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09F_210Exam2_solns

# 09F_210Exam2_solns - ECE 210/211 Analog Signal Processing...

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Unformatted text preview: ECE 210/211 Analog Signal Processing Fall 2009 University of Illinois ' Allen, Basar, Trick Exam 2 Thursday, October 22, 2009 —— 7:00-8:15 PM Section: circle one Class: ECE 210 ECE 211 circle one Please clearly PRINT your name IN 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) 1 Total (100 points) Problem 1 (a) Compute the phasors associated with three signals below. = ' 2 ~ 'é0b -‘l' ° 2 f1(t) 251n(t+.6) I F1: ‘2 e; :2 C :2 ‘60 C 3 : :2. eox({;+rr£_ﬂ0 =— a 0 - '1"... W 2cm £1315?) =1 m f3(t)=sin2t+Cos 2t _ - A's/6:" - (ﬁr/‘6 0 Z f= :iu: I—Jzﬁlj’s" FF we =55” C) J (b) In the following circuit, ﬁnd lVl and AV . (c) For the following signals, ﬁnd period, fundamental frequency and average power for a IQ resistor. z a 7. _ , V—_ n— 9 _ 2. 5‘ wa‘sré/ I ‘ 37—51 levy” (ﬁiéﬁii (6) (i) f(t)=2Cos 10t+5 sin 1005t : Z 4. 254 : xzﬂd T: 'S , (Do: Pav= (4) (ii) f(t)=8+6Cos6t+6Cos(9t445°)‘ T: £77753 (no: 3P5 PW: W,;5y€jf=?37f5 _ 2 [a Z .0; L— :. W )7 _ (g) + - MAL/em; av Problem 2 (a) For the given circuit ﬁnd the open circuit voltage Vn (phasor) and the Thevenin equivalent impedance at terminals a-b. First draw the phasor circuit in the box, then ﬁnd V0 and , —— ‘2(5”o +J5’0l (b) What is the maximum available average power from the source, and what load impedance ZL connected to terminals a-b is necessary to receive the maximum available power? dated v 1 ,. w; E’s21m; y“) 4x/3’0 w McIchle {gm/W £1. 3 ET '3 0V; ASZ’ [MKK'ZL feVMCM/K M4“ “Veizi/a£l€ ITIOWCV 85' *7 " 7' 6‘ :1— : —- We =—e——— Mil VX2525: ’7’” M) r w Problem 3 (a) Determine the frequency response H(co) = % for the following circuit. flu) 2- y .4 7; : /+J 2: / /+JZ‘”+ @sz ([+J‘1w)(’+\/‘2L9{‘I s ' '/ Luz/4,24. J‘ﬁ’uJH .2- ¢w1+j¢w mm): .2 —¢Lo"+4/ I‘m (b) Frequency response function of an LTI system is given as jm Hm =____.____ () 4-m2+3jco (i) Find its magnitude |H(co)l and sketch the magnitude spectrum for w _>_ 0. HCO) = O H/ 7—) = = g/ ]H(co)| moo)! = 14 v a, F J" .50 #0)” "34‘; ﬂ 0 2 0) (ii) If f(t) = 2 + 5 Cos tfor this system, what is y(t) ? - - 5%) = mm + xywﬂyﬂ) Problem 4 Justify your answers or no credit. (3) It can be shown that the Fourier coefﬁcients for this waveform are Fn = i cosnn,n=:t1,:t2,etc. mt a ‘1’ T Given the Fourier series f(t) = ——°— + 2(ancos n (OOH-bnsin n (not) w I 77— x/O r/ 2 n=1 '1‘ 6) I: .r 3 ' 5 3 a0 7' ‘- 0» 2. --1 q I. L , . wﬂw £25.10, 7609) 4&9 041 car asp-<9 ~ ' , 3i emtqéi A? i m E ii“ 3; C} 229 I F; : ‘1 162.: (b) Repeat Part (a) for this modified waveform. (c) Repeat Part (a) for this modiﬁed waveform. (465): Ht i150); 140:7; ’72: I; 6‘5"?“ view” 40 ’3: : _Z//f (wag bf "if, ...
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