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Unformatted text preview: g.)— Wow EECS 20N: Structure and Interpretation of Signals and Systems QUIZ 3
Department of Electrical Engineering and Computer Sciences 9 November 2005
UNIVERSITY OF CALIFORNIA BERKELEY FIRST Name
Lab Time LAST Name o (5 Points) Print your name and lab time in legible, block lettering above. a This quiz should take you up to 15 minutes to complete. You will be given at
least 15 minutes—Fup to a maximum of 20 minutes—to work on the quiz. o 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 elec—
tronic 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 prematurely or continuing beyond the
announced stop time—is a serious violation of the Code of Student Conduct. a The quiz printout consists Of pages numbered 1 through 4.._ When you
are prompted by the teaching staff to begin'work, verify that your copy of
the quiz is free Of printinganomalies and contains all of the four numbered
pages. Ifyou 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. o Unless explicitly waived by the specific wording of a problem, you must ex
plain your responses succinctly, but clearly and convincingly. _0 We hope you do afantusiic job on this quiz. (23.1 (10 Points) Consider a discrete—time system F:[Z—>R]——>[Z—>R]. It is known that F is linear. It is not known Whether it is time invariant. The following inputoutput signal pair (3:, y) is a behavior of the system. The
signals :6 and y are zero outside the regions shown. x(n) m '  y(n)(1)(2])(1) 4 n 3 4 5 n
it)
Lot/W \ (a) Could the system F be causal? Explain your reasoning succinctly, but mm” clearly and convincingly.
Fals linear _—~_‘~; zero {'4 null, rmclvUES new cal—{adv EL {2’} [email protected]):o Va is 7ft: zero shrub, 7733f! gz(n)=0 V71 is If: airCl".
may zmmcm wags, Lita/Emirate) (2 m3. We‘re one, F
WﬁW‘lﬁw Cannot [Ge (“‘34. l D 3 (b) Could the system be memoryless? Explain your reasoning succinctly, but clearl and con incin l .
E 3 Y V g Y Msww NC kr'LO‘D all memcngSS SUfSlENLS are Causal) clan, C) . Hemogless :> (“5J1 _ I
WW mace} “0+ CWWSJ 7—5 Mol' W L? 1 (c) For this part only, suppose F is also time invariant. Determine the im
/ pulse response f of F by providing a welllabeled plot of the impulse
response sample values ﬂu), or explain why it is not possible to deter C" l3 mine the impulse response based on What is known about the system. Milky“ Ind.— Fl‘l fine I‘ddalm.“"/t‘ me“ 8(4):}(01TH‘) ﬂeckﬂs h(nl=&(’\tlt'))c..cv (2) Mm» ‘ (l) 0 ) lO} Q32 Version 1 Q32 (20 points) Consider the ﬁnitestate machine composition shown below: (react, absent} Let the set D x {0, 1, absent} denote an alphabet. For every pair (32101), 56201)) 6
D2, :31 (n) and mm) denote the top and bottom input symbols in the figure,
respectively. The nth output symbol y(n) E D. For each of the following guard sets G1, G2, and for each of the machines
B and C, determine Whether the machine is wellformed (WF) or not well—
formed (NWF) by circling one choice (WF or NWF) in each entry of the table
below? No explanation will be considered. No partial credit will be given. 01 = {(1,0)} G1={(0,0),(110)} l” {92 = {(1,1)} (m {G2 2 s
01 7~ {(1, G1 ={(1=1)7(0v 1)}
(m) {02 = {(031)} (11/)ng {(070), (1:0)} is
[do nmsthﬂlfg M
for 5 or C NOTE: The answer to (I) shows that B not wellformed DOES NOTIMPLY
C is not wellformed. 3 . ; ' ' f1” Q32 Version 2
Q32 (20 points) Consider the finite~state machine composition shown belOw: {react absent} —’ c _ Let the set D = {0, 1, absent} denote an alphabet. For every pair ($101) 33201)) 6
D2, calm) and 33201) denote the top and bottom input symbols in the figure, respectively. The nth output symbol y(n) E D.
For each of the following guard sets G1, G2, and for each of the machines
B and 0, determine whether the machine is wellformed (WF) or not well formed (NWF) by circling one choice (WF or NWF) in each entry of the table
below? No explanation will be considered. No partial credit will be given. (I) {a a {(1,0)} 1 (H) {Gi={(0,0),(1,(1);} 02 : {(0,1)} G2 3 {(011)3(1: }
01 = {(13 1)} G1 = {(010)2(110n
(1”) {G2 = {(0,0)} (IV) {02 = {} Q3.3 (10 points) Consider a real, discretetime periodic signal 3:, which is modu—
lated by a real, periodic impulsetrain signal '1". The signals a: and r are shown
in the figure below. x(n) (3) (3) (3)
(2) (2) (2)
 (1) (1) (1) 424012345 n 1’0?)
a (1 l —3—21012345 n l (1) (1) Let q denote the resulting signal. The sample values q(n) of the signal q are
given by: (101) = WW”)
Determine the period p, the fundamental frequency rag, and the Fourier series
coefﬁcients Qk, k 2 0,1,.. . ,p — 1, of the signal q. The following complex exponential Fourier series expressions for a periodic discrete—
time signal having period p may be of potential use to you: (10%) = Z Qk 8mm Qk =  Z (IMF—WU”:
he pmm
_ Where we 2 2g and (p) denotes a suitable contiguous discrete interval of length p.
“a (1)
N012». Win/l :r‘ﬂn) : Z gtmsg) I j , . .
' no» ~73 .0 s A
" T
. 3 _£kh\°r\ F13 lube:2 ‘gg‘r‘ “Ml; Z
r ? Wt
.‘ int) k . ' 0 439° "t o
:J— 02 >1—l—‘=—' ﬁnk—'k‘oxlax
3G, 103. + 3 3 3 ) ...
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