{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

08FMT2SOL - ECE 301 Midterm#2 8—9pm Thursday October 9...

Info icon This preview shows pages 1–8. 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

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

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 301, Midterm #2 8—9pm Thursday, October 9, 2008, PHYS 114, . Enter your name, student ID number, e—mail address, and signature in the space provided on this page, NOW! . This is a closed book exam. . This exam contains multiple choice questions and work—out questions. For multiple choice questions, there is no need to justify your answers. You have one hour to complete it. The students are suggested not spending too much time on a single question, and working on those that you know how to solve. . There are 10 pages in the exam booklet. Use the back of each page for rough work. The last page contains the formula for Fourier series. You may tear the last page for easier reference. Do not use your own formula sheet or any kind. Using your own formula sheet will be considered as cheating. . Neither calculators nor help sheets are allowed. Name: 50 (‘4 M7“ Student ID: E—mail: Signature: Discrete—time Fourier series mm] = Z akejk(27r/N)n k=(N) ak : _ Z m[n]e—jk(27r/N)n n=(N) Continuous—time Fourier series Discrete—time Fourier transform 1 . x[n] = g 2 X(jw)ej‘”"dw X039“) = Z x[n]e‘jw” Continuous—time Laplace transform 1 0° ‘ 33(75) = 2—6“/ X(0 + jw)ej°"tdw 7T —00 X(s) = /00 $(t)e_8tdt —OO (10) Question I: [24%] 1. [4%] What does the acronym “LTI system” stand for? 2. [6%] Let :1:[n] and y]n] denote the input and output of a discrete LTI system that has an impulse response Mn] Consider the following two equations: $[n] = Z $[k]6[n — k] (1) yln] = Z mlklhln—kl- (2) From the perspective of coefficients, test signals, the output of test signals, the weighted sum of signals, and the LTI system, answer the following questions. What is the role of 6[n — k]? What is the role of Mn — k]? What is the role of :c[k:]? Consider a continuous—time LTI system as follows. ’I’l yln] = Z We». <3) kz—oo 3. [14%] Find out the impulse response h[n] of this system and plot h[n] for the range 72 = —2 to 2. (l [4454, 1L;Me ' I'm Vdrldnf- 2. 55¢] a,“ ,LAe +8“; {Dru/yr +5 xézheJ Je/fcr, at «4,; ”J“ (a; +4: Myth! I‘M/om/xe I’L'Jflovse 4 AlZij ‘l'5 +46 vhf/“f: (-4! [He r‘ck’nb a! {(c 7LCI¥ 1‘an 0: (5)” "20 3. 1.4"] 3 Z [[lz] 2/ :f “<0 [<3'00 0 t e)” me] x [k] we Question 2: [28%] Consider a continuous—time LTI system S described by the following impulse response Mt): W) = 2"(W) — um — 2)). <4) 1. [4%] Is the system S memoryless? Is the system S causal? 2. [4%] Plot Mt) for the range 15 : —2 to 5. 3. [16%] Given the input being 56(t) : 2tU(—~t), find out the output y(t). Plot y(t). 