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ECE3337Fall2006Final_0003

# ECE3337Fall2006Final_0003 - ANALYSIS I ELEE 3 337 F inal E...

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ANALYSIS I ELEE 3337, Final Exam, December 13, 2006 Part A Name: 1( 30) 2 (70 Part A Part B Total a b a b c d e 10 20 15 10 10 15 20 100 100 200 IO , I ID o .) tn 7ts b'7 lq5 Rules of the Game: Put your name at the top of this page. Staple the problem sheets to your solution sheets and return the complete package. Books nor claculators are allowed, but a self-prepared 'crib-sheet' (2 pages) can be used. Cheaters will be prosecuted! Answers that do not provide sufficient detail as to how you arrived at thern will receive partial credit only! Maximum credits for each question are shown in the table above. 1. The signals a(t) ar'd z2(t) are obtained by 4(t):[r(f)*[email protected])'Y(t) and z2(t) : ["(t) ' y(t)]x h(t), with a(t) : u(t - 2) - u(t - 4), h(t) :26(t * 3) and a(t) : e-tu(t)' lt (a) Determine the Fourier transform Zr(r) of a(t). t' (b) Prove, by doing the multiplication and convolution in the time'domain, that a(t) I z2(t). 2. The relation between input r(i) and output g(f) is given by the following differential equation: U-2il*2Y:2*' The relation between input and output can also be written as y(r) : r(t) * h(t) ' You may assume that the system is at rest for t < 0.

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ECE3337Fall2006Final_0003 - ANALYSIS I ELEE 3 337 F inal E...

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