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exam2soln

# exam2soln - EEE 203 Exam 2 This is a closed book closed...

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Unformatted text preview: EEE 203: Exam 2 March 26, 2009 This is a closed book, closed notes exam. You are allowed one cheat-sheet. Please Show all work to get full credit. Good Luck ! _.._...._._..‘f_w.ﬂwu_ﬂ:e..j MW..." \Wﬁg 1. Determine the Fourier series representation of the signal \$(t) = cos(t + If the impulse response of the LTI system is Mt) = e‘3tu(t), What is the output y(t)? JC’HWat) a» ewe) Q + 3C0?) z 00\$[f +7774) 2- Wmmmém . ~ J4: r JKZ’Oot :7 (gm/4 QJt + 9.31/4. 9- 1 20%? a" ‘ “7 a 1 am" 5 0’ : g";ng l a ’I 2 M46): {at Mt) “I 2,! “a 7 3!: 'J Meat 055 HQKWQ) ’ f 9 W615) ‘9 ' ‘90 ‘Kt go JEQKHOOUC ac ._ .—\; _ HCJK) : f a 3t" 9 (ix; -’ I Q 0 VG O J ﬁg 5“ ._ ; _, Q C / ’ 3+Jk 3+JK 0 ) \ij _ H k— a :- O‘lH t) ed ,1. OLE lit N . _ Tl] ‘" .Lg'm __I_. eft 9'9“, 4 “J7 8 - a 3J2] ’2 3:} 6%”) (3’0 eﬂwwf); : R2,? 9') 3’ F: I'D . 5+3 (3“: to?” 2.(i) Compute the Fourier series coefﬁcients of the periodic signal 3:05) = cos(t) sin(2t). ‘1: .3211,— gt -J 32% ﬂ ICC) : <2 Jr 6 )(e “63 ) ‘ 2 . QJ , . ” -ﬁ _, i 33?: “riﬂe 't : 0‘ng 4- 03€ “1‘ an, (ii) Let \$05) 2 ﬂy be a signal that is passed through a low pass ﬁlter whose response is given below. What is the output of the ﬁlter in the frequency domain? , W) AO'TT “ J i | l 2TI Sui/@6137!) (‘4’ J I “AU: MW— DTI TI 3.(i) The Fourier transform of a signal \$(t) is given by X ( jw) = sincﬁu — 2). What is 5:06)? ( [/2- _.——~——-————-§ f - I ALA/Lo, (03) 4—2.:- t gum) 46-0] a _.— g '2, Heat]. gin/34f / Al-M0(W”2) —=;- 5% | [Mal-’14) » [2(3ch )1 ‘. i.4.....__.__..__._._--.-......____...___-i (ii) What is the Fourier Transform of the signal e‘4tu(t — 2)? i , »2 (“x/L064): e 43 2). e - “(*0 * e’g. QCCch); mm 'Xf'ﬁﬁenﬁwﬂ- I 4. Compute the Fourier transform of y(t) = m1(t)a:2(t), where \$103) = u(t + 2) — u(t — 2) and \$26) = cos(t). mfg 1 ﬂ <——> leH/Q): 2.2 su‘nc (200) £ ‘ 4-SWC[?w) "2. '2 126:) : 0mg) H x/Qw) : 7211? x106“) ave x2 3.») :J_. Am:- 56m(‘2m)* [qutwgwrﬂ 2W : 2 gm CZCoo-JD + '2 gmqmmm. 5. The transfer function of an LTI system is given by H(jw) the input is \$(t) = e‘tuﬁt)? ‘ ._ __J._._ XCJUJ) __ ij we) : moo)ch = What is the output y(t) if ...
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