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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 axes  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 ElliI3” in a row; if u formula, is: given1 provide a formula. : Signal {time} Fourier transform of the signal [froqueney]
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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.
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= 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
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(and tauUSU 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 proresizior1 you realize that since you have a periodic input with known fundamental Frequency, you can process the return in the frequency domain. {a} {It} giti) 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:
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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.
 Spring '07
 Chakrabarti

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