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Exam I Fall 2004

# Exam I Fall 2004 - ESE 337 Name Exam I ID no Fall 2004 1(a...

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Unformatted text preview: ESE 337 Name Exam I ID no. Fall, 2004 1. (a) Are the sinusoidal sequences sin 3.17m and sin 512, with T = l, peri— odic? If yes, ﬁnd the fundamental period for each sequence What are their frequencies? (10 points) (b) Consider the CT sinusoid :c(t) = sin 31). What. are the frequencies of its sampled sequences with T : 0.5, 1, 2, 3? Which sequences have the same frequency as sin 32?? (10 points) SW! 51)"! L6?) (/6 [jMIIDdOIC ' . i ' '. ,, ii _ .FWZWM PM“ ~ ’9’ 391 '* (Ii/Fla : (—72 "“3 .3 1')va We: 3.]ﬁ/277,217 : ”gm? ., gin I?) [’5 M0], FW/ﬂigib (IQ/l: R ": Him/w 7 (5/ 7243.1”- .20 “W? 4 numb /<:3i) 5 ("ﬂ/{f3 ) (’57) E771] \ 2. Compute the CT Fourier series of the periodic signal 23(1!) 2 2cos 5012 — 3 cos Wt (10 points) Plot its magnitude and phase. Is the magnitude plot even? Is the phase plot odd? (10 points) , , E 47%“? "1%?" Amt 3 ‘7»:23’ 44wa «New +6 ’36” Wilbur: WJ;/b? (,7: ’is' cfr/ qr; C7:~/f g/Liilgznwvfnoif Fiﬁ-t 160%“ Wad/gm F/pf 424/00 ( 1’ 61‘) as aw 8V5“ ﬁmcﬁ-Em ) 0?, [3/1448 f/VZL (ﬂipé ‘ ( 10f) V5 («‘1 WM {9W6 4””) 3. Compute the frequency spectrum of the sequence x(nT) = 1 for T =. 0.5 and n : —2 2' 2 and x(nT) = 0 for other n, at w : O, 7r/2, w, 31r/2,27r. (10 points) Use the values to sketch roughly the magnitude and phase spectra of the sequence inside the Nyquist frequency range. (10 points) do a _ Xvi (Lu): ; Q/(nTje’J’qwf {4:120 MJ = 22 8 ” if >4sz . Plot the frequency spectrum (not the magnitude or phase spectrum) of the signal in Problem 2. What are the spectra. of its sampled sequences if T1 : 71145> T2 = 7r/60 and T3 : 1r/180, From which Ti can you recover 73(1)? (5 points each) .. ' : 2 5%r0‘f , 351,, 70 i Effigy/111.691 3/763va ”7L 0(a) ‘ IMHO): 2 (ﬂ 6(ui’ruj4- 775£°v2+\$91)’-3 (ﬁp’{‘w«7a) + ﬁ;(l¢+79)) :Xl‘d) me) 21'! W (rd/5) ...
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Exam I Fall 2004 - ESE 337 Name Exam I ID no Fall 2004 1(a...

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