{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

228_f06_mid_sol

# 228_f06_mid_sol - SOLUTION ELECTRICAL ENGINEERING...

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

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

View Full Document

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

View Full Document
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

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern