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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 ParsevalPlancherelRayleigh 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 continuoustime 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 ParggoJPlomclﬁ as l— Roxal’a Talent SlXL”\l&&V: 3W lldﬂﬁ ell : 01W lfﬁ'SRr 3(5”“]'22*2(C*m{11
Hm 90 :an/ lﬁ>ﬂ+g({Q—A)TR(CE\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‘Vwhlfﬁ {5 zero everawlteoe QxetLF—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) 40511) —~$, (HagShae)
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_3ﬂ’ tl.¢l3 *tuTC ...
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 Spring '08
 EdwardA.Lee

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