exam3_fall07sol

exam3_fall07sol - EEE 203: Exam 3 November 29, EDD? }...

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Unformatted text preview: EEE 203: Exam 3 November 29, EDD? } .r" Name: '53 LUTIDNS ASUII}: This is an open book, closed notes exam. You are allowed one cheat—sheet. Pleaee shew ell mark 130 get full credit. Good Luck I 1. Consider the following interconnection of discrete—time LTI Systems. If F11 [n] = {U.5j“u[fi], what is HIE”)? Ifhgfifl] = cosmflwn], what is Hgfejmj‘? What in HEij)? we- -- W o — .fl L1¥C~i FF. l ,H u w In 211m) “ii-“T4 : h f r V J; o “H ) MT‘MQ‘FW” . 93m . "Wm o1‘ ow) + r“ “'3‘ " . 9" W 1M“ J K" "“" J It:st 2. Compute the Nyquist rate of the signal sampled at T = [1.25mfllisemnd. $3} = {$12—$31}? Plot the Spactrum if the signal i3 -:: 7‘4“; a 116%) TH:— E H __ 54M Dom-f) flthfl-i‘tfl EC X‘Qw) :- g {a lW‘iQDGQ" d 0 Wmfl _ w xjm): % Xt(~lm)* Xif-J ) mm) I Laminar“ i l' 5’ 41 mi; *mw a w ____ W hm“ a mum: ‘firnflo‘fi 419mg 5 2m: WW "7" '3 it} iii-'9 DC!- (.0 3. The Fourier transform of a signal at: [t] in given by Xcijw] = y+ 171W] — 145145, — 1hr). We want to sample such?) to obtain the oontinnoua and 5amp1ed signal split} = Ef:_m $¢{aT}5{t — 111"], where T is the sampling period. (3.} Plot Xfljm}. What is the Nyqnist rate? {b} Wth T = 11.05 second, plot the Fourier Transform Xpfiw) of mph}. Does aliasing occur? ‘iiii'hf,r or Why,r not? [0.) When T = [Ll second, plot the Fourier Transform prjw} of cup ft}. Does aliasing occur? Why or why not? XCGN) ED?“ 4- Consider an LTI system with impulse reepense h[1r1] = flirt] — fin. — 1]. [a] What is Hfz}? (13] If fil'fl: = [fl.5j“u[n], find the Z-Traneferm of y[n]. Sketch the pole-zero plot along with the RUG. Does the Discrete Time Fburier 'I'Ianeform of fin] exist? Why or Why not? 09 win] : gfn] F gfn—Ij ng) : r — z" PM 111‘”) en) fin] i CD’S)“: min] XL?) : Tfeasf' RUG [1’ 706 gm : 91W 7* hie] yfiz) : Matt?) 5.[a} The E—Transform of a signal min] is given by sz) = 1_ 93%. Plot the corresponding pole—zero plot and R00 if {i} $[n] is a. left—sided signal and {ii} .T['I‘1] is a. right—sided signal. [1)] Plot 3. signal whose Discrete Time Fourier Transform XII:ij has its imaginary component 0, i.e., Im{X{eJ'wj} = fl. Justify your answer [Lin]: the charactefistim of the frequency domain represtatinn with the time-damain IEpI‘EEEDtELtiOn uf such SigJaJsJ. “Few-[r9 m 13:15PM {1L ZDTF T} a1» «91] L1 mum/J Mm Xfigim) 1m mull. oral m. 15h] ...
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exam3_fall07sol - EEE 203: Exam 3 November 29, EDD? }...

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