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Unformatted text preview: EECS 20N: Structure and Interpretation of Signals and Systems QUIZ 2 Department of Electrical Engineering and Computer Sciences 04 October 2007
"UNIVERSITY OF CALIFORNIA BERKELEY — LAST 'Name /“ MC ‘es ‘ FIRST Name V Lab Time Asa 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 elec
tronic form at any time during the quiz. Computing, communication, and
other electronic devices (except dedicated timekeepers) must be turned off. V 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. 0 We will provide you with scratch paper. Do not use your own. 0 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 printing anomalies and contains all of the four 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 ex
plain your responses (and reasoning) succinctly, but clearly and convincingly. e We hope you do a fantastic job on this quiz. (22.1 (25 Points) Consider a continuoustime system F : [R ——+ R] —> [R —> R] hav
ing input signal a: and output signal y: x F y The system is a squarelaw device having the inputoutput characteristics shown be—
low: The figure shows that‘y(t) = x2(t),Vt E R. Suppose the input to the system is the sinusoid x(t) = cos wot, Vt, where wo > 0. (a) (9 Points) Provide welllabeled sketches of m(t) and X (w), the timedomain
signal values and the spectrum of the input signal, respectively. You must
explain how you obtain the spectrum; a mere plot will not suffice. Ia Jerk ____,
‘— Arie 0 “do l'rttTuuer\cie,§: LO; OU’UJL LJ'° 211 1‘4 X663 (J o +0.7; (4" (b) (9 Points) Determine a simple expression for, and provide a welllabeled sketch of, the output signal yak).1 In plain English, articulate how the sketch
of y(t) differs from that of a:(t). 3(lltc—os‘lw'l' : Li— LUS‘Q‘Jol— o a A .
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0, o . Wm cafe of x. (c) (7 Points) Provide a welllabeled sketch of Y(w), the spectrum of the output signal. Explain the appearance, in the output signal, of any frequency not
present in the input signal. Be brief but convincing. Lot (amt 4m, 4. ‘ fez
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4 4r 0 PM levcse, 90a «angles 04‘: at», «AA “3&3 (‘QSKXk— S’MM lexe Swarlna ol; ﬁe, iquj’ SlamA,w\r\ic\(\ is o\ nonlinear afﬁxlion.
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mUx limeﬂ'exerQoa «Ilia V l 3 <7qu roxat VALKQ “k? ("l—E) Z, )l’\ C°V;l’r0\S\’ l?) Xﬁ’spuhlck l‘le cm «utmae Valqu 01L ZQPO (\‘QVKQ’M CQQEVCX’Q w;o\)' 1You may find the following trigonometric identity helpful: cos2 a = E + l cos(2a). 2 3 Q2.2 (15 Points) Consider the continuoustime system F shown below: x F y The system F is known to be time invariant. Moreover, suppose the input signal a:
is periodic with fundamental period pm; that is, m(t) = x(t + p1), Vt, where pg, > 0. Select the strongest correct assertion from the following choices. Explain your rea
soning succinctly, but clearly and convincingly. (I) The output signal 3/ must be periodic, and its fundamental period py must be
equal to the fundamental period of the input signal; that is, py 2 pm. .The output signal y must be periodic, and its fundamental period pg is at most
equal to the fundamental period of the input signal; that is, pg 3 p1. Provide an example of a system F such that the inequality is strict (py < p9,). (III) The output signal y may or may not be periodic. If it is periodic, then its
fundamental period py must be equal to the fundamental period of the input
signal; that is, py = pm. (IV) The output signal 3; may or may not be periodic. If it is periodic, then its
fundamental period py is at most equal to the fundamental period of the input signal; that is, py 3 1),. Provide an example of a system F such that the
inequality is strict (py < p9,). (V) The output signal y cannot be periodic. l—‘il’ 2H“): Mimi) . "Ken 3%) :36?wa loe Cams: the sasl'éw is
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