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antonia_final - Name DLM’HD EEE 303 Signals and Systems...

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Unformatted text preview: Name: DLM’HD EEE 303: Signals and Systems Final Exam Lela}? S, EDDIE Pref. Papendreeu-Suppappela You meet answer all prebleme for full credit. The number of points for each part of a problem is given. .2" Fer full credit, show all steps end label ell axes. This area. is. for official use only: m... 1. Consider a. continuous time lines: time-invariant [LTIjr system whose impulse response hit} and input signal fit} are given by: 71?} 47(1) M1) } 1 2 —t+A : i‘ 0 4-,». {5+1 1 fl 2 “i: -l U (a) {“3“ pts} Using convolutinn, evaluate and plot the output Left} = fit} e hit). {b} ('5’ pts} Justifying your answer! determine whether this system is [i] memeqlees and {ii} heuiided—mput. houndedaeutput stable. {-2} {6 pts] Find the step response of this system. __| Mr; £s|>lé {>3 g.) Mt memsgm mu. NEHFKSH}; we 1. are fit LJEO sum! Luwew ,1, SD (IL-“03‘s. a. 2 :1 «'9 313:: chelaie it} gw iflfing NHL 396): _%1+2t argue} 35032 {22‘ 2. Consider the following Fourier transform {FT} property that results in the. FT of'the nth dorhretive of a signal EH]: 3% we} <—> one” We) {a} (1" pair} Find the Signal TH} whose FT is Rr’jw} = —w26[w — %}I by using the above FT property. {1)} {flats} Find the FT of the sigmal git} = cos {gthflL Y {e} (E ptsj Find the FT of yflt} : —t3£{—-t ~— gj. State which property {prop-arms} you used. (“*3 iIHB area-ml- MN) Haw—L. X[JQ)35{0JF%J '3; W" s noflegs’c . err. “15:1: fiftilziil 6.3 ;..LUELELJ3 firfigakorgfi- 3041 At mi 3: $1:qu *I-t. LL) flit): e05 got (“7) 9"" rim +1“) ; t f“ :1: {RUIME'EIB 4. .1- (J 3 J _ as“ 5 (”1 4'??? a; a) W'E‘t) ’ if; T?— f N - ' §5[“" ”a"; " If g %L as — (rt): We) 1' ’5 glrtl H’ :1" Ed " . 5% 1'3 - Iii-'1‘: E1“ w 1;. -~"_"“ a ’3?! 1‘5: 3Lk\ .. EL (‘3) 3 # J 5 (1:31- HJEU} ‘L fill-Ev) , :11; l ‘9' :- :f e 3. consider the LTI system mo} : Jain] — .7:[ri — 1] that corresponds to a discrete difierentistor or first—order difiel‘enoe filter. {a} {5 pts} Find and. plot the impulse response Mn] of the system. {hi {T rats] Find the za—transforni {ET} H {s} of Mn] and provide the region of convergence {ROG}. {e} {8 pt?) If rho] = (sign she], find the ET of yI-nbm provide the ROG. Does the disorete—time Fourier transform of yin] exist? Why or who,r not? 51M”; Fifi-[v Us} “afnl: xifl3ri‘ifimil 6 1R— lL”1-§[fl3 5'9 (a, owl: him} fl”1"J£W31 U") was) * i * ‘2" “a” LL) “kiwi: 31$an fifth-1:] w-r : Q3-Hjflmcwr1 - €53”) HZH'J] We); We} 2" X/fleflred} We) .. {*f" [27/ >9” ,_ H' 2‘ 1|- 042'! I my ”I, Ht {5 Linc-{UM ti W W 4_ Consider the following interconnection of corgisrflous-time LTI systems: [a] {5 pts} Find the overall impulse response Mn] of the system in terms of mks] for i = 1_. . _ . ,5 Note that no specific functions are to he used; your answer should he in terms of tile], habit. halo].- Mn]? hale]: hslfil- {h} {5 pts) Find the metal] {requeuey response H {elm} of the system in terms of the discrete—time Fourier transforms of hiin] for i = 1,. . . ,6. Your answer should he only in terms of Effie“), Heidi Haidt Heels}, Half-5W: Hue-F's). . _ {c} [Iflpts] Evaluate wajm-(mi meat) hfln] = (31+ 1} (0.5)“ uln] hfin] = BCEEU.2H'H] Fight] = 5 huh] = lei-M“ helm] = (0.2%an hsifll = lfl-4llxfl-[Til- ll . La) title (widening) #1” [.41 + @m i, tow Mad? Mad} to filter“) - W”) + twister) + Hoot is a. You were asked to analyze Edge sinusoidal data :rft] = oos {wot} collected and sampled at a commu- nications base station in order to decode the transmitted information based on the frequency of the sinusoid. The following information was given to you: the data is stored inibtvariable x in It'facrtan5 the number of data points is N = 1024, if a}, = 4flir then the decoded information is “Yes" and if too = filh' then the decoded information is “No”. {a} (10' pts} Supposed you were told that the sampling period used was T = [m1 and that Eflilo“ was transmitted. After loading the data in Manse using load 1:, {i} provide Marten 5’ commands to plot the data in the frequency domain with the axis correctly labeled in Hz, {ii} provide the resulting plot. {iii} what is the duration [in seconds] of your signal in time? .03 {b} {If} pts] Supposed you were told that the sampling period used was T ='&' and that the “a transmitted information is W. Plot the corresponding MATLAB plot of the frequency domain 13M” diner. deans-hi, meta-m 7‘ of the received data. Can you correctly decode the nformation? 1‘r‘ifhy or why not? Lately 1;Tpflaali l) a) {Ll 1:5: #«I’ l U" k g hesitant-EL £5}: Na”) K x new (PM 13) ,50 a 30 Plot (P, abs{ )0); alsbeH' R'Liy-EmU-jy} Hs') , 3"”- Ieofi Us) ‘T: Dell; =3qu "‘35:; . éGFPfl;ffifllr £91 Slam. w”: _ 1:" N“ :5}. We ”33* :3 ‘r‘jfiilfioivj ' .I I. D‘ sateen _ r; Immigrant?“ ’9 dot”— iCu oiio-wwfi ...
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