20065ee102_1_102-F06-HW-2[1]

20065ee102_1_102-F06-HW-2[1] - FALL 2006 Put First Letter...

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FALL 2006 Put First Letter of LAST Name in the corner →→→% Name (LAST, Middle, First):———————— ——————————— EE102: SYSTEMS & SIGNALS HW :#2 ALATEHWISNOTAHW ! Posted: October 12 Hand In: October 18 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 R −∞ e t ( t τ ) U ( τ t ) x ( τ ) dτ, 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 e t U ( t ) ( −∞ , ) , and the input x ( t δ ( t ) e t U ( t 4) ( −∞ , ) . Find the corresponding output y ( t ). (iii) A system S whose IPOP relation is b ( t )=2 Z t −∞ a ( τ ) dτ, where a ( t ) and b ( t ) denote input and output, respectively. Find the IRF h ( t ) of S , and ±nd its response due the input U ( t ) — called the step response denoted by g ( t ).

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20065ee102_1_102-F06-HW-2[1] - FALL 2006 Put First Letter...

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