20082ee102_1_2008ee102_hw2

20082ee102_1_2008ee102_hw2 - SPRING 2008: Put First Letter...

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Put First Letter * of LAST Name in the corner →→%% (* Otherwise Your HW will be LOST) PRINT: (LAST, Middle, First):——————————————————– HW: # 2 A LATE HW IS NEVER A HW! Posted: April 10 Hand In: April 17 Attach This Sheet To Your HW 1. Let x ( · ) and y ( · ) denote input and corresponding output of a system S , respectively. Given the following IPOP relations: (i) y ( t ) = x (4 t ) , t ( -∞ , ) , (ii) y ( t ) = Z -∞ e - t ( t - τ ) U ( τ - t ) x ( τ ) dτ, t ( -∞ , ) . In each case verify whether S is: L , TI , Causal . 2. Calculate the following integral: y ( t ) = Z -∞ e - ( t - σ ) U ( σ - t ) U (1 - σ ) dσ. 3. The IRF h ( t ) of a L, TI, C system S is h ( t ) = δ ( t ) - 2 e - t U ( t ) , t ( -∞ , ) (i) Use BT to write down input-output relation of S . (ii) Complete output y ( t ) of S given that its input is x ( t ) = U ( t - 1) U (4 - t ) . 4.
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20082ee102_1_2008ee102_hw2 - SPRING 2008: Put First Letter...

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