fa2001_exam2soln

fa2001_exam2soln - ECE 210/211 Analog Signal Processing...

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Unformatted text preview: ECE 210/211 Analog Signal Processing Fall 2001 University of Illinois Basar, Hasegawa-Johnson, Munson Exam 2 Thursday, October 18, 2001 —~ TOO-8:15 PM l? Name: ,3 a fay—Han: Section: 9 AM 10 AM 1 PM (circle one) Clearly print your name and circle your section in the boxes above. This is a closed book and closed notes exam, however you are permitted one side of an 8.5" x 11" hand-written c1ib sheet. Calculators are not alloWed. Show all of your work on Problems 2-4. Backs of pages may be used for scratch work if necessary. Good luck! l—Problem 1 Problem 2 J_Problem 3—l_Problem 4 I Total Score —l 1. {Multiple Choice, gircle the correct answer, 4 pts. each) ._ jg: a) Let c = 3 FIE . Then c =M eje in polar coordinates where (M, 6) = .430 1+6 5 L). r U: .27 c :1 ‘ '3 fj‘iro i) («5,45") iv) (1,—45°) ’ o7 “38 :3) (J14?) @ 0,90") '70" 3 I e7 iii) (1, 45°) i i h) (j)2 + (-«j)2 can be expressed in rectangular form a + jb where (a, b) = - l :E .L F...”— 1) (ONE) iv) (1,0) @931). (a? Uigeauej ‘* (“w/$0) v) (fin/E) iii) (0,2) .;_ ,1 wig- : 27:1 raj-f c) V02) = J5 cos(500t + 45°) + J? sin(500t + 45°) can be written as A cos(500t + e) where (A, e) = 'qs‘" , 'Lm’ @(2,0°) iv) («5,45“) vie? flyufie7 3 ii) (2,45") v) (2, 90") Ff’J . 5.9 fwd- iii) Hie“) [ti/£2,236.99 :Uzfiai (a???) '3 2 d) A system described by + )1 +1!) V Misha a 1'45"” 4-54“- W' éo d: ad.‘ L J 5T %:—ZX+5%+43’(t)=cos(2t) ,wlyfjuiy+qy : [£90 Jaéd. 012;;04JI has steady~state output A cos(2t + B) where A = -qY+jl0V-i"1‘Y 7-! i) % 1V) 2 -% J—w ii) % v) 1 Y” :0 .u-L . #- 0 ‘ q a . . . 25 14% 3+ {flyorff ‘3 e) T he periodic Signal 9 90 o A I I J— «70;— f(t)z%2%cos(nt+90) ffif—f 2‘ 7 _ % n=l L we 2 t can be expressed as a complex-exponential Fourier series with coefficient F3 2 iv) .. — 1 11) 6?: v) E 11!) 37: f} The signal f6) = Z —~2--2~ejn21 is input to a linear system with frequency response nan 21(1—411 ] magnitude 60,, 1'- 2 2 [HUDN :% SacouJ Add/man}! :1 w 37) wfil‘ch I“; “+6: 4. Pqéiifimé ~1 1 ‘0 The average power in the second ha1m0nic of the output is - -1 t 1 2 1) 15¢: 1") -- 2 II) “TS—TE 0 2 2 111) g) A linear system with the input f(t) = cos(3t) has the output y(t) = —\/i——Ocos(3t + tan—1(3)). Which of the following is a possible frequency response, HUD), for the system? ' A _J_ ,_ ’4 i) iv) 12 mm» “(175‘ ZH{3)*‘/" J“) 1+0) J -- .l03 1 -1 #3 "" u) 1+jt!) @l—jw ‘3'“ZH/3)= ’43?» (‘7' ‘37,?” (‘3) l 1“) I+ju1 h) The circuit to the light has frequency reSponse + 1 . H(u)) = . . What is the value of L? l + 33(1) fa) e y(t) GD 45 H iv) 3 H _ i1) 1H v) 5H 13" I _ - -- - - ............................................. _. 2. {22 pts.) For the circuit shown: cos tot R V0) 2) Write an expression for the phasor V associated with v(t), in terms of a), C, L, and R. "V’e #mfmfl/ .500 4+5 .— R+ e V: F 290C. b) What value of 0) (in terms of C, L, R) will maximize the amplitude of V(t)? f— | -. H a. g. f ‘ h: WMMIZZ— (VI) Mint/nIZe. fid- pr CW! M e. I Zero: java )7 c) As to —> 0, what will be the amplitude of v(t)? As to *9 co, what will be the amplitude of v[t)? farmer mac or wvew I‘m- 17—3'90 7—79 #220. Ampl(w—>0)= 0 Ampl(u} —)- no) 2 O d) For (1) = 5, C = 0.2, L x 0.6, R :2, find V(t). Z A V7 , a 2 . 2+-—:—'+7~3 2-172 / I '45“ ,n __ $3”; “— H”;- V5 e) In Part d), the average powers delivered to C, L, and R are IV!1 ! PK; 2R 2 #8 3. (22 pm.) Consider the periodic waveform fit) 62‘ .4 F2 2 4 6 t a) What is the fundamental frequency (00 of this signal? fl... .— (00: (’7‘ / '- 2 ’29 We ’ /l b) Determine the coefficients Fn of the complex exponential Fourier series for this signal. 2. 2. s 1‘. fr ‘I {T Ff, 3' "i" Kali—e. jmj-dif 1'3 é’ S0562 ‘7’“)tdf O eKZVAAW)f/ 2““ ¢{’27j”m2 »—- l ’2 (2’7"?) 0 ‘1’”??r777" Z c) If fit) is the input to a system having frequency response -J3w Jan 3}; _ IOe 2 <co< 2 9 0 otherwise find the output signal y(t) in real (sinusoidal) form. Y” 'r- H(HW)Ffl ) éd flzfiJtl 4V2- M’i- ZWaeJ 42+ 45/ ‘ ' 41‘7" ’ ‘3"? 4,; m — 7” 3: Z r057 6” _ e. a w a we” r 'n’li"(f"3)l : l0 (em-:9 4‘3: 4:732:13: ‘37 -1 u ! __ 1 .9 ['15 _ Note. 472” #1 {MIL e275? (3.) ya)— ___ _ (e‘L-l) . fl H wall/(7')» '2: {e443 .+— 3;???” caJ(’W(,+ .35) + +1“: 4. {24 pm.) All parts of this problem make use of the following frequency response function: H00) = 1 + jw 3) Sketch the magnitude |H(o))| and phase 1mm). Be sure to show values of these functions at 03 z 0 and as o) a co. mm! :- W 11/450) = film—IQ) mom % Awe): 0' 1-,) Kay“) [4(0033’7‘93 é 1: 7m, Suppose the input is f(t) z 3 + Zoos + sin(2t). What is the output y(t)? Your answer may contain trigonometric functions of constants, e.g., cos'1( 16) would be acceptable as part of your answer. 4. (cominuea‘) c) Your company, NOISY SIGNALS, INC. (NSI), sells customizable circuits with the following configuration, where the impedance 2 can be made up of any combination of resistors, capacitors, etc. If y(t) and fit) are related by HUD) = 1 + jo), write the impedance 2 as a function of (u. ...
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fa2001_exam2soln - ECE 210/211 Analog Signal Processing...

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