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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