EECE 301 Note Set 27 CT Laplace Transform

EECE 301 Note Set 27 CT Laplace Transform - EECE 301...

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1/18 EECE 301 Signals & Systems Prof. Mark Fowler Note Set #27 • C-T Systems: Laplace Transform… “Power Tool” for system analysis • Reading Assignment: Sections 6.1 – 6.3 of Kamen and Heck
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2/18 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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3/18 Diff. Equations describe systems – Differential Eq. for CT – Difference Eq. for DT Convolution with the Impulse Response can be used to analyze the system – An integral for CT – A summation for DT Fourier Transform (and Series) describe what frequencies are in a signal – CTFT for CT has an integral form – DTFT for DT has a summation form – There is a connection between them from the sampling theorem The Frequency Response of a system gives a multiplicative method of analysis – Freq. Response = CTFT of impulse response for CT system – Freq. Response = DTFT of impulse response for DT system What we have seen so far…. We now look at two “power tools” for system analysis: Laplace Transform for CT Systems Z Transform for DT Systems Extension of C TFT Extension of D TFT
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4/18 Ch. 6 Laplace Transform & Transfer Function Back to C-T signals and systems… We’ve seen that the FT is a useful tool for -signal analysis (understanding signal structure) - systems analysis/design But only if: 1. System is in zero state 2. Impulse response satisfies
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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 27 CT Laplace Transform - EECE 301...

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