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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY
SCHOOL of ELECTRICAL 3:: COMPUTER ENGINEERING QUIZ #1 DATE: 11JUN—10 COURSE: ECE 2025 NAME: STUDENT #:
LAST, FIRST Recitation Section(2 points): Circle the day 85 time when your Recitation Section meets: L01: M 2:404:25 (Taylor) L03: T 10—11345 (Hunt) L05: T 2—3345 (Romberg) L02: M 4:406:25 (Taylor) L04: T 1200—1315 (Hunt) L06: T 45315 (Romberg) 0 Write your name on the front page ONLY. DO NOT unstaple the test. 0 Closed book, but a calculator is permitted. However, one page (8%” X 11”) of HAND
WRITTEN notes permitted. OK to write on both sides 9 Unless stated otherwise, JUSTIFY your reasoning clearly to receive any partial credit.
Explanations are also required to receive full credit for any answer. 0 You must write your answer in the space pr0vided on the exam paper itself.
Only these answers will be graded Circle your answers, or write them in the boxes provided.
If space is needed for scratch work, use the backs of previous pages. 1 32
2 33 

 we Problem 01.1: Each part of this problem is independent of the others.
(a) (8 points) Find TWO values of 9 satisfying —7r < 6 5 1r such that Re{(2 + ﬂew} = 0. 91: I'lozn‘ 92:;7‘9345/ J .‘2‘63GJ
= 21531 6 '1‘
“faded— b3» % .4é3é 0"” (TT/zqt.’*~r‘£3é) (b) (8 points) Plot the complex vector (1 + 3%”.
o'lt_ ‘(1I)Mbdq ‘ “J: :01 .“9
W513: 3I (c) (8 points) Make a. plot of e(—1+j2"}‘ over 0 S t g 1. [Be sure to notice the magnitude bars!) \’\.: Ie‘t ‘16“an
W W54)
6“" 1— (d) (8 points) If 5.6 exp(0.312j) = ﬁnd a and b. a:geaf’b:.4%% a”, 4+5?“ _ 1.043)
3 aec‘wm'“ rJCﬁWU Problem Q12: Each part of this problem is independent of the others. (a) (8 points) Express 3 cos(wt + a) + 3 cos (wt + 16) as A cos(wt + 95), where A and gt are functions MW (55)
4 e: ‘3 1 COW“ W) C Wig if
Eff't 'ZQﬁfﬁj
(b) (8 points) Simplify the following expression: 1
xmemiamm_5tmtj k=0 You should be able to do this without doing any explicit calculations! Sketch
ated with the terms, and give an intuitive explanation for our answer. (194:. phasors assoii  m XS“ (’6 4"“ W“ t ” d A 5.592158 C (3%“!133 $531 53” 57 F J ‘I «« 2'
Wﬁ%£wm sg~mu gm?fe
.1 f .. IA a? II/,...—:. (i) (9 points) Plot the twosided spectrum of 55(t) 0n the graph on the next page. Be sure
to label all components of the spectrum with their frequency (in radians/sec) and their
Complex amplitude. (092(046)9V: (
‘ v f db .Jdé ‘ J
c Edi+5”! X67 +6? )(Cﬂjigj
MT L " 2;
'u Jute Mi", 4%
sew” rt: M c J frequency in rad / sec (ii) (8 points) Find its fundamantal frequency in Hz. 1% = /2 n ﬂ: Mai, ‘
*3” "1967 “ML? 5'3 W [9%) 5% W???“ C. “3: /§* Problem Q13: (3) Over the interval 0 < t < 1, y(t) has instantaneous frequency fmﬁ) = 200.9(27r2t) in Hz. (i) (8 points) Sketch fyiﬁ) in the space below {113+ 96% ’ m w / 5 Jit’kjaucix (jib “mam«5) azﬂ’
AA: gnu— 5? r? m" 371"";
z/p'f @§{4ﬁ%)§6f 3; + 4? :2”? t. 14 a ur + 5%47Ff #4 (b) A real signal
:50) = Acos(1501rt+ 95) + Bcos(w1(t — 7)) + CCUSﬁdgt) + D has the following twosided spectrum: 53—3517,” 5 563‘an — 100 —75 ~50 0 50 75 100 f frequency in Hz (i) (8 points) Determine A, B, C, D, L01, Leg, (,5, and 7' the signal $(t) with the above spec trum. EL "Dr: Dc: 3 B=m/_’_‘~3___ {ML like C=__:.;“l' _ “an wit: 1?? T Q
D=mﬁﬂ_ ﬁeiwvhwkf be _ 5’3"”? cfmfanwt’f'lz r
$‘ ﬁnal GI: _. L} '2? 1:—
“1” "2—: my w W ’1 if
“i “7‘ R " .
w2 =£.:___r_9 '3 «5 'L
.... U;
T:_ {6:35:38} (ii) (8 points) Is the signal 3:09) is periodic? If so, determine the fundamental frequency f0,
of the signal f0 ‘3" ...
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