20111ee102_1_homework1

20111ee102_1_homework1 - x ( t ) + Z t ( t- ) x ( ) d,t 3....

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WINTER 2011: Put Discussion section number in the corner →→→ (* Otherwise Your HW will be LOST) Name(Print) (LAST, Middle, First): ————————————— Student ID : ——————————————————– HW: # 1 NO LATE HOMEWORK POLICY! Posted: January 06 Hand In: January 13 IN CLASS Attach This Sheet To Your HW 1. Given z = 1 + i and w = 3 - 4 i . (i) Compute the real part and the imaginary part of: ( z - w ) 2 , z w and zw. (ii) Re( i ¯ s )=? and Im( i ¯ s )=?, where s is a complex number and ¯ s is the complex conjugate of s . 2. Verify whether the following input-output transformations are linear, non- linear, time-invariant, time-varying, causal, non-causal, or memoryless. y ( t ) =
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Unformatted text preview: x ( t ) + Z t ( t- ) x ( ) d,t 3. Consider the linear system, with input x ( ) and output y ( ), described by the following equation: 1 dy ( t ) dt + 3 y ( t ) = x ( t-2) ,t > with y (0) = 0. a) Find the input-output relation for the system. We are only concerned with output for t 0. b) Is the system time-invariant? If the x ( t ) = 0 for t < 2, does your answer change? c) Is the system causal? 4. Sketch the following functions: (i) f ( t ) = U ( t-2) U ( -t ) (ii) g ( t ) = U (-t ) U ( t + 1) 5. Compute: I 1 ( t ) = Z t- ( t- ) e-2( t- ) U ( -2) d, t >- I 2 = Z 4-1 e-2 t U ( t-2) dt 2...
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20111ee102_1_homework1 - x ( t ) + Z t ( t- ) x ( ) d,t 3....

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