20065ee102_1_102-F06-HW1[1]

# 20065ee102_1_102-F06-HW1[1] - FALL 2006 Put First Letter of...

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FALL 2006 Put First Letter of LAST Name in the corner →→→% Name (LAST, Middle, First):———————— ——————————— EE102: SYSTEMS & SIGNALS HW :#1 ALATEHWISNOTAHW ! Posted: October 4 Hand In 1 : October 11 Attach This Sheet To Your HW 1. Consider the di±erential equation: dy ( t ) dt +2 y ( t )= dx ( t ) dt 2 x ( t ) ,t 0 , y (0) = 0 ,x (0)=0 . (i) Solve for y ( t ) in terms of x ( t ). (ii) Find y ( t ) given that x ( t te t U ( t ) . 2. Compute: I 1 ( t Z t −∞ ( t τ ) e 2( t τ ) U ( τ 2) dτ, I 2 = Z 5 1 e 2 t U ( t 3) dt. 3. A system S is described by the following IPOP description: y ( t T [ x ( t )] ,y ( t Z t −∞ e t e 2 τ x ( τ ) dτ, t > −∞ , where x ( · ) is input and y ( · ) is output. Is this system TI or TV? Find the output y ( t ) when the input to the system is x ( t e t U ( t 4) . 1 To me (NL) at 8:50 am break 1

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4. Consider the “RC-circuit” of Fig 1.2, p.3, of BestText. Now, let x ( · )be input voltage and i ( · ) be output current, i.e.,
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## This note was uploaded on 10/31/2009 for the course EE ee102 taught by Professor Levan during the Fall '09 term at UCLA.

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20065ee102_1_102-F06-HW1[1] - FALL 2006 Put First Letter of...

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