EEE 377 DIGITAL COMMUNICATIONS [PERHUBUNGAN DIGIT]

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1 UNIVERSITI SAINS MALAYSIA Secod Semester Examiatio 05/06 Academic Sessio Jue 06 EEE 377 DIGITAL COMMUNICATIONS [PERHUBUNGAN DIGIT] Duratio 3 hours [Masa : 3 jam] Please check that this examiatio paper cosists of TWENTY ONE () pages ad Appedices SI (6) pages of prited material efore you egi the examiatio. This examiatio paper cosist of two versios, The Eglish versio ad Malay versio. The Eglish versio from page TWO () to page ELEVEN () ad Malay versio from page TWELVE () to page TWENTY ONE (). Sila pastika ahawa kertas peperiksaa ii megadugi DUA PULUH SATU () muka surat da Lampira ENAM (6) muka surat ercetak seelum ada memulaka peperiksaa ii. Kertas peperiksaa ii megadugi dua versi, versi Bahasa Iggeris da Bahasa Melayu. Versi Bahasa Iggeris daripada muka surat DUA () sehigga muka surat SEBELAS () da versi Bahasa Melayu daripada muka surat DUA BELAS () sehigga muka surat DUA PULUH SATU (). Istructios: This questio paper cosists of SI (6) questios. Aswer FIVE (5) questios. All questios carry the same marks. [Araha: Kertas soala ii megadugi ENAM (6) soala. Jawa LIMA (5) soala. Semua soala memawa jumlah markah yag sama] Begi your aswer to each questio o a ew page. [Mulaka jawapa ada utuk setiap soala pada muka surat yag aru] I the evet of ay discrepacies, the Eglish versio shall e used. [Sekiraya terdapat searag percaggaha pada soala peperiksaa, versi Bahasa Iggeris hedaklah digua pakai] /-

2 - - [EEE 377] ENGLISH VERSION. (a) A Fourier series trigoometric represetatio of sigal s(t) is give as follows; s ( t) cos( 400πt ) si( 400πt ) 0.058cos( 800πt ) si( 800πt ) cos( 00πt ) si( 00πt ) 0. cos( 600πt ) si( 600πt ) cos( 400πt ) si( 400πt ) 0.07 cos( 800πt ) + 0.4si( 800πt ) cos( 300πt ) si( 300πt ) cos( 3600πt ) si( 3600πt ) Based o the aove equatio; Fid the period of s ( t). (0 marks) (ii) Fid the expressio of oe-sided form for the first 0 harmoic compoets of s ( t). (0 marks) (iii) Draw the sigle-sided magitude spectrum of the first 0 harmoic compoets of s ( t). (0 marks) (iv) Draw the sigle-sided average ormalized power spectrum of the first 0 harmoic compoets of s ( t). (0 marks) () A commuicatio system is desiged as show i Figure (a) attempts to trasmit a periodic sigal s ( t) aove via a chael that acts as a o-ideal low pass filter with cutoff frequecy is khz. The trasfer fuctio (frequecy respose) of the filter is as show i Figure (). 3/-

3 - 3 - [EEE 377] Trasmitter s(t) Chael o-ideal Lowpass filter adwidth f c khz r(t) Receiver Figure (a): Commuicatio system with o-ideal lowpass filter H(f) f (khz) Figure (): Frequecy respose of the low pass filter Examie your aswer i part (a)(iv), the calculate the average ormalized power of s ( t) that ca pass through the chael. (5 marks) (ii) Suggest o how to icrease accuracy of the system. (5 marks) 4/-

4 - 4 - [EEE 377]. (a) A PAM system usig the sic-shaped pulse trasmits iary stream via a asead chael. If accuracy requiremet dictate that 00% of the sigal s average power spectral desity must e withi the adwidth chael of 50kHz. Determie the maximum trasmissio speed of the system. (0 marks) (ii) If accuracy requiremet dictate that 90% of the sigal s average power spectral desity must e withi the adwidth chael. Determie the adwidth of the chael, if the trasmissio speed is 50,000 its/sec. (0 marks) () Figure (a) elow show the sample ad hold receiver of the PAM asead trasmissio receiver. The received sigal is sampled at the ceter of it period T t 0 ( i ) T + ad the sample is compared to a 0V threshold for decisio of the demodulated iary data. The received sigal is corrupted y oise i the chael which has uiform proaility desity fuctio as show i Figure (). 5/-

5 P [EEE 377] Sample i ceter of each it period Received sigal LPF Comparator if sample 0 0 if sample < 0 f c adwidth of trasmitted sigal Threshold 0V Figure (a): Sample ad hold receiver for PAM asead trasmissio f ( x) a a x Figure (): pdf of uiform distriutio of oise f ( x) 0 for a 0 x < a for a x for x > where a ad are always positive umer. 6/-

