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sysc3501test1w09

# sysc3501test1w09 - SYSC350l Communication Theory Page I of9...

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Unformatted text preview: SYSC350l Communication Theory Page I of9 Test # 1 SYSC3501 Communication Theory Winter 2009 1.5 hours )EAdrian Chan III Andrew Marble (check one) 1. Put your name and student ID at the top of every page of this test. 2. You may use a non-programmable calculator. 3. You are permitted a one-side crib sheet (8.5" x 11”). Total number of pages Q1a Q1b Q1c Q2a Q2b Q2c Q2d Q3a Q3b Q3c Q3d Total (30) (40) (30) (25) (25) (25) (25) (25) (25) (25) (25) (300) Carleton UNIVERSITY Wim‘er 2009 SYSC35OI Communication Theory Page 2 of 9 Question #1 (100 marks) The function X(t) con be expressed mothemotioolly as the sum of two rect() functions, x(t) = TEE-1(g) +rectﬁf — D5) Part 1a (30 marks) Write the mothemotiool expression for X(f), the Fourier Transform of X(t). Winter 2009 SYSC35OI Communication Theory Page 3 of 9 Part 1b (40 marks) The function y(t) is d periodic extension of x(t). As periodic function we con express y(t) ds (:1 Fourier Series y(t) = Egmcﬂgrmrar, where fo is the funddmentdl frequency of y(t). )0"; tht is the volue of fo? Find (:1 mothemdticol expression for On. “Po ti": ’1 ’XC'K’) »’\$ OM. {DA—4p dﬂ % / CMWFZt‘ m7 CM; Q XKnrQ) éo Jar; murmurs/74m Part 1c (30 marks) tht is the power of y(t) of 0.5 Hz? 1C“); g #1» fDW MW FS'DADL‘FM7UM/47 (14: Mg Mir“ , Afr 65”? Mr ELM’MW W ”05’ - (1 WA ._ \$5; A 2 A, ‘0 \ [/4 J”- ; ‘2; 'JTZ/‘F L FQOS H%= (c_2)" .i— Icsf" r— 2 (ca)? =2+€7WCL)*5W(¥)& 1: LI i5m¢U3+\$MC(—é)¢_jﬂjll W0): gab — Z “7‘72 L L. .1 .‘_ ‘- L Fa 7‘ 2 Z (El-f .: 2:13. 5*“ij ﬂ —-.:-. 2. 7? W9 Winter 2009 / SYSC350l Communication Theory Page 4 of 9 Question 2 (100 marks) The function m(t) is modulated using amplitude modulation. The time domain waveform m(t) and frequency domain spectrum M(f) are shown below. Part 2a (25 marks) n(t) ”mm SAMDSBcU) k“ ] c(t)=Accos(2nfct) AMDSBC modulation is shown in the system diagram above. Sketch the signal n(t) = kom(t) + i (assume kg = l/4). Winter 2009 SYSC350l Communication Theory Page 5 of 9 Part 2b (25 marks) Sketch AMQ‘SBgsigndl sAMDsch), assuming 0 corrier of c(t) = 2cos(200nt). Elva MUSE/M (S SWZ’DSEC [H Part 2c (25 marks) - ~—3. { Assume the receiver is on envelope detector with d gdin of l (i.e. the dmplitude of the envelope is unchdnged). Sketch the output of the envelope detector eAMDsch) dssuming the received signdl is SAMDsch). Part 2d (25 marks) Sketch the EAMDSBC(f) the Fourier Trdnsform of the envelope eAMDsch). Winter 2009 SYSC35OT CommunicoTion Theory Page 6 of 9 Question 3 (100 marks) Shown below is (:1 Type of ompliTUde moduloTor oolled o Weover moduloTorl. We hove noT covered This moduloTor in oloss. The poinT of This quesTion is To use your knowledge of AM To show how The Weover moduloTor works. Part 3a (25 marks) The Fourier Transform of The messoge signol m(l) hos o speoTrum wiTh o widTh of 2W Hz as shown below. As shown in The block diogrom, m(l) is moduloTed by The complex ij27f(%wl exponenTiols e /’ .SkeToh Mc(f) onol Ms(f), The speoTro of The moduloTed signols mc(l) 0nd ms(l). (,P) A Mm ML _ M L a) M (0) \ (F -bioyni ”L. 2.? l D. K. Weover, Proc. IRE, Dec. 1957 WinTer 2009 SYSC35OT CommunicoTion Theory Page 7 of 9 Part 3b (25 marks) The moduloTed signols nexT poss Through ideol low pass filTers (LPF in The diagram). The filTer response is shown in The figure below. lT hos o ouToff of W/2 Hz. SkeToh Nc(f) onol Ns(f) , The specTro of The filTered signol. A|H(f)| MC. (JP) MLi) 1 l _K K f _w 0 w "I; 2 2 ‘2‘, 2 “5(9) / Mic) L2 0 LJ Mp .— L L Part 3c (25 marks) The filTered signols ore moduloTed ogoin, wiTh complex exponenTiols oT The carrier frequency fc, ie. eiﬂ’ﬂ’. SkeToh Sc(f) onol Ss(f), The specTro of The moduloTed signal. 34 CT) mo) WinTer 2009 SYSC35OT CommunicoTion Theory Page 8 of 9 Part 3d (25 marks) As The IdsT sTep, The modUIdTed signdls we combined dgdin. SkeToh The signdl specTrum S(f) . thT kind of modUIdTion is This? SOD) WinTer 2009 SYSC35OI Communication Theory Page 9 of 9 Extra page Wim‘er 2009 ...
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sysc3501test1w09 - SYSC350l Communication Theory Page I of9...

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