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20111ee102_1_homework3

# 20111ee102_1_homework3 - π 3 U t(iii e-αt sin 2 ω t U...

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WINTER 2011: Put Discussion section number in the corner →→→ (* Otherwise Your HW will be LOST) Name(Print) (LAST, Middle, First): ————————————— Student ID : ——————————————————– EE102: SYSTEMS & SIGNALS HW: # 3 NO LATE HOMEWORK POLICY! Posted: January 20 Hand In: January 27 IN CLASS Attach This Sheet To Your HW 1. The IPOP relationship of a system S is y ( t ) = Z t -∞ x ( τ ) + Z t e t e ( - τ ) x ( τ ) dτ, -∞ < t < Write down the IRF h(t) and the USR(Unit Step Response) g(t) of the system. 2. The IPOP relation of a SISO system S is: x ( t ) -→ [ S ] -→ y ( t ) y ( t ) = Z t -∞ e - ( t - τ ) x ( τ ) dτ, t ( -∞ , ) . Write down the IRF h ( t, τ ) of S. Then compute its output y(t) given that its input x(t) is x ( t ) = e - ( t - 1) U ( t - 1) + U (2 - t ) , t ( -∞ , ) . Hints: Decompose x ( t ) into x 1 ( t ) + x 2 ( t ) . 3. Find the Laplace Transform of the following signals: 1

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Unformatted text preview: π/ 3) U ( t ) (iii.) ( e-αt sin 2 ω t ) U ( t ) ,α > . 4. Show that (i) L s [ tf ( t )] =-dF ( s ) ds , L s [ f ( t a )] = aF ( as ) , a 6 = 0 (ii)For n ≥ 1: L s [(-t ) n f ( t )] = d n F ( s ) ds n 5. Given the following systems: (i)System S 1 with IPOP relation: y ( t ) = Z t-∞ x ( σ ) U ( σ ) dσ,t >-∞ . (ii)System S 2 with IPOP relation: z ( t ) = ω ( t ) U ( t )-Z t-∞ e-( t-σ ) ω ( σ ) U ( σ ) dσ,t >-∞ . here z(t) is output and ω ( t ) is input. Compute h 1 ( t ) and h 2 ( t )–IRF of S 1 and S 2 , respectively–and h 12 ( t )–IRF of S 1 S 2 . Then compute H 1 ( s ), H 2 ( s ), and H 12 ( s )– the Laplace Transforms of the respective IRF. What can you tell the wide world from what you have computed? 2...
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20111ee102_1_homework3 - π 3 U t(iii e-αt sin 2 ω t U...

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