6 - 6 - [EEE 377] Based o the Figure (a) aove; Explai the use of lowpass filter i the receiver desig. (0 marks) (ii) Explai the ature of the sigal after the lowpass filter. (0 marks) (iii) Startig from the fact that the proaility of it error; P P { ( t ) < γa} + P{ ( t ) γa} o o o o where the γ A is the term to idicated the atteuated received sigal. Show the proaility of it error P ; P dx for a γa γa a (30 marks) [Hit: Use Appedix for appropriate useful relatios] (iv) A commuicatio system trasmits the PAM sigal with 4V pulse ad the chael is assumed to have the uiform distriutio oise as i Figure (). By the time the sigal arrive at the receiver, the voltage is oly 0% of the trasmitted sigal. Calculate the proaility of it error P where a ad are 0. ad. respectively. (0 marks) 7/-

7 - 7 - [EEE 377] 3. (a) Badpass modulatio is the techique that eales data to e trasmitted through a aspass chael ad limited y such as, usig a carrier sigal. A Phase Shift Keyig (PSK) modulatio techique is used to modulate a iary sequece that should e trasmitted with it rate r 50,000its / sec. Give that adpass frequecies are f 00 khz ad f 300 khz ad the carrier frequecy is f c 00 khz. Draw the modulated sigal S PSK ( t) with timig sequece of iary ad idicate the umer of cycles per it period. (0 marks) (ii) Give the mathematical expressio of S PSK ( t) sigal i terms of asead ad carrier sigal ad draw the correspodig asead sigal. (0 marks) (iii) Draw the correspodig average ormalized power spectral desity G PSK ( f ) ad idicate for 90% ad 95% of the i-ad power. (0 marks) () Suppose you are goig to desig a PSK adpass commuicatio system with the followig requiremets; accuracy is 90% adpass chael with f 00kHz ad f 300 khz commuicatio is supposed to fully utilize the adwidth of its adpass chael. carrier frequecy is f c 00 khz. Sequece 8/-

8 - 8 - [EEE 377] Draw a diagram of the commuicatios system (with a trasmitter ad receiver) ad idicate the followig terms o the diagram the followigs; Chael (spectrum of the adpass chael), source iary data, trasmitted sigal S PSK ( t) (just this symol), trasmissio rate (require to e calculated). (0 marks) (ii) Suppose that the accuracy is chaged to 95%, calculate the trasmissio speed ad commet o the differet values otaied as compared i part (). (0 marks) (c) A PSK commuicatio system trasmits 00,000 its/sec usig sigal with a peak amplitude of 0.V. By the time the sigal arrives at the receiver, its voltage is oly 40% of the trasmitted voltage. The oise at the iput to the receiver is Gaussia oise with average ormalized power spectral desity as show i Figure 3 where the costat perfectly sychroized; N o 9 volts.6 0. Assumig the system is Hz Discuss whether the receiver is symmetry or asymmetry. Show your appropriate steps for the coclusio. (0 marks) (ii) Calculate the proaility of it error of the correspodig receiver. (0 marks) 9/-

9 - 9 - [EEE 377] Figure 3 : Average ormalized power spectrum desity of oise at the iput of the receiver 4. (a) It is stated that the miimum Hammig Distace is the same as the miimum Hammig Weight. Do you agree with this statemet, ad if so, discuss the reaso ehid it. (0 marks) () State your uderstadig of Geerator Matrix ad descrie its implemetatio i codig. Use (7,4) Hammig Code as a example. (0 marks) (c) A differetial pulse code modulatio (DPCM) yields 4-it words as output, which are to e protected agaist radom sigle errors. Determie the umer of parity its eeded if lock codig is employed. (0 marks) 0/-

10 - 0 - [EEE 377] (ii) Determie the geerator matrix ad parity matrix. (40 marks) (iii) Build the parity check matrix, H (0 marks) 5. (a) A geerator matrix for geeratig liear codes is as follows: Determie the message legth for this code geerator, ad the code legth. (0 marks) (ii) Determie the codewords for the possile messages. (30 marks) (iii) Determie the miimum distace. (5 marks) () From geerator matrix i Q5 (a), determie the parity check matrix. If a received code is 000, fid the corrected message. (45 marks) 6. (a) A istataeously adaptive delta modulator adapts its step size expoetially, i.e., if the predictor is uale to track the iput the step size is douled. Thus, the steps geerated have the values give y s, where,, 3,, 0. Determie the etropy of the step geerator if the proaility of a step, s is P(s ) /s for,,, 9 ad P(s 0 ) P(s 9 ). (40 marks) /-

11 - - [EEE 377] () A digital data stream is ecoded with (5, ) lock Hammig code with the capaility to correct all sigle errors. The coded data is PSK modulated ad trasmitted through a AWGN chael. Determie the geerator matrix y usig the parity check equatios. (50 marks) (ii) A message word is ready to e trasmitted, determie its correct codeword at the output. (0 marks) /-

