20092ee102_1_S09-102-HW-2-Sols

20092ee102_1_S09-102-HW-2-Sols - Spring 2009: Put First...

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Unformatted text preview: Spring 2009: Put First Letter of LAST Name in the corner %% L (Otherwise Your HW Will Be LOST!) PRINT: (LAST , Middle,First): LEVAN, NMI, Nhan EE102: SYSTEMS & SIGNALS HW: # 2 A LATE HW IS A NON-HW! Posted: April 09 Hand In To Me 1 : April 16 Attach This Sheet To Your HW (Otherwise It Will Be Lost!) 1. Let x ( ) and y ( ) denote input and corresponding output of a system S . Given the following IPOP relations: (i) y ( t ) = x ( t ) , t ( , ) , where is a real constant. (ii) y ( t ) = R sin( t ) U ( t ) x ( ) d, t ( , ) . Show whether: in case (i) the system is TV while in case (ii) the system is NC. SOLS. We are going to use BT throughout this HW as much as we can. So the first task is to put any given IPOP relation into the so-called BT-Form, i.e., t ( , ) : x ( t ) [ S : L, h ( t, )] y ( t ) y ( t ) = Z h ( t, ) x ( ) d (i) First, given the IPOP relation of S : y ( t ) = T [ x ( t )] = x ( t ) Then S is clearly L (if you do not believe this then do the L test). Secondly, You do not need to consider the trivial case = 1. Then You have, for non-zero 6 = 1: y ( t ) = x ( t ) = Z ( t ) x ( ) d = Z ( [ t ]) x ( ) d 1 during the break of the Thursday Lecture 1 Therefore, by BT: 6 = 1 : h ( t, ) := ( [ t ]) 6 = h ( t ) S is TV (ii) For the system described by: y ( t ) = Z sin( t ) U ( t ) x ( ) d, t ( , ) = Z t sin( t ) [ U ( t ) = 1] x ( ) d, t ( , ) Therefore, by BT, S is NC....
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This note was uploaded on 03/29/2011 for the course ELECTRICAL EE102 taught by Professor Levan during the Spring '09 term at UCLA.

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20092ee102_1_S09-102-HW-2-Sols - Spring 2009: Put First...

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