Sirindhorn International Institute of Technology Thammasat University

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1 Name ID Secion Sea No Sirindhorn Inernaional Insiue o Technoloy Thammasa Universiy Miderm Examinaion: Semeser / 07 Course Tile: ECS33 (Principles o Communicaions) Insrucor: Ass. Pro. Dr.Prapun Suksompon Dae/Time: Ocober, 07 / :00 - :00 Insrucions: This examinaion has 6 paes (includin his cover pae). Condiions o Examinaion: Closed book (No dicionary, No calculaor Calculaor (e.. FX-99) allowed) Open book Semi-Closed book ( shee(s) pae boh sides o A paper noe) This shee mus be hand-wrien. Do no modiy (,e.., add/underline/hihlih) conen on he shee inside he exam room. I should be submied wih he exam. Oher requiremens are speciied on he course web sie. (-0 p i no ollowin he requiremens.) Read hese insrucions and he quesions careully. Sudens are no allowed o be ou o he examinaion room durin examinaion. Goin o he resroom may resul in score deducion. Turn o all communicaion devices and place hem wih oher personal belonins in he area desinaed by he procors or ouside he es room. Wrie your name, suden ID, secion, and sea number clearly in he spaces provided on he op o his shee. Then, wrie your irs name and he las hree diis o your ID in he spaces provided on he op o each pae o your examinaion paper, sarin rom pae. The back o each pae will no be raded; i can be used or calculaions o problems ha do no require explanaion. The examinaion paper is no allowed o be aken ou o he examinaion room. Also, do no remove he saple. Violaion may resul in score deducion. Unless insruced oherwise, wrie down all he seps ha you have done o obain your answers. o When applyin ormula(s), sae clearly which ormula(s) you are applyin beore pluin-in numerical values. o You may no e any credi even when your inal answer is correc wihou showin how you e your answer. o Formula(s) no discussed in class can be used. However, derivaion mus also be provided. o Excepions: o Problems ha are labeled wih ENRPr (Explanaion is no required or his problem.) o o Pars ha are labeled wih ENRPa (Explanaion is no required or his par.) These problems/pars are raded solely on your answers. There is no parial credi and i is no necessary o wrie down your explanaion. Usually, spaces (boxes or cells in a able or rows o dashes) will be provided or your answers. WACSP sands or wrie your answer(s) in he correspondin space(s) provided. When no explicily saed/deined, all noaions and deiniions ollow ones iven in lecure. For example, he sinc uncion is deined by sinc(x) = (sin x)/x; ime is denoed by and requency is denoed by. The uni o is in seconds and he uni o is in Hz. Some poins are reserved or accuracy o he answers and also or reducin answers ino heir simples orms. Wach ou or roundo error. Poins marked wih * indicae challenin problems. Do no chea. Do no panic. Allocae your ime wisely. Don ore o submi your is online sel-evaluaion orm by he end o oday.

2 . (6 p) [ENRPr] Sinals x, y, and z are ploed below. Suppose y c xc c and z c xc c Find he values o he consans c, c, c3, c, c5, and c 6 : c, c, c, c, c, c ( p) [ENRPr] Consider hree sinals m, 8 r, and. The maniude plos o heir Fourier ransorms are shown below. 5 8 In he ime domain, suppose r cm c and c mcos c. 3 Find he values o he consans c, c, c 3, and c : c, c, c, c (++++ = 5 p) [ENRPr] Each par below shows he plo o a sinal and he correspondin maniude plo o is Fourier ransorm. Find he values o he consans (correspondin o he zeroes and he peaks) shown in he plos. (a) x X c - c 3 c (b) 3 c - 6 c 5 c, c, c, c, c. 3 5 Pae o 6

3 (+++ = p) [ENRPr] Consider a cosine pulse o he orm Acos 0,, p 0, oherwise. P sinc sinc. Suppose is Fourier ransorm is iven by Find he values o he consans 0,,, and A :,,, A (8 p) [ENRPr] Consider he DSB-SC modem wih no channel impairmen shown below. Messae (modulain sinal) A cos c Modulaor A cos c The Fourier ransorm o he messae is ploed below. LPF Demodulaor Le A, A, and c = 30 Hz. a. (3+ = 7 p) Plo X and V in he provided space above. b. ( p) Suppose he low-pass iler (LPF) is ideal wih requency response, 50 HLP 0, oherwise. ˆm m. Find he value o ha makes. 6. [ENRPr] (3+** = p) Evaluae he ollowin inerals: a. 3d b. 5 0 e j d c. 3 d d. 3 d Pae 3 o 6

4 7. [ENRPr] (7 p) Consider each deined below. Le G be is Fourier ransorm. Plo G rom o 6 a. ( p) 6e j b. (3 p) 6cos 6 Hz c. ( p) 6 6 d. (* p) (6 p) Consider he DSB-SC modem wih no channel impairmen shown below. Noe ha he messae isel is also ploed above., 50, Le A, A, c Hz, and HLP 0, oherwise. A cos c A cos c a. [ENRPa] (3+ p) Skech x and v rom ime 0 o ime. LPF - - b. (* p) Will ˆm m - -? Don ore o jusiy your answer. Pae o 6

5 9. (5+* = 6 p) [ENRPr] Consider he DSB-SC modem wih no channel impairmen shown below. Messae (modulain sinal) LPF A cos c A cos c Modulaor Demodulaor Le A, A, c = 07 Hz, and H For each o he ollowin m cos 56 m cos 356 cos 6666 cos 8888 cos 3 sinc 55 m m m m m LP, 777, 0, oherwise. m, ind he correspondin ˆm. ˆm 0. (0 p) [ENRPr] For each o he ollowin sinal, ind is (normalized) averae power P. Do no use any approximaion. P 30e j ( p) 30 30e 0e 30 0 ( p) j j ( p) 30cos30 30 ( p) 30 cos cos 0 0 ( p) 50cos cos cos ( p) 30 j e 30cos 30 Pae 5 o 6

6 . (6 p) Consider a sinal below. 3 3 Calculae he ollowin quaniies: a. ( p) b. (3 p) enery E c. ( p) averae power P d. (* p) G,sinc where G is he Fourier ransorm o. ( p) a. ( p) Do no ore o submi your sudy shee wih your exam. b. Reminder: i. Make sure ha you wrie your name and ID on every pae. (Read he insrucion on he cover pae.) ii. The online sel-evaluaion orm is due by he end o oday. Pae 6 o 6