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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  7:008:15 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) ﬁndZ= «((2 /= ~HS°
" ‘j)3 ‘ \ .. o (b) Convert each of the following time domain signals into phasor form F. L ' flt=C tS'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 \wpbqﬁ 511’: %L+)_o Ears stave: d . . — 3
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ii) If the input f(t) =3 +CosZt, ﬁnd the steady state solution. 5
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28? L Problem 2 The following circuit is given. Find v(t). su press a source «and «Chef.
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59 ﬂat ad anta an open. v(t)= MUDa» M’ an ”149 +.‘— (721—1:
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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—Jr—SO—l— determine the “halfpower” (—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) wDo 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“ [Jri) 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 [1337):£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 ‘
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Frm ’MJJ‘QL " ’
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