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Unformatted text preview: SOLUTION ELECTRICAL ENGINEERING DEPARTNIENT
CAL POLY, SLO EE 228: ContinuousTime Signals and Systems Winter 2006
John Saghri Midterm Examination Monday October 30, 2006 This is a closed~book and closednotes exam
You are allowed to use your calculator and two pages (one sheet) of notes The exam includes 3 problems on 4 pages (including this cover sheet). Make sure you have
all the problems Good Luck! Problem 1 (15 points) Consider the system y(t) = 2 x(ont) where on is a constant. Based on the value of 0: as shown in the table
below, indicate whether the system is linear, timeinvariant, causal, dynamic, or instantaneous. Fill in each cell below with “yes” or “no” ES 3
0
‘83 Problem 2 (30 points)
Find the impulse response h(t) the "system described by the differential equation y’(t)+2y(t)=x’(t)+3x(t), with X(t)ﬁ6u(t) and y(0)=7
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n 2S\K\:_:4’—d,TkZ—Fh‘ .MMWWWWMm—mmmgww; Problem 3 (35points)
Part a (IOpoints) Analytically obtain the ﬁinctions y1(t) and y2(t) deﬁned below. Note that u(t), r(t), and “:k” represent, a
unit step function, a ramp function, and the convolution operator, reSpectively. Note m) = tum. y1(t) = 116) * HG) ' Answer: y1(t) =
Yzﬁ) = I“) * 11(t) (5pofnts) :j:y{,\wtt_ 4):“ :fwquXWCtkﬁlk F6” )\ OH ?\"" — 1—26 Ukt) Answer: y2(t) 2w Part b (15pointg (5p0ints) Using the result obtained in part a, analytically obtain the convolution of the two functions showu below. Hint: represent 1‘; ( t) in terms of ramp and unit stepﬂmctz'ons! fl(t) f2(t) W3 = rec—ii) ~1MU—WUV‘)
ECU ?‘ all) =' [r (JrH) 1nttlmrlt—\)_]ﬁ~ U ("E e n mien) «1 Mt) 4— UH Latte)
t:+\)1u\L’C 4d) ’2. VCE)_ Answer: f l(t) =1: f 2—(t) — 2 k
Part c (10points) f1“) * f2“)
Sketch f l(t) =1: f 2(t) obtained
in part b. ‘ we» LI 3
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I Problem ; (20 points)
A periodic signal XPCL') consists of the two sinusoids shown on the grid below. Part a (3 points) _2 I I
Obtain the fundamental frequency f0 0f XPU). Note that the time axis shown is in milliseconds. §
Penoch”: I ms 404?: ‘ ‘000 H; m1 “z Part I) (Spoinfs) I K I O :.: \ \< H "L I Express X P02) in polar Fourier series representation. Hint: answer should be in terms of cosine and dc terms only. XPCU: SW‘IIZRﬁI t) +—— BSIA (Z mggt) whet? ( : mm Hg,
XI “0 = “Swot€— J ~« . was) Answer: x (t) =
Part C (7190mm) P E
E
I
I Plot xP(t) on the same grid shown below 1.0 , . .
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__..I4.I»I“I Time ms 0 0.2 0.4 0.6 0.8 1.0 1.2
Part {I (5 points)
Plot the magnitude and phase spectra of xp(t) Amplitude ...
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 Fall '08
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