Exam2_Solutions EEE303

Exam2_Solutions EEE303 - {—51 Name: ;Q L”- 2 ft?an EEE...

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Unformatted text preview: {—51 Name: ;Q L”- 2 ft?an EEE 3&3: Signals and Systems Exam 2 March 29, 2Dflfi Prof. Fapandreou—Snppappola You must answer all 4 problems for full credit. The number of points for each part of a problem is I given. For full credit. show all steps and label all axes. u{t] is the continuous—time unit step. and {fit} is the eontinuous~tirue impulse. a denotes convolution. 1Where appropriate: in show all intermediate steps a label all axe-s - circle the final answer This area is for official use only: Emblem 1 Problem 4 Extra Points 1. [24 pts] Complete the following table. If text is given1 provide text for the miming Elli-I3” in a row; if u formula, is: given1 provide a formula. |:- Signal {time} Fourier transform of the signal [froqueney] tit) X 11ij box (- triangle Shh c sgumwl mu ii iii 1Q; W multiplication of two FTs 51 it) “if”? 53(tj+2ii[tj 5 X0”) + 9H lflX{ji:} QED .Tr 1 (#9) reverse iirvawquesnnj.r variable in “lake 1’ {war 53— real and oven Eignal {aka 33 {um 2. 0» Given the following Fourier transform {FT} pair: <—> mm} = —‘-— = hi:— ufl} E4 +jwjg and using FT properties. find the FT of the follawing signals. (a) [13 PM yfl} = [éfi'2'-1}UE¢J- (b) [I3 pats) zfi] ={fngfl—4:+12u{t_33. " ' ( Ln») «ELF: :— 1f§>~uifid Z) r1)“ij '“ afiJ‘T‘S—m) swim ,1 an __ 4H + 17970)) ‘3 LL; +3 an) 2- was :— ‘ “#3) . _‘3<.J at) : £3 a gm: *5.) (a 29m i X (id £3 "E‘inu. erE-Fl; F JJLJ = a. 3. Consider the i'ellerwing interconnected linear time—inmiant system: I“) m where £11 [£3 =: 5e'-2t flit}: hflt} ens {Ella}, and haw) = 5m. Recall that when Systemfi are in series! the eversl] system impulse respense is given by Mt) = hlftj 1, 3mm ,R ham. {5] [15 gets] Find the overall system frequenej,r response HUM} {bl [14? pts] Find the werall system impulse respense Mt} by computing the inveme FT 0f HUM} frern part [25,). \Y“ “H3 it?) (i We) MWW JLCJ- _ s El .5 mares) 4,. 5T Sits-SD) sjse satire ill ‘ICT lEII-‘L‘blEJ _,‘5 .[Z . kL-t) T, 5/“; if D + EL 85943 (and tau-USU 4. Assume that you are working for a signal processing company that wants to detect the presence of a bend inside a water pipe by transmitting a sinusoid and then analyzing the return. The sinusoid you are transmitting is = Encore: and the return signal corresponds to the output y{t]l of a linear, time—invariant system with impulse response Mt] = Ee'g'giuft}. For ease of processing, assume that there is no noise added to the system. As a signal pro-resizior1 you realize that since you have a periodic input with known fundamental Frequency, you can process the return in the frequency domain. {a} {It} git-i) Find the Fourier series {FS} representation of the input signal slit) = Sees I: [bl {1.5 pts} Find the output yEt} using the FS representation of fit) and the frequency response HI:ij oi your system. Extra points: [5 pts} In a realistic scenarioT noise should not be ignorerl'| thus. the received signal is actually y[t] = slit} ac Mt} + tuft] where w{t} is additive white noise. Knowing that white noise is spread over all frequencies and based on your answer in (h), what type of filter (limitless, highpass. bandpass, stophand} 1would you design in order to suppress as much of the noise as possible"? What should the cuttoff frequency at: of your filter he? (‘1‘) 10¢) =r 5WfIt) aged?" + 5 align: 3 “L :5 LJ 7: — s} v 75:; “herds-‘51.} “as—‘3} “ii-'1 I Jone. QB) Lt) .: é Dr’s. Hie-l fi- “ir w. t - 4-51 em. may ,a._ H tenets are) (to. sue) s-aflw a? U63} f a") 6 Jr ‘5 E’ a :— éLE-e L “h ire-+3112; Jaajrai: ylfiwh m3 Sihwgu'a {u LT'J: {Easy-w :3 Smfltd mama's mac-é : Eel-m -. Six-it; Hit—I‘leA'g‘hTt glib-1* 't EFQFHTP’JLE) =9 U411 imfimj 4;;be shoe tattug e smash 1% at“) 3 i .____:}L,} 'wL—nif'l “If! “{— ...
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This note was uploaded on 09/29/2008 for the course EEE 203 taught by Professor Chakrabarti during the Spring '07 term at ASU.

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Exam2_Solutions EEE303 - {—51 Name: ;Q L”- 2 ft?an EEE...

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