EECE 301 Note Set 33 DT Z Transform

EECE 301 Note Set 33 DT Z Transform - EECE 301 Signals...

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1/16 EECE 301 Signals & Systems Prof. Mark Fowler Note Set #33 • D-T Systems: Z-Transform … “Power Tool” for system analysis • Reading Assignment: Sections 7.1 – 7.3 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) DFT & FFT (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 Ch. 11 Z-Transform & D-T Systems Z-Transform does for DT systems what the Laplace Transform does for CT systems Z-T is used to Solve difference equations with initial conditions Solve zero-state systems using the transfer function We will: - Define the ZT - See its properties - Use the ZT and its properties to analyze D-T systems
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4/16 −∞ = Ω = Ω n n j e n x X DTFT ] [ ) ( : Periodic in Ω with period 2 π Section 7.1 Z-transform definitions Given a D-T signal x [ n ] - < n < we’ve already seen how to use the DTFT: Recall : For C-T case, the FT doesn’t converge for some signals… the LT mitigates this problem by including decay in the transform st t j t j e e vs e +
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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 University.

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EECE 301 Note Set 33 DT Z Transform - EECE 301 Signals...

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