Quiz%201%20Solutions - EECS ERIN Structure and...

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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 0 the 1;; if“? — he an s amt? 1: EU.“ 3? We} Aerial era gift“ 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 E‘ “all c/Ld" E l fis‘ M49571”: l“: QROQOTF seem -. "l l[ ‘ ._ H3" 05' {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 $1.13”: {1-1 mw‘fi—I call—N {- L “'9, Hence, FF. H45 Cos [—fl} ——'i:in(-Q\ __ ‘1“{9 firm J 'S-llq([email protected]'\ c0563.) u “5an 101.6 Elnflfi i“; lfifit‘fllbk iota Eqfig—FWLfi—‘EA il—E 'lV'NEF'S-E TEE-o. 3x “Wig: loa- QWJFD 3x“ flair—fig-oflfi - {21.3 {In Points} Assume to he true that: "At least one EECS student is ovenvorked”; and "Every overworked person is tired"; and "No Journalism student is overworked." For each independent assertion {a} and {h}, select the strongest correct characteri- zation from among the following choices. "The assertion must be true"; “The as- sertion could be true, but does not necessarily have to be true": or "The assertion cannot be true.” Explain your reasoning succinctly, but clearly and convincingly. (a) At least one tired person must be an EECS student. M mil,— lofi Jl—i“ WE. . ‘P‘LT lEflifi-ll— fine. EEL‘S ETAlfivdfx‘s QUEFMF El 35:) uamgt' OWE I. Ever-g meonktaal f'er‘wr‘t is in: . EEC?” fill-HAEs-Cll— it. Tiff: iii“: PVT Ema—isn't. TWEJ fEf‘i‘i‘“ i“: =~~fx EEC-'3 shale. * + {b} No Journalism student is tired. Ca.le lot This: ' naT nEtEE-sncgii Lil-l:— Ow é “- f’er‘ififi is gamer mil “H T" Q R Ear-5°.“ c H TEFEI '. OH 13515 .5.— ‘g M» rcxfi‘fi its Etta ain‘t-“u H I .. _ :5 juicy, R f a = a ==~$ “10W in“. TEE-st: Twas fnfi'mthfijj Gui ail-“5T” shack Trait; fiOVxl , “‘6 internal“ st:\~>\fl. and, a—gwrnplxlwu—x. i3 'i‘ll'N will. For :Rafipllfl, at. ‘E-aft :‘Hi-A. ‘5 will Jl—F ma LE. 119%; ‘1',“ 0‘ rE'f-ifiofi , {31' fig“ listing sufirvfiaflfii ;%/-5qa from l’luwgfir". ...
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