EECE 301 Note Set 26 DTFT System Analysis

EECE 301 Note Set 26 DTFT System Analysis - EECE 301...

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1/20 EECE 301 Signals & Systems Prof. Mark Fowler Note Set #26 • D-T Systems: DTFT Analysis of DT Systems • Reading Assignment: Sections 5.5 & 5.6 of Kamen and Heck
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2/20 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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3/20 5.5: System analysis via DTFT ] [ n h ] [ n x −∞ = = = i i n x i h n x n h n y ] [ ] [ ] [ ] [ ] [ Recall that in Ch. 5 we saw how to use frequency domain methods to analyze the input-output relationship for the C-T case. We now do a similar thing for D-T Define the “Frequency Response” of the D-T system We now return to Ch. 5 for its DT coverage! Back in Ch. 2, we saw that a D-T system in “zero state” has an output-input relation of: −∞ = Ω = Ω n n j e n h H ] [ ) ( DTFT of h [ n ] Perfectly parallel to the same idea for CT systems!!!
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4/20 From Table of DTFT properties: ) ( ) ( ] [ ] [ Ω Ω H X n h n x So we have: ) ( ] [ Ω H n h ) ( ] [ Ω X n x ] [ ] [ ] [ n x n h n y = ) ( ) ( ) ( Ω Ω = Ω H X Y ) ( ) ( ) ( ) ( ) ( ) ( Ω + Ω = Ω Ω Ω = Ω H X Y H X Y So… So…in general we see that the system frequency response re-shapes the input DTFT’s magnitude and phase.
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EECE 301 Note Set 26 DTFT System Analysis - EECE 301...

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