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Exam3_Solutions EEE303

# Exam3_Solutions EEE303 - Neurue EEE 303 Signals and Systems...

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Unformatted text preview: Neurue:_-.-... EEE 303: Signals and Systems Exam 3 I"u’I:1_',.r 1, 2006 Prof. Papandreuu—Suppappula YUM JrIHHI HIIHWl‘II' hi +111 prohiwns for full {-mt‘lit.. The Ilurnhvr {If puintr; fm' ﬂﬂi'h part Uf H pruhlmn 'lH gin-n. Fur full ["I'ﬂdiT. Hhmr H“ 51mm and lubnl HI] ELX'EZ‘H. This aim i; - I Pl'nhlnm ] Tulul—l 1. Ctlllfiiilﬂl' the discrete—time signal J:[n] == (ﬂ.ﬁ}”uf1r:-]. {a} [7" pix] Dom the discrct-n—timn Fourier imiwtbrm {D'l‘FT} X134”) 0f .r:[n] exist?! Dmuunstmln ymlr answer. Prmiide XE”) ifit.exi.t;1.s. {h} (5' yrs} Find the- DTFT of yin] = {fi.ﬁ]"_1ii.[ﬁ. — 1] using DTFT properties. Show all the HIPI‘JH and simplify ynur result. [r] [9 pin] Find Hm DTFT night] = [11+ 1}[I[J.I[:i]"-u[-n] using DTF'l' prnpertim. Show all the steps mui simplify ynur rr-r-zuit. .J if? pl. In Hygtg Saul,“ : _ I J ’- ﬂing, “:3 ~ ' "' ,: 3' <1?" rrﬁ'ﬁ M5 D‘Ticf ’JF’S'W biggie YIEJH): 1' PE! VJ rJTI" _ _ ..... .-_. I, Ir- 5 6-3."ij 3 - ' r ,. ,3 min _e:-=___ . iwc - 3-" riﬂe?” I ’3”? J 33 _. “Uni 1 : Iri- Tr r-ﬂﬂ _._L”J\Jl J'— r- a ﬁf‘JJJ b r 0-45 E-JHE' J (JrG-ﬁr {map-Ia 3T [Q 2. Consider the continuousstime si a1 3.: t = ﬁmjwhose Fourier transform is iren 1) En rrf g :l'r 5:. X: = { D. II:- irpﬁ} = Z \$r.(ﬂ-T}5i{t — YET} Twhere T 13 the sampling period. HZ—Eﬂ {a} (5 PH} {bl {5 Fiﬁ} [cl {3 pm} Whﬁ' or why not? {d} {Tots} or why not? w sf. 1711' I I . We 1Want to sample cc“) to obtain the continuous and sampled signal otherwise Plot Xcijw}. What is the largest frequency of merit)? When T = [1.05, what is the sampling frequencyr ms? When T = Ilﬂﬁ, plot the Fourier transform prjtu} of my“). Does aliasing occur? When T = Ill, plot the Fourier transform Xptjw} of £3313}. Does aliasing occur? Why Xef it'll !' _ . [0“ r—i’] , z “r We CM '33: __.'_1; ___T_ — Leaf WNW "r" o u:- - "h. [‘rv‘ul “mg, «iJJhlLAu? Uf-Ltlf‘: Trth it? : Stu—l" t:l s‘ﬂsfrﬂ h _ ___‘H’? 7-H “'9‘” Lu P if 111 D H“ ff; 035' 11911 55.”?- ! a; _ ,_. __.x ._\__ ___ __ ___ V oi LEG—7'7 ' so 'i ' ' ' J-J'e :- 51—” _. "i‘i cup. at Bra-I'DFIT glbﬂﬁlcgr GrﬁLL “:- JEFLL u- _T _._ / I o # [Jo—r. I ——J—?d H“ u so 5 lot .rlo.“ 4 __s‘ t __ __"v X'H. _ ll :5,“ ...
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Exam3_Solutions EEE303 - Neurue EEE 303 Signals and Systems...

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