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20082ee102_1_HW-3

# 20082ee102_1_HW-3 - (i e-2 t sinh(5 t U t(ii e-t cos t-π 3...

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SPRING 2008: Put First Letter * of LAST Name in the corner →→%% (* Otherwise Your HW will be LOST) PRINT: (LAST, Middle, First):——————————————————– EE102: SYSTEMS & SIGNALS HW: # 3 A LATE HW IS NEVER A HW! Posted: April 17 Hand In: April 24 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. Calculate the Laplace Transforms of those functions on the Table(in the Text) which have NOT been calculated for you in class. In each case clearly indicate the DOC on the PZP of the transform. 1

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4. Find the Laplace Transform of the following signals:
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Unformatted text preview: (i.) e (-2 t ) [ sinh (5 t )] U ( t ) (ii.) e (-t ) cos ( t-π/ 3) U ( t ) (iii.) ( e-αt sin 2 ω t ) U ( t ) ,α > . 5. Calculate the following integral: y ( t ) = Z ∞-∞ e-( t-σ ) U ( t-σ ) σU ( σ ) dσ,t ≥ . 6. 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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