12Spring_exam2_solns (1)

# 12Spring_exam2_solns (1) - ECE 210/211 Analog Signal...

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Unformatted text preview: ECE 210/211 Analog Signal Processing Spring 2012 University of Illinois Basar, Franke, Jones, O’Brien Exam 2 Tuesday, March 13, 2012 - 7:00-8:15 PM Name: 5 O ! Utlows . seam": 9 AM 10 AM 1 PM 2 PM (Circle one) Class: . ECE 210 ECE 21 l (Circle one) Please clearly PRINT your name lN CAPITAL LETTERS and circle your section in the boxes above. This is a closed book and closed notes exam. Calculators are not allowed. Please show all your work. Backs of pages may be used for scratch work ifnecessary. All answers should include units wherever appropriate. Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) Problem 4 (25 points) Total (100 points) Problem 172 ng‘ﬁ +333“) +1 (USE ‘J Sum > _\:5 ____—a ' Gasmﬂswmyx—G‘Gm :zS—JSufﬂ—i‘) (a) A complex number Z is given as '3: L . L in 'J'V ,5 l . _ 2e +2e 2 _ = _. 0 \ ii) z=((1'1J)3 jz) ﬁnd|Z|= «((2 /= ~HS° " ‘j)3 ‘ \ .. o (b) Convert each of the following time domain signals into phasor form F. L ' flt=C t-S't 1) () os 1n F]: E L‘S‘O 11) 12(1) = —2 Sin 51 iii) 13(1) = -3 Cos(10t — 365) (c) A circuit is described by EX d t + 23'“) = ﬁt), y(0) = 4 i) If f(t) = 4 Sim, ﬁnd zero input and zero state solution. Leno \wpbq-ﬁ 511’: %L+)_o Ears stave: d . . — 3 ﬁLléL+§=HSUAE UAW 3i0>=0 gth—e’ 33935-0 e ; 5;; ._.>F‘— EL: O (3&3? 3‘“: Ag ”at Ll ,Z-E: f- - K1C#3%+\LL\$W\E \$w‘>§,\r. \vﬂ-o DE 5'21— _9’*__ . Ikxv‘d \4-\ (AMA LL K1: ——.EL LL: J3§_ 3’25: 1 at: fiCm-b +<§_\$wdc ¥+ ii) If the input f(t) =3 +CosZt, ﬁnd the steady state solution. 5 o _ (. ; H\o\:.\. Hm)- L: 44—“ £+Zd L46 QLH > H “A LTAUJ 2’ Z-VLA 2V2. E) 4’: _Q¢O>C +11 sate sst‘r): H\o\.3+ 1mm £149.»: + 1.3») ”’9 _\__,E‘ < o Vssa): 1+ La l-E’LLS > —— 2‘3 + Lszt—Lﬁg 28? L Problem 2 The following circuit is given. Find v(t). su press a source «and «Chef. 8/! Whirl (0:1 I”; \ Phqsor Dammlﬂ ﬁr“ 15L - reduces +0 ‘i’inis ci'ruifjf ioeoqus-L tkp sné. and <59, W 4* CQSane-Je 59 ﬂat ad ant-a an open. v(t)= MUD-a» M’ an ”149 +.-‘--— (721—1: ”'13,- 5(ﬁ @co( 17L) SHWFES—S‘ currean Saur¢¢ 5 ' . 2’7“" ““- 3 a. .i 1T 1‘ 3; .e- . ar- #65 TV? 542 Problem 3 (:1) Determine the frequency response, H(co), ofthe following system. l 03 0 Han) = ‘ 2 + J w (b) For a system with frequency response H(co) = l—J-r—SO—l— determine the “half-power” (—3dB) _] . (0 frequency) (00, and express the magnitude frequency response,|H( (1))l , and the phase to» M r,esponse A H((o), ofthis system as real valued functions and sketch them over FILTER -50<(1)<50. £51m lHCw¥~ 5' ; M [H093]: 0} (LPF) w-Do w—aoo Problem 4 (2!) Given the periodic waveform f(t) for which the trigonometric form of the Fourier Series is f(t=) if; Sinm 8A2 Sin 3m+ 8A2 Sin 5m; (3713) (51;) 14\$! m3 mi determine the exponential form; coefﬁcients Fn: Pram 4,, 7}; +Fn) ' 1/0" "‘7 in) F0: 0 ’ 1* a) —_____— ” 0’” M" ‘7 r My; 5 =0 ' FWW'AEW’Q 15. W F]: M - n , J L 5 p F2: 0 F0 = f; 2 FL," 9"“: E2: F "’ ( a)’ “a! 77; __0__ 5 ’ 2 7f}, . (b) For f(t), determine the compact formb coefﬁcients [cn Cos (n00n t+ 0n 'bg/b :g/fn/iQ’:A_F_ Fz—gbn/glgj: bn/V/ﬁm “'5- ‘ C7. -_ C ' : "0° 9 ’{9 ’49 a 2A.. _ C .4 3% 9,= Zr“ [Jr-i) 9D. C=2/ﬁ/=07/jw7rv’ﬁ" +1.: + 5% 9,,1...”</ ‘7” C‘3 '2/6/7 2/ +JL3t’Jv/7 [37)1/ <3 .——/'\ Co: 0 00: ﬁ/ﬁpﬂM/A 5/1 = 3/} 2 5w 5W °1 A” 9‘ 78L!) WVW my [13-37):£n Mam! «2w C2= 0 OF med / “‘3‘” ' — - 03: M ~93: 661(3er 1' 42/) ﬂ”) (9:) (c) Using f(t), determine the exponential form coefﬁcients F n and the trigonometric form coefﬁcients an and bn for periodic waveform g(t). g0) G0: 0 a0= O b]: 0 G‘= (4%” a1: YA/or‘ bz= 0 G1: 4A/yv a2: ———0— b3: 0 G_2= 0 G3: ”A/{J'fy’ G : LMr/{S )V — mgr/v 3 qr ‘ . 31,147,) 3/J'3ya)é7ﬁéfﬁg,b g , d", A”: W ﬂy” s e '1’: 2. S ‘9 0‘7, ’2'“ —r p TV t n 2. U): @(.7i+/2,> - wwé a . F3 3 >Fe apﬂé”/L=7W”>Qna Frm ’MJJ‘QL " ’ dm‘rf/Z G": Fm ) a 4 — 0 - 06, PC ’9 ‘, wen :- ’ Ll ’ ' a = 6°49 if”??? 2; 0V — ‘22. «Jaw, ‘!A Le— 49M 5% 0 G‘Fa ' ['3 Fv>e ’IYVLﬂ—r" war I I 17 1 A p” ("M/0’ 7 W” (ti/1111 =‘ﬂ/ﬁsﬁ’f» G5 "6?: 8 ii (.39, Ewyl @‘YY ”90% M M ...
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