EECE 301 Note Set 34 DT Using ZT to Solve

EECE 301 Note Set 34 DT Using ZT to Solve - EECE 301...

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1/16 EECE 301 Prof. Mark Fowler Note Set #34 • D-T Systems: Z-Transform … Solving Difference Eqs. & Transfer Func. • Reading Assignment: Sections 7.4 – 7.5 of Kamen and Heck
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2/16 Ch. 1 Intro C-T Signal Model Functions on Real Line D-T Signal Model Functions on Integers System Properties LTI Causal Etc Ch. 2 Diff Eqs C-T System Model Differential Equations D-T Signal Model Difference Equations Zero-State Response Zero-Input Response Characteristic Eq. Ch. 2 Convolution C-T System Model Convolution Integral D-T System Model Convolution Sum Ch. 3: CT Fourier Signal Models Fourier Series Periodic Signals Fourier Transform (CTFT) Non-Periodic Signals New System Model New Signal Models Ch. 5: CT Fourier System Models Frequency Response Based on Fourier Transform New System Model Ch. 4: DT Fourier Signal Models DTFT (for “Hand” Analysis) (for Computer Analysis) New Signal Model Powerful Analysis Tool Ch. 6 & 8: Laplace Models for CT Signals & Systems Transfer Function New System Model Ch. 7: Z Trans. Models for DT Signals & Systems Transfer Function New System Model Ch. 5: DT Fourier System Models Freq. Response for DT Based on DTFT New System Model Course Flow Diagram The arrows here show conceptual flow between ideas. Note the parallel structure between the pink blocks (C-T Freq. Analysis) and the blue blocks (D-T Freq. Analysis).
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3/16 ZT For Difference Eqs. Given a difference equation that models a D-T system we may want to solve it: -with IC’s -with IC’s of zero Apply ZT to the Difference Equation Use the Transfer Function Approach Note… the ideas here are very much like what we did with the Laplace Transform for CT systems. We’ll consider the ZT/Difference Eq. approach first…
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4/16 , . .. , , n n x y n bx n ay n y 2 1 0 for ] [ ] 1 [ IC ] [ ] 1 [ ] [ : Given = = = + Solve for: y [ n ] for n = 0, 1, 2,… Solving a First-order Difference Equation using the ZT Take ZT of differential equation: { } { } ] [ ] 1 [ ] [ n
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This note was uploaded on 02/29/2012 for the course EECE 301 taught by Professor Fowler during the Fall '08 term at Binghamton.

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EECE 301 Note Set 34 DT Using ZT to Solve - EECE 301...

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