ................................................................................................................................. 926 23.5.4 Windowing. ................................................................................................................................ 927 23.5.5 FIR Filter Design Using Windows . ................................................................................ 929 23.5.6 Selection of Windows . ......................................................................................................... 931 23.5.7 Summary. .................................................................................................................................... 932 23.5.8 MATLAB Experiments. 933 23.6 SYSTEM RESPONSE TO ARBITRARY INPUT SIGNALS . .................. 934 23.6.1 Introduction. 934 23.6.2 System Response to Energy and Power Signals. ..................................................... 934 23.6.3 Filter Comparison. .................................................................................................................. 936 23.6.4 MATLAB Experiments. 940 23.7 CHAPTER SUMMARY. ....................................................................... 942 23.8 HOMEWORK FOR CHAPTER 23. ...................................................... 944
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896 Chapter 23 Frequency Domain Analysis of Discrete-Time Systems In Chapters 21 and 22 we have developed several system representations and their interrelationship. In Chapter 20 we discussed several representations of a signal. In this chapter we will study the relationship between the input and output signal and the system. We will adopt the following terminology. Given an input signal the system will produce an output signal. We say the input signal propagates through the system. This terminology is consistent with the definition of a system, which defines the system in terms of the input and output signal. This terminology suggests that the relationship between the input and output signals and the system can be studied by comparing the input signal to the output signal. The change between these two signals can be attributed to the system. We shall pursue this idea in this chapter. We begin by studying the response of the system to a sinusoidal input signal. It turns out that the output signal is also a sinusoid at the same frequency. Furthermore, the amplitude and phase of the output signal can be determined from the transfer function of the system. So the output signal of a system is directly related to the system representation and the input signal . This result is precisely stated in the frequency response theorem which is discussed in this chapter. This theorem is the basis for establishing the relationship between the system and the signal propagating through it. The linkage between the input and output signals and the system in the frequency response theorem is of immense importance in many aspects of signals and systems. The frequency response theorem identifies the frequency response function as the system property that links the system to the signal propagating through it. This function is identical to the DTFT transfer function, and it can be easily calculated from the z -transform transfer function. It is really the frequency response function that is of central interest in this chapter.
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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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23_Dis_Freq_Resp - Chapter 23 Frequency Domain Analysis of...

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