EE3TP4_4_LTI_SystemResponse_Lecture 7

EE3TP4_4_LTI_SystemResponse_Lecture 7 - Linear...

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Linear Time-Invariant (LTI) Systems • Because of the LTI property, the total response of an LTI system can always be broken down into the superposition of two simpler responses. • Let's look at a simple example . .. LTI System x t y t
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System View: EE 2CI5 and 2CJ4 showed how to model this physical system mathematically : Recall “RC time constant” Given input x ( t ), the output y ( t ) is the solution to the differential equation. dy t dt 1 RC y t = 1 C x t Input x ( t ) = i ( t ) Output v ( t ) = y ( t ) Simple Circuit Example: LTI system x ( t ) y ( t )
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t dt 1 RC y t = 1 C x t dy t dt e t / RC 1 RC y t e t / RC = 1 C x t e t / RC which gives d y t e t / RC dt = 1 C x t e t / RC . Therefore t 0 t d y t e t / RC = 1 C t 0 t x t e t / RC dt y t e t / RC y t 0 e t 0 / RC = 1 C t 0 t x t e t / RC dt y t
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This note was uploaded on 02/01/2011 for the course ECE 3TP4 taught by Professor Drterrencetodd during the Fall '10 term at McMaster University.

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EE3TP4_4_LTI_SystemResponse_Lecture 7 - Linear...

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