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EECE 301 Note Set 2 CT Signals

# EECE 301 Note Set 2 CT Signals - EECE 301 Signals Systems...

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1/22 Note Set #2 • What are Continuous-Time Signals??? • Reading Assignment: Section 1.1 of Kamen and Heck EECE 301 Signals & Systems Prof. Mark Fowler

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2/22 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).
3/22 1.1 Continuous-Time Signal Our first math model for a signal will be a “function of time” Continuous Time (C-T) Signal: A C-T signal is defined on the continuum of time values. That is: f ( t ) for t ∈ℜ Real line f ( t ) t

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4/22 Unit Step Function u ( t ) < = 0 , 0 0 , 1 ) ( t t t u . . . u ( t ) 1 t Note: A step of height A can be made from Au ( t ) Step & Ramp Functions These are common textbook signals but are also common test signals, especially in control systems.
5/22 V s R + C The unit step signal can model the act of switching on a DC source… t = 0 V s u ( t ) R C V s u ( t ) R C +

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6/22 Unit Ramp Function r ( t ) Note: A ramp with slope m can be made from: mr ( t ) . . . r ( t ) 1 t 1 Unit slope < = 0 , 0 0 , ) ( t t t t r < = 0 , 0 0 , ) ( t t mt t mr
7/22 Relationship between u ( t ) & r ( t ) What is ?

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EECE 301 Note Set 2 CT Signals - EECE 301 Signals Systems...

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