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EE20-01-Quiz-01-2010-09-16-SOL - EECS 20N Structure and...

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Unformatted text preview: EECS 20N: Structure and Interpretation of Signals and Systems QUIZ 1 Department of Electrical Engineering and Computer Sciences 16 September 2010 University of California Berkeley LAST Name KOMf/C k2- FIRST Name SQT LabTime NEVER/[i - V II o (5 Points) Print your name and lab time in legible, block lettering above. 0 This quiz should take up to 20 minutes to complete. You will be given at least 20 minutes, up to a maximum of 30 minutes, to work on the quiz. 0 This quiz is closed book. Collaboration is not permitted. You may not use or access, or cause to be used or accessed, any reference in print or electronic form at any time during the quiz. Computing, communication, and other electronic devices (except dedicated timekeepers) must be turned off. Noncompliance with these or other instructions from the teaching staff—including, for example, commencing work premature/y or continuing beyond the announced stop time— is a serious violation of the Code of Student Conduct. 0 We will provide you with scratch paper. Do not use your own. 0 The quiz printout consists of pages numbered 1 through 3. When you are prompted by the teaching staff to begin work, verify that your copy of the quiz is free of printing anomalies and contains all of the three numbered pages. If you find a defect in your copy, notify the staff immediately. 0 Please write neatly and legibly, because if we can ’t read it, we can’t grade it. o For each problem, limit your work to the space provided specifically for that problem. No other work will be considered in grading your quiz. No exceptions. 0 Unless explicitly waived by the specific wording of a problem, you must explain your responses (and reasoning) succinctly, but clearly and convincingly. c We hope you do a fantasticjob on this quiz. Problem Points Your Score Name 5 ’7 1 25 9‘5— 2 15 l S- Total 45 LP; l0“ (7,.) sTrch-l’d‘s l6" l<l§JI ”L M (X TRTQIQ, VA vLC§ fig, K ‘Kd’ CONUPOHJ l3 Ills-lam V" \UkU) k Mal 3 [Arm canlingvts i/‘mlvtCS ’L/‘C ilk {Micgl/ «X 13% Q1.1 (25 Points) The two parts of this problem are related, but you may tackle them in either order. Be sure to explain your work succinctly, but clearly and convincingly. (a) (10 Points) Determine every complex number that can be expressed as a sum of two distinct 3ml roots of unity. That is, determine every number Z : x —l— y, where x and y are distinct, and x3 : y3 : 1. Identify these numbers Z on a well— labeled T_diagram of the complex plane. l—hé. fiilf'ol ”097—5 07; Mali. N‘e E. LIK firk = —l9, l('l “l 0"“ afierifime cnnfgaaws wlutes ethyl) 5", leT’ 2.3— l -Cxl\/3 ”To. _. ’ Z_\:_e I Z,‘ :6 Jr 54A ”left fire. ‘Tfirtt 17am uJiSQ AJJ—fi‘ans 0‘]qu ,‘Z ’\’Z [5058\le (’ , 30“le Combina'i'ricmll‘; Iflc‘l-MeJ If“ IS C5\_‘5 .. /_3> leG-Jm _. '2“ L-ZTT _ Z_\+Z\= at ("r VS =7fi/Zc ( i373) _2c08(2l:l:. “l .W/ Z0 +7“ - l tell“ 3 — _(€‘ /3 * 9'73): "7/3 —2coslu )_L 6. e z" t ‘4 = \ + t““/3 = (1 +62% :6: gig?! V} (b) (15 Points) Evaluate the sum of al/the distinct 3ml roots of unity (11/3). Then, use your result to show that 2 Zcos (Z—WkJr g>zzsm<21k+ 7;): 0. L — —¢ T - . KfioriTfi Z— l+e all/5+6 “é Ziefl; . r 3,, -ca ““7375 IL: 0 [Vl~l‘l;rla (Mln fil’ltloar 6%: gel (“%\L+T%l:0 Tn 7%ch lfifir’QISifi m [71/- Sacred «low-7L ll 2 'Rng—k Lk 2 Lgclg =0 filo—:0 L kf¢)t.0 =3 lécos '31 Q1. 2 (15 Points) You may tackle the two parts of this problem in either order. For each part explain your work succinctly but clearly and convincingly. IT I7 ml A) —‘:.C95 3 . 6666 We'll-C viii/3) _ é/z _5.,‘C73)—_ ATS/CC) C l+KE “SQ: V1 Jig/,1 “CC 'IT “LACY/5 CCCJo LIN/3 ym <r*. L- «ll—A 3£/&\ :[ 5L/3\‘V '5 ‘8 _<:LLT/€>:<c‘ Z) C“ C74) 1‘ C sing/a 7—) l—HIl’: —elllWE:,(oH trle ler Hal; 5 ‘H- _ 2) (b) (7 Points) A discrete—time signal X is defined as follows: C I) L“ X(n7 X(n):6(n)+6(n—1)+26(n2), for all n. > . . _ _ O \. l n DetermIne and prOVIde a well— labeled plot of the SIgnal y defined by A Sex lwmr cl yIn) =x 33w) x( —n+2).>< 4 Xl’ll Kl,“ (I llmll": ’5':le X(nl= “n+1 )5XL h'lh’x l“ \ (llllll (Minx m lfllltllalelet \ l1 WI "QS QC -2 -—l 0 2% :(n) \) l ' +R' {all 2 X(o —x—1+2=x(a Wmlfl, I s 7% & l’sélpjl tn 3(n)=x(n);;’(n) x a N ’t. - Xl\\:>\ ’\Tl\:fi(lW:Q(—l\ n (2) l1) TEA: x(—o+;\: Mal 52(0) I (I) 0 I 3. n ...
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EE20-01-Quiz-01-2010-09-16-SOL - EECS 20N Structure and...

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