This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: NAME gokW—‘l’\0k§ Michigan State University
Department of Electrical and Computer Engineering ECE 366 INTRODUCTION TO SIGNAL PROCESSING Practice Exam 1
Spring 2011 February 24, 2011 a One side of 8.5” x 11” paper consisting of hand—written notes is permitted. (Please
turn these notes in with your exam. And, don’t forget to write your name on your
“cheat” sheet!) 0 Calculators are NOT allowed.
0 You will have 60 minutes to complete this exam. 0 For those problems that allow for partial credit, please show your work clearly to
maximize your score. 0 Good luck! 1. (25 points) True/False. No partial credit will be given, so it is not necessary to show
your work. You will receive 2.5 points for each correct answer, —1.25 points for each
incorrect answer, and 0 points for no answer. Wammmmmwmmm (a) Periodic signals are energy signals. False. PU!“ moire st%w.ml8 are, fewer" §i,%$\iabeg. (b) The signal ﬁt) = tsin(5t) is odd symmetric. Fads e . 15G) 1r even rgmmdrtc (odoiiwmw 00100. (c) The system y(t) = fix) $(T)d7‘ obeys the superposition principle.
TFLLQ. (IR—{"Q‘ﬁ seat: on (r or linear" operalvrgr)
(d) 6e) = M (ii TTWE. (e) The two signals f1(t) m sin(3t) and f2(t) = sin(6t) are orthogonal. —Twre.LgtkmrouﬁsOikiﬂ¥hrea+m&e7ueamar cur a ort’Loyomml.)
Fourier Series analysis is not applicable to aperiodic signals. (1”) F”.
FkLgé‘ the F5 LQJ’L rgpresam‘f’ CW» KQQFﬁQCAEC
{L‘ﬁwa/ oner a "FMMHLQ renewal oFi'l’ww/Lé. (g) The power in the nth harmonic of a periodic signal is not dependent on its fre—
quency or phase. Ti‘LLE_ The EOwE—T D‘F‘Tl’hg saw“ {KQIWLQASC if;
(Okla agaaoieaiL Darts awhraele.) Fouri analysis may be utilized to study unstable systems. h) POLLS Q. Th e l: T 09er next QAOLS‘TL‘ woof mkéodn 460/:
S‘ L <15 m ad r u (i) It is possible to exactly represent a ﬁnite duration signal with everlasting sinusoids. TF‘LLE. CHILL? [S UOCLOCIL \HKQ, FT 1.8 all «berg/’1’) (j) The magnitude of the Fourier Transform of a real signai f(t) is always even
symmetric. Trig. CWLS LS cleats Conkgurgejie Jamme+gaj l
i
g
l 2. (30 points) Show all your work to receive partial credit. Correct answers without
accompanying work will not receive full credit. Consider a linear and time—invariant system Whose output response to the input 331(7?)
is 31105) (a) Sketch (and carefully label) the output response @905) of the system to the input 232“)
(1)) Sketch (and carefully label) the output response y3(t) of the system to the input
(63 (t).
x1e) y1 (t)
3 3
2 2
1 1
O O
1 _1
2 —2
—2 O 2 4 6 —2 O 2 4 6
X2“) x3(t
3 3
2 2
1 ‘l u
0 O
2 —2
~2 0 2 4 6 —2 0 2 4 6 WWW Mammam— Extrasheet:
Thus. QPDWQM goon be. Someoﬁ (03 {msPec’lLtoA, JFLLSJF Hum [CQ SLMPQAS‘ POMJHMR q +1Me “MUMMRCU a) KLL‘E‘): XICJr)’ Xt(+'k\ "memuwmw = . .. MWmemmp—QWW 3. (25 points) Show all your work to receive partied credit. Correct answers without
accompanying work will not receive full credit. Consider the signal 1305) = u(t + 2) —— u(t — 2). 93(15) >2: a:(t)
mm*we—2y+ao+5e+2) (a) Compute and sketch y(t)
(b) Compute and sketch 2(t) ‘VL {*2 ’t i i be ”kiwi <“QJ %£+) :: O (NO {30%th \) E For ++13 *1 “F +~Q ‘ ' 3‘ UH [U3 ”“1 &k&leﬁowf})/ ﬂ ++2
w I C i i jlld’r‘: ’t _
1 Reg ‘
For +4 2»; t +44; L\Hl&30w+JQ' ‘(Q‘WL‘ "2 rﬁg+jr+igtlldr= ”tr : 14%;)“ Ltd: +4. 3:“ we 21 ) %C+) m (M New U Extra sheet: “Ir—MM «(Hf at) ﬂrCJr) + {galmg) VPFOM ‘er. o\\s+rtﬁaw+xa11+% “'7 COWUG (”C’LW’L 60/0»?! “SUM vac+ma%ww{ !
@mi 5M 4‘“ ,LQVCIAA, f 4. (20 points) Show all your work to receive partial credit. Correct answers without
accompanying work will not receive full credit. Suppose we are given the following information about a signal 33(t). (a) 33(16) is a periodic signal with period T = 2 and has Exponential Fourier Series
coefﬁcients D“. (b D” is non—zero only for n_ w —1 O 1. ( ( l c) 33(t ) is real and even. cl) The average value of $(f; ) is equal to 1.
) (e 1229“) (t)—2dt— 9.(Think Parseval’s relation!) Specify the two signals :1:(t) )that satisfy all of these conditions FT‘DM (“0L3 / {ML—f): 2V @ﬂﬁamoow" U01, 2' 2U" 3 TI, ...
View
Full Document
 Spring '08
 STAFF
 Signal Processing

Click to edit the document details