EECE 301 Note Set 12 FS Motivation

EECE 301 Note Set 12 FS Motivation - EECE 301 Signals &...

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1/18 EECE 301 Signals & Systems Prof. Mark Fowler Note Set #12 • C-T Signals: Motivation for Fourier Series • Reading Assignment: Section 3.1 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 Ch. 3: Fourier Series & Fourier Transform (This chapter is for C-T case only ) 3.1 Representation in terms of frequency components i.e., sinusoids And… it is easy to find out how sinusoids go through an LTI system Q: Why all this attention to sinusoids ? A: Recall “sinusoidal analysis” in RLC circuits: Fundamental Result: Sinusoid In Sinusoid Out LTI System - Section 3.1 motivates the following VERY important idea: “signals can be built from sinusoids - Then Sections 3.2 – 3.3 take this idea further to precisely answer How can we use sinusoids to build periodic signals? - Then Section 3.4 – 3.7 take this idea even further to precisely answer How can we use sinusoids to build more-general non-periodic signals?
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4/18 “Why Study Response to Sinusoids” (not in Ch. 3… See 5.1) Q: How does a sinusoid go through an LTI System? Consider: h ( t ) ) cos( ) ( 0 θ ω + = t A t x ? ) ( = t y LTI: Linear , Time-Invariant To make this easier to answer (yes… this makes it easier!!) we use Euler’s Formula: ) ( 2 ) ( 2 0 0 0 ) cos( ) ( θω + + + = + = t j A t j A e e t A t x The input is now viewed as the sum of two parts… By linearity of the system we can find the response to each part and then add them together.
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EECE 301 Note Set 12 FS Motivation - EECE 301 Signals &...

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