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20085ee102_1_F08-102-HW-2

# 20085ee102_1_F08-102-HW-2 - FALL 2008 Put First Letter of...

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FALL 2008: Put First Letter of LAST Name in the corner →→ ( Otherwise Your HW May Be LOST! ) PRINT: (LAST , Middle, First):——————————————————– EE102: SYSTEMS & SIGNALS HW: # 2 A LATE HW CANNOT BE A HW! Posted: W, October 8 Hand In To Me 1 : M, October 20 Attach This Sheet To Your HW (Otherwise It May Be Lost!) 1. Let x ( · ) and y ( · ) denote input and corresponding output of a system S , respectively. Given the following IPOP relations: (i) y ( t ) = x (2 t - 1) , t ( -∞ , ) , (ii) y ( t ) = -∞ e - τ ( t - τ ) U ( t - τ ) x ( τ ) d τ , t ( -∞ , ) . In each case verify whether S is: L, TI, Causal . 2. (i) Use BT to write down the IRF h ( t, τ ) of the system of Problem 1(ii). (ii) Given the IRF h ( t ) of a L,TI,C system: h ( t ) = te - t U ( t ) , t ( -∞ , ) , and the input x ( t ) = U ( t + 4) - e - t U ( t - 4) , t ( -∞ , ) . Find the corresponding output y ( t ). (iii) A system S whose IPOP relation is b ( t ) = 2 t -∞ a ( τ ) d τ , where a ( t ) and b ( t ) denote input and output, respectively. Find the IRF h ( t ) of S , and find its response due the input U ( t ) — called the step response 1

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20085ee102_1_F08-102-HW-2 - FALL 2008 Put First Letter of...

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