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exam1_sol - ECE 301 Exam 1 Daniel Aguiar This exam will be...

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Unformatted text preview: ECE 301 Exam 1 Daniel Aguiar June 21, 2011 This exam will be 60 minutes. It is closed notes, closed book and there are NO CALCULATORS to be used on the exam. There are FOUR problems. Name: SAM/Mn; Problem 1 (20 points total) State if the following systems are linear, time—invariant, causal, and/ or stable. Showing work is not necessary. Part a (5 points) Part b (5 points) Part c (5 points) 1 > —2 I 1+|m[n]! ” — y in] i 0 n < —2 Part d (5 points) y [n] = Z 93 [kl Lfﬁéor Til/1"! ’fﬂv (tr/Wm -/ (dwgd/ {Vail/e 4 140 /65 /€; ya 1) m9 ﬂ: /“ W M "0 Y“ #5 Problem 2 (40 points total) For each of the following signals, ﬁnd its energy, power, and state Whether or not it is bounded or periodic. If it is periodic, state the fundamental period. Part a (10 points) Part b (10 points) Part c (10 points) h(t)= Z (u(t—2k)—u(t—2k—-1)) k=—oo Part (:1 (10 points) 9 = cos (7m?) 4: g ; (M J~T(2l(/m;(2g///1Jer 0"“ /T;L{/+Zmﬂ{/\$wl/2‘//v/f °0 T‘BOO ~/ T9” "T . T . n a (m I (3%,; far/20% ééar/Yé/jfz’ ‘ w PM 4 . 'r ‘ (f 4 .— ﬁ 2 P00 =79; 51:17 {E} f 224/25; 7%(0/73/16- r; 27/39/24- 00 we) I: livach ( /2(/e//<z/ A’N/ [.r form/,2 VIM ﬂail] W . 6” N-w “"4! 3 H NW N ,v 1 4 Mil (AX/w LV _2_." [A Z: .. ~/ CIA '3 ~/ z (154‘ ([+2h22/(3 ):N~aﬂ( h:¢(3 //V.2 I é / A/«M» 1-; “'( 1 f 3 ’V [4/ P = I‘m .1 2: (i) . AFN 2M1 142’” M a mid ( W1 W? 2vsz ,3 N07 pawl/2 ht) \ (X5 7. L- : M [T Z (%{£-ZA/~%/t-z&-I//Jt = ‘1“ g f (W/é-zé/~il/é’ZA7/jo/{ “J T9” ‘7 ’5‘4 T900 Loo «7 % Z (l/ 2: 00 l l<=~oo (I. 7- ‘” I Pw ‘ T30, {L7 [7 Em(26/6-Zé/ﬂc/tvzév/M = 24 M) :6 émJec/ {ma/la) 4(6) «3 ﬁnk/,2 (,344 fr/f/j 2 v w N a 12:” C’w‘qm'z/ 5 2 {W14 (ix/25747/ : Z i1[/H/‘ W ’ n—w h—-o(, :5 4/,” / (1/ Problem 3 (20 points total) Let 33(15) : e‘mﬂmm. Part a (10 points) Find and sketch the real and imaginary parts of a: Part b (10 points) Find and sketch the magnitude and phase of a: ‘ -‘rr/él 9c“): 8 Z/He J 1 6-i/f/Cw 5 ~ {Hi/r»: (MW/ IMZM 65/} (MU Problem 4 (20 points) Find the partial fraction decomposition of C 6+j13w—5w2 : if I3 + W Iﬁv ( 1W? [0—24, 3{/+'2/+C(/+-0)2 : a +J/}</’J—</l Aﬂﬂwﬂ/v‘jlw/ %/ J 0 J A(/~/'J3R/ "24/7 7" 3(f/J'Zu/f (,(MU'ZQ -01/ 1. M +23 MC: /3 AW 7% = (a) -214 '28 “Rh/2 ' ]_ +24 :/3 w/ 4443/” I3 A 3 ( 1110/4 +4) : 5 /Iv:( 5’) (:3 ...
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exam1_sol - ECE 301 Exam 1 Daniel Aguiar This exam will be...

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