# MT1SOL - ECE 301 Midterm#1 6:30—7:30pm Thursday LYNN 1136...

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Unformatted text preview: ECE 301, Midterm #1 6:30—7:30pm Thursday, January 28, 2010, LYNN 1136, . 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. . Neither calculators nor help sheets are allowed. Name; SI, {on/7V4} Student ID: E—mail: Signature: Question 1: [15%, Work—out question] Consider a continuous—time harmonically related signal: “(13) = amt. (1) Let g(t) = Ev(:t2(t)) denote the even part of 33205). 1. [6%] Is g(t) periodic? If so, What is the fundamental period? 2. [9%] Compute the average power of g(t) between 0 and 271'. 76,61?) ‘1‘ 752.611) 2 Q 36(7)“ .‘b-L -761, 2r” ~+€ 1 H :: 405 (612) Question 2: [10%, Work—out question] Consider a discrete—time signal f [n] such that f (t) = 6"t‘21- (2) Find out the expression of I [0 f(t)e-jwtdt. (3) k v: ‘t+2)€ "Wt DO ~+2._,' (W) fpo 6 J 01‘6'1‘ QtQJWtdi , wt W enlwt _€2£: €0j)0(t+QZL e 3 0k a— iWZ -2. 0-1-41») 2 == 9‘1 e . 4- Q Q t (ij l+gw «‘zéw «zjw :r' Maw” + Q « [—- gw H 2"“ 7:: "74W 2 € W & Question 3: [10%, Work-out question] Find out the real values of a, b, c, d, e, and f such that they satisﬁes a + c + e _____i_____ (4) b+jw (dﬂw)2 f+jw_(1+jw>2<2+jw)' Question 4: [30%, Work—out question] Consider two signals: One is a discrete time signal 1 if 0 g n S 1 93W = ~ . , (5) 0 othe1w1se and the other is a continuous time signal t+ 1 if —1 g t < 1 h(t)= 1—75 if0§t<1 . (6) 0 otherwise We can then construct a new signal: W) = Z W — @ch <7) kz—oo 1. [12%, Outcome 4] Plot h(t) for the range t = —2 to 3. Let 2(t) = 1 — h(1 — 2t). Plot 2(t) for the range 75 = —2 to 3. 2. [5%, Outcome 1] Is y(t) a continuous time or a discrete time signal. 3. [8%, Outcomes 3 and 6] Plot y(t) for the range if = —2 to 3. 4. [5%, Outcome 1] We note that this “system” takes input :1:[n] and generates output y(t). Show that this system is a linear system. 1 hi“ 2M (AL i ) t t ,1 -’/ [ 2— 3 ,1 -/ i" I 1 3 Z, Crnﬂnhaui - Hrme Jule—k) :-—;L>c[vzl[\/f+z) k ?r[r/J1,(H// ye WEJLH/ + 2r;7]4/€-1/+ W W :0 >0 ”We will :0 z ' aft 1/10 % = M) + Lle'l) [HI z 0( 34/644 ml} + 424leka ; o</,/é/ 1L ﬂ/L/e/ :) medﬁg/ Question 5: [15%, Work—out question] Consider the following two discrete—time signals e‘1t if0<t t = _ 8 ﬂ ) {0 otherwise ( ) —1 if t < 2 t = _ . 9 g( ) {0 otherwise ( ) Deﬁne W) = / f(8)9(t—8)d8- <10) 1. [15%, Outcome 3] Plot h(t) for the range t = —3 to 3. 75(5) A“) i 5’ <, )5 53¢“ ﬂt") -( W _( f—SS 7. “Z t< 2 Law I b’zéd/ ‘00 S ~S/N_ _1 AN):/ e ("HI ' e 0 0 b-L 5 0 {7’1 >0 {3 372 46%) Ldfé H ” w -5 / - 4/00 3’6 r/€}:£[email protected][’(c/I'6 (7-1 /// J '6"). .6 <2 Question 6: [20%, Multiple Choices] Consider the following continuous—time signals: 271(t) = cos(t) sin(t) \$205) 2 sin(cos(t)) and discrete—time signals: 8 x3[n] : sin (—3171 + 1) x4[n] : ejm. 1. [10%, Outcome 1] For 161(t) to x4[n], determine whether it is periodic or not. If it is periodic, write down the fundamental period. 2. [10%, Outcome 1] For \$105) to \$471], determine whether it is even or odd or neither of them. Hint: sin(o; + B) = sin(a) cos(ﬁ) + cos(a) sin(ﬂ). (I Y] fa’ (VJ/‘4 I Prér/‘IJ W XL 3 (1 9/11! {I}, / per/(J I.” S 3 7f lag/[10,16 fﬂrflJ LCM (7/! /) " 3 ' I r (4/! : 2 X7: [NH/Jig Per/4] L (1, U 2 X, ‘ 0 11 7Q 3 even y, ,‘ rid/+49" 767: even ...
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