exam1_sol - ECE 301 Exam 1 Daniel Aguiar June 21, 2011 This...

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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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This note was uploaded on 02/14/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Fall '06 term at Purdue University-West Lafayette.

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exam1_sol - ECE 301 Exam 1 Daniel Aguiar June 21, 2011 This...

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