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EECE 301 Note Set 7 DT System Recursion

# EECE 301 Note Set 7 DT System Recursion - EECE 301 Signals...

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EECE 301 Prof. Mark Fowler Note Set #7 • D-T Systems: Recursive Solution of Difference Equations • Reading Assignment: Section 2.3 of Kamen and Heck

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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).
We saw that Differential Equations model C-T systems… D-T systems are “modeled” by Difference Equations. The quotes are used here because we aren’t really modeling some existing system with difference equations but rather building a desired system with difference equations. So in that sense, difference equations aren’t just models they are the system. ] [ ... ] 1 [ ] [ ] [ ... ] 1 [ ] [ 1 0 1 M n x b n x b n x b N n y a n y a n y M N + + + = + + + A general N th order Difference Equations looks like this: Most “Advanced” Output Sample Least “Advanced”

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EECE 301 Note Set 7 DT System Recursion - EECE 301 Signals...

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