{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

228_f06_mid_sol

228_f06_mid_sol - SOLUTION ELECTRICAL ENGINEERING...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: SOLUTION ELECTRICAL ENGINEERING DEPARTNIENT CAL POLY, SLO EE 228: Continuous-Time Signals and Systems Winter 2006 John Saghri Midterm Examination Monday October 30, 2006 This is a closed~book and closed-notes 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, time-invariant, 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 Fang gxefia_ineul (meek: VESPOTVSELkofi) , . \no K) + 1 ‘ADGU : K (it) fie: Choracllflt'glfi‘c efimjlion 8+2. :0 YOOJY 943—2. “file—WNW) milk Nob-I 421: —7_(@() “0&3: \461 (Mt) ——2>lr\0(0)=\ r—é lzke Fe: \<=l I -1E Molt)“ affine) remit}: -25 we +gm Sis/ma eyelet/m in \inear __5 MK‘QJAIOK’QJr’ShOk) -‘L .. "i: we) :- [:2 e7" o(t)+ sttflgazuw t -=- azuith— £3 CC) _ JE €12 um + ER) Answer: h(t) = i a ,, , 5' WWW...“ i’ For Section /\ OHKZ Fmok. V3" (WP-J56 {6’s (ban—96 4QV/ yak) +Lxr Ht) -\— 3761): x Ga Wax myrwm M0) =7 _ 7’10) Chalmgtefish'c EflUa {Gm-2. _.3_t _ : \HQC) 1'7 CC): {K e. t+kle 3 meg) \/(0)~:0 €>kvyk2fi=9 N \ 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):“ :fwquXWCt-kfilk F6” )\ OH ?\"" — 1—2-6 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 (Jr-H) -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 , 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. § Pen-och”: 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 , . . -.5. I - I I I | I’ .l I I I i I I “ I 'l I I I 9 | 5 I -l I l I it I i '_ :I I '1 a -. V I k ..... J; _______ L ——————— 4 ________ + _______ e ____;1- I I l 1 , 1 t I I 3 I l I I t l I i l I I a I I g ' is I I I I : I I a a i I I I 0 5 I ________ ' __________ I ....... , ........ ,_ _______ 1 _______ 1 ........ j ........ ._ t ‘ l l ' I a I I I I’ I I I I I x I I I I ' I I I g , | I 3 I . I I g g I I I i I ~ . y’mx . - A . x .......................... r _____________ T ....... 1. ______ ,._ I H ‘ I I 1" I “i I ' I ‘ J IE (”I I ' : ‘K' E } I I a I I I I v I I ’ I . i I 1| as r I I \g 1 | 0 ...... 1 _______ i ________ r ————————————————————— r_——-HL_T ........ r _______ r -4- . I I I E 1 I i X I I I r I i ‘ i I I I It i F F I I I . 3 ,i '1; J ~. .3 _ I 3" I I 1‘ i ‘ ............... \— —__—H' _ -__-___ __-w..-.. .. ‘_ ____|. -___-_1_-------r_____tz. __-__--_5__ I x i s. W I I “ i I' I I 2 z I I S I I I: I t I I Is _____________________________________________ W’an‘mw'mnmmu _______fi-- l I l J I I l I I I i F -I-_.___-- I I I I l l I I —l I l I I 4 i l "I I I I I I >5 I I I I I l I -_-_-.---.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 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern