EE3TP4_19_CT_AperiodicResponse_v2_Lecture 27

# EE3TP4_19_CT_AperiodicResponse_v2_Lecture 27 - 5.2 Response...

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Unformatted text preview: 5.2 Response to Aperiodic Signals-Impulse Response h ( t ) is a time-domain description of the system-Frequency Response H (ω) is a frequency-domain description of the system Recall that: Because h ( t ) and H (ω) form a FT pair, one completely defines the other. h ( t ) and convolution completely describe the zero-state response of an LTI to an input – i.e. h ( t ) completely describes the system. Thus: H ( ω ) must also completely describe the LTI system HOW? Conv. Property from Chapter 4! Step 3: Exploit System Linearity (again – Step 2 was the first time) -Total output is a sum of output components y t = 1 2π ∫ −∞ ∞ [ H ω F ω ] e jωt dω = F ω e jωt “ Proof” Step 1: Think of the input as a sum of complex sinusoids-Each component F ω e jωt H ω F ω e jωt Step 2: We know how each component passes through an LTI-This is the idea of frequency response- is the out. component that is due to the input component 1. Time-Domain : y ( t ) =...
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EE3TP4_19_CT_AperiodicResponse_v2_Lecture 27 - 5.2 Response...

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