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12Spring_exam2 (1)

# 12Spring_exam2 (1) - ECE 210/211 Analog Signal Processing...

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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: Section: . 9 AM IO AM I PM 2 PM (Circle one) Class: . ECE 210 ECE 21 1 (c1rcle 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 if necessary. 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 1 (a) A complex number Z is given as in ') J1/2 i) z:_2_§_+:f__3_ ﬁnd '2': [2: ﬁe_J%+\/§ej% ii) 2:04,); ﬁnd [2]: /= (b) Convert each ofthe following time domain signals into phasor form F. i) f] (t) = Cost - Sint Fl: ii) f2 (t) = -2 Sin 5t F2: 7: m) f3(t) = -3 Cos(10t - -—] 6 F : 3 (c) A circuit is described by dy _ — + 2y(t) = f(t), y(0) - 4 dt i) If f(t) = 4 Sint, ﬁnd zero input and zero state solution. yZl : yzs : ii) If the input f(t) = 3 + CosZt, ﬁnd the steady state solution. yssﬁ) = Problem 2 The following circuit is given. Find v(t). 3 29 W) = Problem 3 (a) Determine the frequency response, H(co), of the following system. H(60) = (b) For a system with frequency response H(o)) = -—5— determine the “half-power” (-3dB) l+j0.lco frequency) (00, and express the magnitude frequency response,]H(co)| , and the phase response, 4 H(o)), ofthis system as real valued functions and sketch them over -50 < co < 50. WWI coo = u) u) 50 rad/sec ”1(0)”: A (co) 4 H1 co) = a) (o 50 rad/sec Problem 4 (3) Given the periodic waveform f(t) for which the trigonometric form ofthe Fourier Series is 8A Sin nt- 8A Sin 3nt+ 8A 7 2 2 Sin 5m W (M) (5n) f(t)= determine the exponential form coefficients Fn: (b) For f(t), determine the compact form coefﬁcients [en Cos (ncont + 9n]. (c) Using f(t), determine the exponential form coefficients Fn and the trigonometric form coefficients an and bn for periodic waveform g(t). g(t) G0: 210: bi: (3,: a1: b2: G_,= a2: b3: G2: a}: (12: G3: G3: ._ ‘F, f(t), peﬁod T _= 2L ' Coefﬁcients "’0 Zﬁwo Fnejnwa: Exponential F,1 : %fT “Heartland, a,, = Fn + Fun by: : j(Fn _ Fen) % + 23:1 an (30801600!) + b,1 sin(na),,t) Trigonometric cn =2|Fnl C70 + 2:02] C" (305(71sz + 0") Compact for real f(t) 6 _ 4F Condition: ' Constant K f(!)(_)Fnyg(!)<_)Gn;"' Scaling Kf(t) <—> KF,, Addition f(!)+g(!)+"""<_)Fn+Gn+ _ Time shift f(t _. ,0) 4—) Fug—Imam df . W 4—) 17160an Delay to Derivative Continuous f (t) Hermitian Real f(t) f(—t) = f(t) f(-t) = —f(t) 17—11213;K Even function f(t) = “70 + 22:10,. cos(na)ot) f(t) = 2:1, 1),, sin(nw,,t) HT |f(t)12dt = 231,00 Im2 Odd function Average power P lll ...
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12Spring_exam2 (1) - ECE 210/211 Analog Signal Processing...

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