# MT3SOL - ECE 301 Midterm#3 6:30—7:30pm Thursday LYNN 1136...

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Unformatted text preview: ECE 301, Midterm #3 6:30—7:30pm Thursday, April 15, 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 16 pages in the exam booklet. Use the back of each page for rough work. . Neither calculators nor help sheets are allowed. Name: (go/“*M‘“ Student ID: E—mail: Signature: Question I: [30%, Work-out question] Consider a continuous time signal \$(t): \$(t):L{(t—7r)—Ll(t+7r). (1) 1. [10%, Outcomes 1, 5] Find the expression and plot the FT X (jw) of :I;(t) for the range of ~3 < w < 3. Carefully mark the height of the main lobe and the points when X ( jw) = 0. Hint: Use the table. 2. [10%, Outcomes 3, 4] Deﬁne h(t) = 26(t — 77) + 35(75 + 7r). Let y(t) = >x< h(t). Plot y(t) for the range of —37T < t < 371". 3. [10%, Outcome 5] Find the FT H (jw) of h(t). Hint: No need to simplify it to sin or cos functions. 47‘ 2;} (/77 7(er 5 {I _. m): ’ M ’ <2) 7 I“ c 0 Mn, U V brush”) ._ -2”, X00) ‘ l 2. AN) : Za'llc—n’) +3a7tnr) m): XMH’LQ} 3 lx/é'v) + 3 Mfﬂf) ﬁt ) Question 2: [35%, Work—out question, Outcome 4] Consider a discrete time signal and its Fourier transform X (63"). Suppose we know that within the range of —7r < w < 7r, X (67") can be described as follows. w+7r/2 if—%<w<0 X(ej‘*’)= —w+7r/2 if0<u1<32I . (2) O if—7r<w<—§orif§<w<7r The following questions are best done in sequence. However, you can also do them separately if you do not know the answers to some of the questions. 1. 5%, Outcome 5] Plot X023“) for the range —27r < w < 27r. 2. 5%, Outcome 5] Deﬁne Y(ej“’) = %X(ej“’). Plot Y(ej“’) for the range —27r < w < 27r. 3. 10%, Outcomes 4, 5] Find the expression of Hint 1: First consider a rectan- gular wave form in frequency. Hint 2: It can then be solved by DTFT properties. 4. 9%], Outcome 4 Find the value of This problem can still be solved even if you do not know the answer to sub-questions 2 and 3. 5. 6%], Outcome 4 Find the expression of for n 74 0. This problem can still be solved even if you do not know the answer to sub—questions 2 and 3. £055") 1. V) .1 ’ I: z I In WI!) “:3! .L E a 2%»— ‘/ Al vw u/ f j?” . , —' "— + Wei") = ewe”) ; WW) ca weed ‘e’ﬁ'zw )6) 3‘)qu 377,, 571(gn) : 4J&25;h7{\$n/ 17“ qr“ Question 5’: [20%, Work—out question] Consider a discrete time LTI system. We know that when the input is the output is y[n] = 30M * hm] = 8 (gram — 5 (gnaw. 1. [10%, Outcomes 2, 4, 5] Find out the impulse response Mn] of this system. 2. [10%, Outcomes 2, 4, 5] When a new input w[n] = cos(n) is used, ﬁnd the new output z[n] = w[n] >I< If you do not know the answer to the previous sub— question, you can assume Mn] 2 Ll[n + 4] — Ll[n — 5]. You will still get full credit if your answer is right. . i J1, _ -u v #5:“. 1.xo~)=~—*,-ic—i~ c 2‘ we» v” , 5- -‘u Wed)“ N ~g—e—J0/{l'i’CJJ We”) : F3161)“ : Y- 75v” '5, ; £765" ‘5' NJ" lege‘d‘“ /- 615v“ z 4—— .o) A (-1) ~ => mm m = % HM Mme" h“ p 3 ~ I 3 -‘n : ‘ _. J" + ‘- J “\$06 21"}6‘) e .- ‘ q , -i[ 4"}!6 a" + (“TCJ,__ v7] 1 H 3%,— ~§mm c Mfg. ‘ngw e’ Question 4: [15%. No need to write down any explanation] Consider the following AM—DSB system: *Qfgt‘stwcx't) {X l3" 3x605 (Wed) 4 ; “2W [LPF 'w, cit—OW” Lowdown“, WWW M) my Cairo WWMWMV We know that the input 110(75) has bandwidth 9ch2 (or equivalently 9k - 27r radian per second), i.e., X (jw) == 0 for all |wl > 27r - 9000. If you like, you can also assume that X ( jaw) is described as follows. , \ X(§LG) ’ i [L ./ “£09690 mam w Suppose the FCC requires that this radio transmission can only use the frequency band between 2.4MHZ to 2.43MHZ and must not use any bandwidth outside the given 2.4—2.43MHZ range. Answer the following questions. 1. [5%, Outcomes 3, 4, 5] What is the allowable range of the carrier frequency we? 2. [5%, Outcomes 3, 4, 5] Suppose we use we =2.41MHZ. What is the allowable range of the cutoff frequency W of the low—pass ﬁlter at the receiver, assuming that is the only signal being transmitted in the air? 3. [5%, Outcomes 3, 4, 5] If we listen to the output signal 56(5), is the volume of the sound going to be louder, the same, 01‘ weaker when compared to listening to the original signal 1 we ~,, Awe/Jam! “to JEN/{e (am Mm) . A 664.22,:{Mt/e7" ‘7/</-(2r = 2.706144% 2.709/W/254/ {2 “NM [435 2,7}«4/3/4? " 7k/‘(2 =2.‘/L/l{/IHi’ Tia I g? 7" U3 7k”; 0/ 77‘ v7” (“7‘ am‘ 56% at \$1! {EJN/ z V5423” ’“l/‘ 7W2 = 9.86% “1.047 MH; : 1/. {NM/7’2 a 1ng 7.81M“ om/ ...
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