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**Unformatted text preview: **EECS ERIN: Structure and Interpretation of Signals and Systems QUIZ 1
Department of Electrical Engineering and Computer Sciences 21 September EDDIE:
UNIVERSITY OF CALIFORNIA BERKELEY LAST Name FIRST Name C0 M [3 ‘EF 1 LabTime ﬁmjjjaae I5 Lsh Ji-c_ . {5 Points] Print your name and lab time in legible, block lettering above. or This quiz should take up to it] minutes to complete. You will be given at least
20' minutes, up to a maximum of SE} minutes, to work on the quiz. 1- 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 electrordc devices {except dedicated timekeepers) must be turned off.
Noncompiiance with these or other instructions from the teaching staff—
inclurling, for example, commencing work prematurely or continuingr beyond the
announced stop time—is a serious violation of the Code of Student Conduct. e We will provide you with scratch paper. Do not use your own. a The quiz printout consists of pages numbered 1 through 6. 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 six numbered pages.
If you find a defect in your copy, notify the staff immediately. :- Please write neatly and legibly, because ifwe 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 e:~:~
plain your responses (and reasoning} succinctly. but clearly and convincingly. II We hope you do a fantastic job on this quiz. I (21.1 {EU Points] Consider a function F : 1R —> [C characterized as follows: e"W2 w E 2000a
ll.” E R1 Flu) = {ill lelslewhere {a} Determine an expression for—and sketch and label the salient features of
the graphs of—the magnitude lFIwa and angle zFﬁej of function F, where F[w}l = iFfm}l fat-4”“ is the complex polar representation of F.
.. t or “zit-3'31: a {gal lwlgqogw' J ll lelggoooii
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1 It'ﬁunll {'o] A function G : R —+ If; is related to the function F as follows:
‘e’w e 1e, G'fw} = e-‘Wr't — Fm}. Provide a clear sketch of the graphs of |G{w}| and ﬁwa], the magnitude and
phase of (3, respectively. Be sure to label the salient features of your graphs. -——- gin)»: 0F luﬂ g aooo? —~? ‘6‘?“ z ‘33 l:lE‘-ttaoll
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{A f “a 2? @651 i l “a ._ , *lgﬂﬂl-r a __‘ _ gain? Q12 [10 Points} Consider the tram—dimensional matrix function H : R“ —: R2
characterized as follows: tin E R2, 1; = H as, where in _ +cosEi —sinti as]
y; _ +siu6' +oosta‘ :52 '
“r-v-F" ‘—--w--—""-v-"
14' H a: The function H rotates the two—dimensional vector x by an angle I9. If 6' :5 II]. the
rotation is counter-clockwise; if ii a I}, the rotation is clockwise. Without using any knowledge of linear algebra, and without any complicated
mathematical manipulation, determine the inverse function H ‘1 ; explain your
thought process. Succinctiy, but clearly and convincingly, explain whether H is
one—to—one, onto, neither, or both. H PaTwT—ﬂ‘y BET $1.13”: {1-1 mw‘ﬁ—I call—N {- L “'9, Hence, FF. H45 Cos [—ﬂ} ——'i:in(-Q\ __ ‘1“{9 ﬁrm
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{21.3 {In Points} Assume to he true that: "At least one EECS student is ovenvorked”;
and "Every overworked person is tired"; and "No Journalism student is overworked."
For each independent assertion {a} and {h}, select the strongest correct characteri-
zation from among the following choices. "The assertion must be true"; “The as-
sertion could be true, but does not necessarily have to be true": or "The assertion
cannot be true.” Explain your reasoning succinctly, but clearly and convincingly. (a) At least one tired person must be an EECS student. M mil,— loﬁ Jl—i“ WE. .
‘P‘LT lEﬂiﬁ-ll— ﬁne. EEL‘S ETAlﬁvdfx‘s QUEFMF El 35:) uamgt' OWE I. Ever-g meonktaal f'er‘wr‘t is in: .
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{b} No Journalism student is tired. Ca.le lot This: ' naT nEtEE-sncgii
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