Lecture#2 - BIM108 Lecture 2 Systems One of the most...

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1 BIM108 – Lecture 2 Systems One of the most important motivations for the development of general tools for analyzing and designing systems is that systems from many different applications have very similar mathematical descriptions. Example Examples: (a) (b) V s + V c C i R f K f v (c) k 1 k 2 r(t) Tissue Blood b(t)
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2 All examples have the form ) ( ) ( ) ( t bx t ay dt t dy = + The output response y(t) resulting from initial condition (0 ) y and input ) ( t x applied for 0 t is give by () 0 (0 ) ( ) , 0 t at a t yt e y e bx d t λ λλ −− =+ . When (0 ) 0 y = , i.e. the system has zero initial energy 0 , ) ( ) ( 0 ) ( = t d bx e t y t t a Block Diagram Elements • Summer 1 xt 2 _ + 123 xt xt xt + • Multiplier 3 + Axt A • Integrator t xtd t −∞
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3 Block Diagram Examples + () yt bxt ayt d t = _ a xt b [ ] dy t ay t bx t dt −∞ += Systems properties All systems have zero initial energy in the follow discussion. For any two inputs ) ( 1 t x and ) ( 2 t x ) ( ) ( 1 1 t y t x H ⎯→ ) ( ) ( 2 2 t y t x H System H is H 1. linear
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Lecture#2 - BIM108 Lecture 2 Systems One of the most...

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