Module3_TFAnalysis

Module3_TFAnalysis - Module 3 Time and Frequency Analysis...

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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 DT-LTI systems in the Z-domain; stability Stability of 2 nd order DT systems Digital filters Bibliography 010 Bibliography The Z-transform (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 minimum-phase 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 DT-LTI systems in the Z-domain transfer functions of systems described by linear difference equations M N- consider taking Z-transforms 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 DT-LTI system having rational H(z) consider ) ( ) ( ) ( z A z B z H = ) ( z N and let , i.e. input signal has a rational Z-transform 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 pole-zero 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 pole-zero cancellation Response of DT-LTI system having rational H(z)- using partial fraction expansion, we have + = L k N k Q A z Y ) ( thus...
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Module3_TFAnalysis - Module 3 Time and Frequency Analysis...

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