4. [4%] A system is called “a t0~delay system” if any input 55(15) generates a delayed output y(t) = $(t * to). Find out the impulse response of the following serially concatenated system (input being x05) and output being z(t)). At) ——(-)———4 tO—delay s I. 157’ [£41 memdr/y 5' ;n(e if hQIA 'k/é) 716/ (6’ 2’ fi/ [5/ 1‘; Cflwfa/ ‘7‘“! 7/ ”3?”li W9 pv’Jf'L /rgjc.,~f i/d/MJ avian/fl 1_ Alt} 1/ 1a 3. ma) ~ HUM» cum—2U ) Me) = fun) (he-2’) MM) Y 1 PM 2' £1 t 1155’». I t“? t“ f“) 30 16+! 6—(0 fl“: zt(l-t/ 056(L o tel 4/. {/0 .4] a Jo A, flats: 4/15) X/f/c [/f' (’a/ m; : zt‘WmMJ - WH’Q-d/ y/E’ 3t :1. Question 3: [28%] 1. [4%] Suppose y(t) = ZZ:_OO 6(t —— 2k). What is the period of y(t)? Plot y(t) where t ranges from —2 to 6. 2. [4%] Suppose 33(75) is periodic with period 4 and 90(75): 1 t/3 ifOut<3 (5) t—3 1f3§t<4 Suppose we also know that 2(t) = m(t) + y(t). Plot 2(t) where t ranges from —2 to 6. 3. [20%] Find out the Fourier series of z(t). ya-” : z J/e-z—zk) = EJH-(LM/ Lei Z=kH = iJfié’Z/ d 7":2 NH 3 )E '1 "r I L 3 ‘f I [ 2(a) 1 4/; L 6 ”2 'l ’ 2 3 ‘1’ f 6 -D’ r + :07]: (f 3}e ”“15 /(6 J .J‘ée =J( ”3‘77ch * y/ZH Jt+7/ (6“3/e J6 J 5% ) - ’3 V" C u=l'}‘ 6”" 6%“.va U 6 l) CU oer—Hg = .gl': €31.” c/Vr‘” “" 3976 a? °<l<' [x J. —7 4’ ‘f if; 4’ El“; ““1? V) 0“). Cam/3 7’ avg”) -—i~ 0 E (H m“) f {£375 _ 1;. (Jim: mm + Q“ 3 (W/c'fik “ 9[J}7:~3J'L /) +1 (%’£/‘(€V%Vé ’/ q - + ['Elc'flr‘ _/ (ft)! +3 + / - c Question 4: [ 20%] 1. [8%] Find out the Fourier series of $(t) = 008(8t) + sin(4t). For the remaining questions, just write down your answers. No need to write down the justification. Consider the following systems: System 1: y(t) = { 1 System 2: y[n] = Z 2%[71 ~ Ir] kz—l 1. [4%] For Systems 1 and 2, determine whether the systems are causal. 2. [4%] For Systems 1 and 2, determine whether the systems are linear. 3. [4%] For Systems 1 and 2, determine whether the systems are time-invariant. - 21-”: 2' 1 xii): “MS/6] +:n{‘(6) T« y 2 I J ‘ ~76 4' a are a :; o<_ = «2, il{eJ“+CJ / *2; (ed ~c / 3) I J 1' d .U 1% ’- j‘f'kt a” : “-1 I 2 :Zo/ked m ;Zo(k€ kw”? 1 5/4““... 1 1‘: CCVMJOI( :)n(e if are; 049, [him-f W/WJ a} X’é/ 7w Cam/”ff )/(é/. ‘ H regain; x[nf1] («4’41 #0 catalog/e /V["] {far {can 2, 7,: AM '(W'I 0/ d ,L” Me) 2 0‘ 2 Z . §){+fm I [5 nm ' (mew {Adm /[é) : (x/fl/ ‘ 1‘5 (4‘46“,- r/vffca. 2 I - (”J L ,c ‘x[..]:ol,’x,(q_] fame I . k [(3% c M») = i 2’79: was; or, may) ': «WE/235"] + daml m J k=—r ; d, x5") ‘l‘xafifl‘J ' “I ' Pane «int/flow! 3‘ 5”” l‘ I d Mir-edge J I. ~ {61%) = 2"?“6") 1 Me) “4/0 e ”I / [vadévéd VFW“ 9764/ 24“,) __) «1/64,; Met/2a “WM acre—e) kff’éd) <0 s {can 2 7; HM: “ht/«Ia; I I i)" / _ < a-“ .15 RA] “"5 [V51 Jc/v, [vfl—nd] : kl- Z 3:[ 4 J Mn : Zkkuhenv'kj WM! X]; , ha] .4 2:4 ...
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