20095ee102_1_EE102_HW-1

20095ee102_1_EE102_HW-1 - Fall 2009: Put First Letter of...

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2009: Put First Letter of LAST Name in the corner →→%% ( Otherwise Your HW Will Be LOST! ) PRINT: (LAST , Middle, First):——————————————————– EE102: SYSTEMS & SIGNALS HW: # 1 A LATE HW IS A NON-HW! Posted: Hand In To Me 1 : Attach This Sheet To Your HW (Otherwise It Will Be Lost!) Notations := means “equal be de±nition” x [ a, b ) means a x < b 1. Given the complex numbers: z 1 = 2 + i and z 2 = 4 2 i . (i) Compute the Real Part (Re.) and the Imaginary Part (Im.) of: ( z 1 z 2 ) 2 , z 1 z 2 , and z 1 z 2 (ii) Let s = α + . Write down: Re. i s and Im. i s , where s is the complex conjugate of s . Given H ( s ) := s s + 1 Calculate: Re. { H ( s ) } , Im. { H ( s ) } , | H ( s ) | and tanΘ( s ) (Note: See WEEPAR-I, p. 9) 1 during the break of the Wednesday Lecture 1 Fall September 30 October 7

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2. Consider the following diFerential equation — together with the initial condition: 2 dy ( t ) dt + y ( t ) = x ( t ) , t > 0 y (0) = 0 (this problem is called an “Initial-Valued Problem”). (i) Solve for y ( · ) in terms of x ( · ). (ii) Calculate y ( · ) given that x ( t ) = te 2 t , t 0 (iii) If y ( t ) and x ( t ) in part (i) are OP and IP respectively, of a system. Verify that the system is indeed L. 3. A system S is described by the following IPOP description:
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This note was uploaded on 10/15/2009 for the course EE 102 taught by Professor Levan during the Spring '08 term at UCLA.

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20095ee102_1_EE102_HW-1 - Fall 2009: Put First Letter of...

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