sp2002_exam2soln - IECE 210:“211 Analog Signal Processing...

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Unformatted text preview: IECE 210:“211 Analog Signal Processing Spring 2002 University of Illinois Hiskens, Kudeki, Ma Exam 2 Thursday, March 14 — 7300-8: 15 PM i l Section: (circle one) Please clearly print your name and circle your section in the boxes above. This is a'closed book and closed notes exam. Calculators are not allowed. Please show all of your work. Backs of pages may be used for scratch work if necessary. Good luck! Problem 1 (25) Problem 2 (25) Problem 3 {25) Problem 4 (25) Total Score (100) 1(a) ( 8 points) (i) Given that f(t) : «5 sin (3t + , determine the corresponding phasor F and express it in the exponential form |Fieje. ‘ fl' tfi-t):-—E Sinfi'f‘iHqu) :fl 1065(3f,.2;) ._. #28; ‘t ,J'. F 2 -—.Jze"" :2 IE e’ e '9 J15. U M” .—. I;- 8 9' no a, :8 , rat‘s/H45 W (ii) Given that g(t) : «ff 003(31; — 141E), determine the phaser of the signal f(t) 4» g(t) in exponential form. _3's’k: G- : [E 6 '47 we '55 J"? '"J ‘6) F 1‘ 5r =— FM 6 + E: :1. "‘2 :3 2 8J7: (iii) What is the phasor of the signal Ell—f? FM): «3,13, Co5{3t+%) m 7ILM/0r‘, mwi‘hfL W J" 1% fizz -j-zg-K Fzsfite e :zzfie. 33:55 (iv) Determine the co-sinusoidal signal h(t) with the frequency 0) = 3 radfs and phase: H=J§+j«/§. K- H'Hzl LHZ'ZF [email protected]£'[_é): 2M5 (flgf‘f’fi') 1(b) (8 points) (i) Based on the input and output signals for the LTI system shown below, is HUD) low pass or high pass? Justify your answer. Low {3063, Tim Ouirpuit 5i ml is smoo’ltlnu ‘me 'HAL inplk'l‘, lfidleu ms Qqumng-S RAW. Lam Qi’tefluuleil' (ii) Can the following systems be LTI? Justify your answer. eos (5t) 4 sin (50 YES; inpw’t‘ + ouipoult Nut SCUM Only dili‘r‘crcme "LS agoth + @lmst ski-H . cos (21mm) 3 cos (2’1U1t + 10") +113- cos (47tnt + 20°) N0, Quipu'l Cesiuin ot¥re1+lma+ (‘3 Ho‘l Presefil (in 'HNL lnPu'l- 1(c) {9 points) Given that f(t) : cosz(4n:t): (i) Write down the exponential Fourier series of fit), , . cm/iimc)=<e- H )x 6 ”‘ *9»... k. _. 2 ‘ a _ ' Err/c + 774‘ a r J l ' J __ — ~— e +« _ + -—» e r (i: ) 4r a ‘f ................................... we“ W {(43) We. 000:9? “id/5 W ) ' 7'313E3i5 to COD L, % (iii) What are the numerical values of Fourier coefficients F0, F1, and F_2? __ ' 4: I 371' L f (e) :w 7; e J ’ ‘SIFJ: %.L +-——-—eJ :9 “f 2. (25 points) Use the phasor method to determine: Figure 1: A network. (a) The phasor of current i,(t). _ \/.*l/.~ Jon-f II: 2, ‘2 ,...'_fi_.. 1+5 29+3j 2. (continued) (b) The phasor of voltage v0_(t). V—"‘Vo (c) The steady state current i2(t) (in its cosine form). Va 15*305; Iz 1: 2 z W 3 l+ 6d {lift-{36" ._{ -—( 166 :- _—-—--—-—., 5(‘2'f‘—f‘aq[’L)—'EM [a "’ ) m 0" D 7 7-ml‘h’C—2 / 3. (25 points) (a) Determine the frequency response Han) for each of the following circuits. / (Note: Your answer must show Ham) 2 .... .. .) [@945 (b) The frequency response for a circuit is given by H013) = m Sketch plots of |H((o)] and 1H(m) for the range ~S < u) < 5. 3. (continued) (c) The signal Ht) 3 2 +%cos(2t +10°)+ 35in (3t * 5“) + 4cos(5t + 20°) is input to an LTI system described by the frequency response shown below. Determine the correSponding output. iHfin)! 4H0”) we 0 x QM(${*1°--JS:>— tiriSI u A .. _ to: 2. ;. ewe-“ M « mm an <36- 4. (25 points) Periodic signal f(t) shown above with the fundamental frequency (on = 2T“ is applied to LTI systems H180) = mgufjm and 112(0)) : a) 01% w as an input signal. System H130) = responds to input fit) with an output y1(t) while system Him) 2 £031.93 responds to the same input with an output y2(t). (a) What is the DC component of the output signal y1(t)? Let Pa cwfwmi 0.; $.80: l2 SikCL \{n 3 Hinwo) Fm) Y0 =3 HID) F9 1 Fa /1 1' LDC, i 9,, is) W F0535— rel-E: it) @de t o i i I, 1 Y5 2': (b) What is the Fouxier coefficient FI of the input signal fit)? ’7" 'wo‘E u __1_ t '" u F1 0H?) WOW—f3:- O t I T ’w t T *Jth t t O! o ) :4. j 4: oi 5 hair-— i To. 0 w,on T Mg 0 -- “w t t ( wot I rJ a E r ’6'].— ’t 6‘) ’0 fl fir/i.) air‘l’ D O * Jami? ' r: '1)” i/ O I“ 15' HT "T M9231 “2411'” _ fl/g 4. (continued) ((3) What is the Fourier coefficient Y1 of the output signal yea)? fl :H2(.nw")E/t \(l:i_pz-(000>Fl Hgthe” =7 “Jack—:1?“ Ti? pow-J90" WOULD» X, \I/r~tl-:4 Fl l _ / M”! (d) What is the average power P of f(t) (in watts, assuming that f(t) is a voltage applied to a 1 S2 resistor)? ‘T ,2 n“ a 'L T :1. Lb)! wit-all 22 4t:— juxt— F T To '7') [3 0 :5 FL! 4/3 T _ J- w T; 3 o 2 (e) Let Pi and P2 denote the average power of output signals y1(t) or y2(t), respectively. Determine whether PI and P2 are greater than or less than % W and explain your reasoning. You do not have to calculate P1 and P2. 3am, pm” 00 I 60 i 2» ( Elm = 3' t Orr/WWW...) => l): '2;+ Elia ) “21? Cl” PM (a) ‘b-(L, WP‘MM ti- 5 %IL£)Zé-o WJ1HFJ-‘gr‘b- m I l I- .03 ‘44:“) = O‘l’MZflC-nc’"(wauen) —'3 ;' Ola ; h F (£1,th am.“ 3’7’/ w grid,” % I f] I iflizl—‘cplz/r g< 9W 10 3 ‘1 ‘r WWI/(##- ...
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sp2002_exam2soln - IECE 210:“211 Analog Signal Processing...

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