EECE 301 Note Set 11 CT Convolution

# EECE 301 Note Set 11 CT Convolution - EECE 301 Signals...

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1/20 EECE 301 Signals & Systems Prof. Mark Fowler Note Set #11 • C-T Systems: “Computing” Convolution • Reading Assignment: Section 2.6 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).
3/20 ) ( ) ( ) ( ) ( )] ( ) ( [ t v t x t v t x t v t x dt d ± ± = = C-T convolution properties Many of these are the same as for DT convolution. We only discuss the new ones here. See the next slide for the others derivative = = t t t d h t x t h d x d y λλ ) ( ) ( ) ( ) ( ) ( The properties of convolution help perform analysis and design tasks that involve convolution. For example, the associative property says that (in theory) we can interchange to order of two linear systems… in practice, before we can switch the order we need to check what impact that might have on the physical interface conditions. 1. Derivative Property : 2. Integration Property Let y ( t ) = x ( t )* h ( t ), then

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4/20 Convolution Properties These are things you can exploit to make it easier to solve convolution problems 1.Commutativity You can choose which signal to “flip” ) ( ) ( ) ( ) ( t x t h t h t x = 2. Associativity Can change order sometimes one order is easier than another ) ( )) ( ) ( ( )) ( ) ( ( ) ( t w t v t x t w t v t x
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EECE 301 Note Set 11 CT Convolution - EECE 301 Signals...

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