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 () is a frequency-domain description of the system Recall that: Because h ( t ) and H () 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 ( ) 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 2 [ H F ] e jt d = F e jt Proof Step 1: Think of the input as a sum of complex sinusoids-Each component F e jt H F e jt 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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