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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 
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. 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 Domf)
ﬂthﬂi‘tﬂ EC X‘Qw) : g {a lW‘iQDGQ" d 0 Wmﬂ _ w
xjm): % Xt(~lm)* XifJ ) mm)
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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 ZTraneferm of y[n]. Sketch the polezero 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 timedamain 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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 Fall '07
 Chakrabarti

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