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Unformatted text preview: Module 3 Time and Frequency Analysis of Time and Frequency Analysis of DT Signals and Systems DT Signals and Systems 10 DT Signals and Systems DT Signals and Systems R Chen 9/16/20 L Module 3 Module 3 : Time and Frequency Analysis of DT Signals and Systems : Time and Frequency Analysis of DT Signals and Systems 1 Content Analysis of DT LTI systems in the Z domain; stability Analysis of DTLTI systems in the Zdomain; stability Stability of 2 nd order DT systems Digital filters Bibliography 010 Bibliography The Ztransform (Section 10.7) of Signals and Systems , 2 nd edition by A V Oppenheim A S Willsky and S H Nawab R Chen 9/16/20 edition by A. V. Oppenheim, A. S. Willsky, and S. H. Nawab. Time and Frequency Characterization of Signals and Systems (Sections 6.0, 6.2, 6.3,6.6.2) of Signals and Systems , L Module 3 Module 3 : Time and Frequency Analysis of DT Signals and Systems : Time and Frequency Analysis of DT Signals and Systems 2 2 nd edition by A. V. Oppenheim, A. S. Willsky, and S. H. Nawab. Learning Objectives Be able to relate causality and stability to the ROC and Be able to relate causality and stability to the ROC and the location of the system poles Understand the stability of 2 nd order DT systems based on pole location Know the properties of ideal filters and the different types of filters 10 filters Understand the concept of minimumphase R Chen 9/16/20 Be able to design various but simple digital filters L Module 3 Module 3 : Time and Frequency Analysis of DT Signals and Systems : Time and Frequency Analysis of DT Signals and Systems 3 Analysis of DTLTI systems in the Zdomain transfer functions of systems described by linear difference equations M N consider taking Ztransforms and applying the shifting property, = = + = k k k k k n x b k n y a n y 1 ] [ ] [ ] [ ) ( ) ( z H z b z Y M k k k = = = 010 1 ) ( 1 z a z X N k k k + = R Chen 9/16/20 system transfer function is RATIONAL ! L Module 3 Module 3 : Time and Frequency Analysis of DT Signals and Systems : Time and Frequency Analysis of DT Signals and Systems 4 Response of DTLTI system having rational H(z) consider ) ( ) ( ) ( z A z B z H = ) ( z N and let , i.e. input signal has a rational Ztransform system is initially relaxed so that ) ( ) ( z Q z X = y [1] = y [2] = = y [ N ] = 0 then ) ( ) ( z N z B z X z H z Y 10 then  assume that the system has simple poles p 1 , , p N and that the ) ( ) ( ) ( ) ( ) ( z Q z A z X z H z Y = = R Chen 9/16/20 1 N input signal has simple poles q 1 , , q N where p k q m for all k and m assume there is no polezero cancellation L Module 3 Module 3 : Time and Frequency Analysis of DT Signals and Systems : Time and Frequency Analysis of DT Signals and Systems 5 assume there is no polezero cancellation Response of DTLTI system having rational H(z) using partial fraction expansion, we have + = L k N k Q A z Y ) ( thus...
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 Spring '11
 ChenandBacsy

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