ee20-06-Quiz-03-2008-05-08-SOL

ee20-06-Quiz-03-2008-05-08-SOL - EECS ZDN: Structure and...

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Unformatted text preview: EECS ZDN: Structure and Interpretation of Signals and Systems QUIZ 3 Department of Electrical Engineering and Computer Sciences 8 May 2008 UNIVERSITY OF CALIFORNIA BERKELEY LAST Name ML FIRST Name U a a Lab Time AH»? _. A I (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 pennitted. 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, corrununicatiou, 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. 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 Iegibly, 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. 0 We hope you do a fantastic job on this quiz. Basic Formulas: The CTFI' and the Frequency Response of a CT LTI System Consider a continuous- time LTI system having impulse response h. If the system has frequency re- sponse H, it is given by H(w)= / h(t)e‘é”dt, men, which is also known as the CTFT Analysis Equation. The impulse response of the system is given by Mt) = mo)de which is also known as the CTFI' Synthesis Equation. CTFI' Differentiation Property If X (m) is the CTFT of the signal Mt), then in (w) is the CTFT of the signal Parseval-Plancherel-Rayleigh Identity Let the signals :5, y : R —> C have respec- tive CTFTsX,Y : R —> (C. Then 1:3(t)y‘(t)dt = X(w) Y‘(w)dw. A CTFI' Transform Pair The signal 3: described by mm={1 Itl s T 0 elsewhere, where 0 < T, is given by X021) = 35111 (wT). Q31 (40 Points) A continuous-time signal 3:, in the shape of a "wedding cake,” is shown in the figure below, where 0 < A < B < C. X (1‘) (3) (1) -C -B -A 0+A+B+Ct (a) (15 Points) Determine a reasonably simple expression for X (to), the Fourier transform of the signal 3:. 7% TO Solvl‘q&_ 1%!!3 Ff‘oblem MI‘AI‘MmI work ['5 I?) Ftcgafll‘aq fial' X l5 flat: Sum of Timed loch funct‘ofisu XUXJ’, Anal X's 08 Show“ LE [0 w‘ ‘. ‘ X‘LH 1 x92le \ X3U'l xm : L 1. fl AYE) _— -fi H t —\3—hAEf _Q——fiABCf \kevel’one) X60} : Xian °r X16” "txglhfl :% [5m (Qh)f sin (u) \S} + sin (b) (10 Points) Determine a reasonably simple expression for +00 / |X(w)|2 dw . Your expression must be in terms of A, B, and C. [is (1 The ParggoJ-Plomclfi as l-— Roxal’a Talent SlXL”\l&&V: 3W lldflfi ell : 01W lffi'SR-r 3(5”“]'22*2(C*m-{11 Hm -90 :an/ lfi>fl+g({Q—A)TR(C-E\X :> (c) (15 Points) We apply the signal a: as an input to a differentiator: X g y dt The output signal is characterized by y(t) = :i:(t). (i) Provide a well—labeled sketch of the output values y(t), Vt. ‘ TE Afif‘I‘Vw-hlffi {5 zero everawlteoe Qxet-LF—ll— «11' file alischrIMEes. AT COUL'A oliseanfinqlgj t O’Qm'wmfiue [5 q Dirac a}; 7% area 5in to #2: AW of fig camera? 5?“): Sta c) + 3(f+5)+ Mm) 4051-1) —~$, (Hag-Shae) I) ‘3 a E C 70M. can fill-«k en's" x. m3: xfijukattq **(+ngfi,wfl_‘rfi) 1'- TEEA exile owl not. fire. lull“ Elia—86" C) E! G —-I (ii) eterrrlim): a reasonably simple expression for Y(w), the Fourier trans- form of the output y. Y( \ [WC t‘ud lg {13?} -—[—__Q_3-fl’ -tl.¢l3 *tuTC ...
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ee20-06-Quiz-03-2008-05-08-SOL - EECS ZDN: Structure and...

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