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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,.) sTrchl’d‘s l6" l<l§JI ”L M (X TRTQIQ, VA vLC§ ﬁg, K ‘Kd’ CONUPOHJ l3 Illslam 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
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54A ”left ﬁre. ‘Tﬁrtt 17am uJiSQ AJJ—ﬁ‘ans 0‘]qu ,‘Z ’\’Z [5058\le (’
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leGJm _. '2“ LZTT _
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;
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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
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(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“ \
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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
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