EECE 301 Note Set 18 CT Periodic Signal Response

EECE 301 Note Set 18 CT Periodic Signal Response - 1/12...

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Unformatted text preview: 1/12 EECE 301 Signals & Systems Prof. Mark Fowler Note Set #18 • C-T Systems: Frequency-Domain Analysis of Systems • Reading Assignment: Section 5.2 of Kamen and Heck 2/12 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). 3/12 5.2 Response to Periodic Inputs h ( t ) H ( ω ) periodic x ( t ) y ( t ) = ? Since x ( t ) is periodic, write it as FS: ∑ ∞ −∞ = = k t jk x k e c t x ) ( ω H ( ω ) t jk x k e c ω t jk x k e c k H ) ( ω ω ( complex : magnitude & phase) Sum these to get output So, the input is a sum of terms Linear System: So… Output = Sum of Individual Responses But each individual response is to a complex sinusoid input ⇒ EASY! Sum these to get input ∑ ∞ −∞ = = k t jk x k e c t x ) ( ω ∑ ∞ −∞ = = k t jk x k e c k H t y ] ) ( [ ) ( ω ω FS coefficient of y ( t ) Indicates “for x ( t )” 4/12 General Insights from this Analysis 1. periodic in, periodic out 2. The system’s frequency response H ( ω ) works to modify the input FS coefficients to create the output FS coefficients: x k y k c k H c ) ( ω = 5/12 Example (Ex. 5.4 with Some Injected Reality) roblem: suppose you have a circuit board that has a digital clock circuit on it. suppose you have a circuit board that has a digital clock circuit on it....
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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 18 CT Periodic Signal Response - 1/12...

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