mt1sol - EECS 20N: Structure and Interpretation of Signals...

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Unformatted text preview: EECS 20N: Structure and Interpretation of Signals and Systems MIDTERl-Vi 1 Department of Electrical Engineering and Computer Sciences 26 September 2006 UNIVERSITY OF CALIFORNIA BERKELEY U ' — -- F ._ «- LAST Name iii/"15V LKC for FIRST Name awry?) it, XI ,: t 5/ Lab Time “faith/spat \J o (10 Points) Print your name and lab time in legible, block lettering above AND on the last page where the grading table appears. a This exam should take up to 70 minutes to complete. You will be given at least 70 minutes, up to a maximum of 80 minutes, to work on the exam. 0 This exam 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 electronic form at any time during the exam, except one double-sided 8.5“ x 11'“ sheets of handwritten notes having no appendage. Computing, communication, and other electronic devices (except dedicated timekeepers) must be turned off. Noncompliance with these or other instructions from the teaching staff—- inciading, for example, commencing work prematurer or continuing beyond the announced stop time is a Serious violation of the Code of Student Conduct. Scratch paper will be provided to you; ask for more if you run out. You may not use your own scratch paper. - The exam printout consists of pages numbered 1 through 8. When you are prompted by the teaching staff to begin w0rk, verify that your copy of the exam is free of printing anomalies and contains all of the eight numbered pages. If you find a defect in your copy, notify the staff immediately. 0 Please write neatly and legibly, because {fare 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 exam. 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. 0 We hope you do afantastic job on this exam. You may use this page for scratch work only. Without exception, subject matter On this page will not be graded. MTIJ. (25 Points) Consider a function f defined as follows: f : R —> C v: e 1e} 1%) = (—1)“. Each of the following parts can be solved independently of the other. (a) Determine an expression for, and provide a clear sketch of the graphs of, [ f(t)| and A f (t), the magnitude and angle, respectively, of function f, where fit) 2 | f(t)| 831;“). Be sure to label all the salient features of your graphs. qt— ”‘htt’n— '*-——"'7 (-‘lnfl = [QTY-m = {WM “=3: Ht) ATM '. ‘ i -..-. e v 0 '12:; _‘ o I 1. 4H”: 0 firm-#0 e’c \ t "W at Tlt’l + “L a“ e ~‘-—e film i“ re" tam > o ~==> T \H+\\= tm , act—(Jr)- o W . -2191 —\ o I 1' 03) Let fe and f0 denote the even and odd components of f, respectively, where, WEIR, magnum), fe(r)=—f‘”+2f‘“”. and fo(:)=——-—f(“'2f"”. Determine fe and f0. You may do this by showing how each of the compo— nents is related to f, or providing the graph of each component fa and f0. Moth fiat {LA-Am, .ue made tad fist-t (fl, VF WA fifl') : 0 MT1.2 (30 Points) You can tackle the two parts of this problem independently. Explain your responses succinctly, but clearly and convincingly. (a) Albert attends the concert only if Sally attends the concert. If Blake attends Le‘l' H: “1 kanlt: TE seem-l masta'hq 3': eTwlth-‘l' To the concert, then Sally does not attend the concert. \ Albert is attending the concert. Is Blake attending the concert? . mfi'finiS 5'. din-ls (b) Determine whether the following argument is valid. La” W PC D '— ‘fiEICIS news cal—economic; A‘QFFVCESWW l 0 Monday, 2 October 2006: If there is no news today of a looming economic depression, nor any revelation of a political scandal in the executive branch, the prime minister will complete the remaining portion of her term in office, and the parliament will pass her educatiOn overhaul bill into law at the end of this week. Tuesday, 3 October 2006: The prime minister announced her resig- nation at 8am today. Therefore, her education overhaul bill will never be passed by the parliament. a S; lhmli (icicle/lien o n " 5 fluvial poll" (“Q C 3 fit. N}. Cairn.fo Q, Luz-4" ‘l’epm in a-FPI‘CQ fa“ Tfi'c 9W5 fill-ACCCEOA E 3 The _ Fairlie-«newt will urgekr s (and . at. be A as} is -. if:ka Pt :3 S (Pills: r'l' A‘l’fiz «is ml 2'9 3"“ “’{EVA‘\ ~ ‘I % —.=-$ -—13 C55" Ahqén'flc“. 49:3» “Ii—Rf”) Say—16. Charla, 1:) -—:[S dials MT1.3 (25 Points) Consider a function G defined as follows: ‘V’uJElRE G(w)= Iw, where can has a fixed positive real value. Determine an expression for, and provide a clear sketch of the graphs of, the mag- nitude [G(w)| and angle éGfiu) of function G, where G(w) = |G(w)| e‘ml‘”). For what value(s) of w does the function |G(w)[ attain a maximum? What is the value of ]G(wfl)|? What are the values of AGO») for w = —wo, 0, +wo? Determine the limits: lim law. lim raw, ljm. Law, and firm may). w—~—oc w—v-i-oo w—>—oo w-—~+oo You may express your answers to these questions by placing appropriate labels on your sketches. lei: “ : ‘ agate-)1Mxl-a10ua MT1.4 (25 Points) Consider the discrete-lime signal f : Z —> IR, characterized as follows: 1 m = 0, 1, 2 0 elsewhere. VmE Z, f(m) ={ You can tackle the two parts of this problem independently. (a) A related signal p : Z —+ R results from modulating f , as follows: Vm e z, p(m) = % [1+(—1)m] f(m). Provide a well-labeled sketch of the signal p. (b) A related signal q : Z ——) R results from the convolution of the signal f with itself; this is written as q = f a: f, or g(n) = (f =x f)(n),Vn E Z. In particular, the signal q satisfies the following convolution sum: vn e 2, gen) = Z f(m)f(n — m). m=—oo Provide a well-labeled sketch of graphm). (This would be a stem plot, that is, a “lollypop” plot.) Hint: Discrete-time convolution is generally simpler than continuous-time convolution. Start by sketching the signal f as a function of m. Also, plot the "time-reversed and shifted” version of f (i.e., f (n - m)) as a function of m, for ,gr Marque, fit) a /lml of #06 Smmmwfig’k A’WC‘ £95531 (Lianme T3 emcean 7%” fit: in: Halo swim T fix» my 1mm)» was 00) FIJP Ml Skill m Kalg_ _._____ j- (i}.[ 'I A} K a El I MA "A "l 0 (n N—Jljgéflfl g __,_l l I {ll-A) K3) (:0] l: in Tl“) , ! II 9” Ham) \ULJL “L! > ' $.23 > 7 (“13% —-—____._.._,______‘_ {(n—nfl slots va OWFLK “/ 1%“) {hr (IQ 0 «ml “7%. lj+wi5t d’u‘ujt 1% +01 T ' e a:a.AQ M ‘m («3. LAST Name FIRST Name _C0'“;2 I“ 099"! Lab'fime M; a" [1 |m ...
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This note was uploaded on 04/02/2008 for the course EE 20N taught by Professor Ayazifar during the Fall '08 term at University of California, Berkeley.

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mt1sol - EECS 20N: Structure and Interpretation of Signals...

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