12 - - [EEE 377] VERSI BAHASA MALAYSIA. (a) Satu seri Fourier dalam etuk trigoometri utuk isyarat s(t) adalah dierika seperti erikut; s ( t) cos( 400πt ) si( 400πt ) 0.058cos( 800πt ) si( 800πt ) cos( 00πt ) si( 00πt ) 0. cos( 600πt ) si( 600πt ) cos( 400πt ) si( 400πt ) 0.07 cos( 800πt ) + 0.4si( 800πt ) cos( 300πt ) si( 300πt ) cos( 3600πt ) si( 3600πt ) Bergatug kepada persamaa di atas; Cari kala agi s ( t). (0 markah) (ii) Cari persamaa seelah utuk 0 kompoe harmoik pertama agi s ( t). (0 markah) (iii) Lakarka magitude spectrum seelah agi 0 harmoik pertama agi isyarat s ( t). (0 markah) (iv) Lakarka spektrum purata kuasa terormal elah agi 0 harmoik pertama agi isyarat s ( t). (0 markah) 3/-

13 - 3 - [EEE 377] () Seuah sistem komuikasi direkacipta seperti dalam Rajah (a) cua meghatar isyarat seperti Jadual di atas melalui salura yag erfugsi seagai peapis lalua redah yag tidak uggul yag mempuyai frekuesi potog adalah khz. Pemidaha fugsi samuta frekuesi peuras adalah seperti yag ditujukka dalam Rajah (). Peghatar s(t) Salura Peuras lalua redah sempura Learjalur f cutoff khz r(t) Peerima Rajah (a): Sistem komuikasi dega peapis lalua redah tidak uggul H(f) f (khz) Figure (): Samuta frequesi peapis lalua redah tidak uggul 4/-

14 - 4 - [EEE 377] Dega memeriksa jawapa ada dalam ahagia a) iv, kiraka purata kuasa terormal yag oleh melalui salura. (5 markah) (ii) Bicagka agaimaa ketepata dapat ditigkatka. (5 markah). (a) Seuah Sistem PAM yag megguaka deyut eretuk sic meghatar data iari melalui salura jalur asas. Sekiraya ketepata yag diperluka adalah 00% utuk purata kuasa ketumpata spektra agi isyarat itu mesti erada dalam salura lear jalur adalah 50kHz. Tetuka kelajua maksima peghatara sistem terseut. (0 markah) (ii) Sekiraya ketepata yag diperluka adalah 90% utuk purata kuasa ketumpata spektra agi isyarat itu mesti erada dalam salura lear jalur. Cari lear jalur utuk salura, sekiraya kelajua peghatara adalah 50,000 its/sec. (0 markah) 5/-

15 P [EEE 377] () Rajah (a) erikut meujukka satu peerima sampel da pegag utuk peghatara jalur asas PAM. Isyarat yag diterima disampel pada pertegaha tempoh it ( i ) T t 0 T + da sampel diadigka dega peada aras 0V utuk memuat keputusa agi proses peyahmodulata perduaa data. Isyarat yag diterima dirosakka oleh higar dalam salura yag mempuyai fugsi ketumpata kearagkalia seragam seperti dalam Rajah (). Sampel di tegah tempoh it Isyarat peerima LPF Komparator sampel 0 0 sampel < 0 f c lear jalur agi isyarat dihatar Tada aras 0V Rajah (a): Peerima sampel da pegag utuk peghatara PAM f ( x) a a x Rajah (): pdf agi fugsi ketumpata kearagkalia seragam higar 6/-

16 - 6 - [EEE 377] f ( x) 0 for a 0 x < a for a x for x > Di maa a da setiasa eromor positif. Berdasarka Rajah (a) di atas; Teragka keguaa peuras lalua redah dalam rekaetuk peerima. (0 markah) (ii) Teragka keadaa isyarat selepas peuras lalua redah. (0 markah) (iii) Bermula daripada fakta ahawa kearagkalia ralat it; P P { ( t ) < γa} + P{ ( t ) γa} o o o o Di maa γ A mewakili isyarat peerima dikuragka. Tujukka kearagkalia ralat it P ; P dx for a γa γa a (30 markah) [Petujuk: Guaka lampira utuk persamaa yag sesuai] 7/-

17 - 7 - [EEE 377] (iv) Seuah sistem komuikasi meghatar isyarat PAM dega deyut 4V da melalui salura yag mempuyai fugsi ketumpata kearagkalia seragam seperti dalam Rajah (). Bila isyarat tia di peerima, voltaya adalah haya 0% dari isyarat yag di hatar. Kiraka kearagkalia ralat it P, dimaa parameter a da adalah 0. ad. setiap satu. (0 markah) 3. (a) Permodulata lalualulus adalah tekik yag memolehka data yag dapat dihatar melalui jalur salura lalualulus yag dihadka oleh, dega megguaka isyarat pemawa seperti. Permodalata fasa eralih peaipa (PSK) diguaka utuk memodulatka data iari dega kadar peghatara frekuesi jalur lulus adalah pemawa adalah f c 00 khz. r 50,000its / sec. Dierika ahawa f 00 khz ad f 300 khz da frekuesi Lakarka isyarat S PSK ( t) dega uruta masa iari da tujukka ilaga kitara setiap tempoh it. (0 markah) (ii) Berika persamaa matematik utuk isyarat S PSK ( t) dega megguaka isyarat jalur asas da pemawa da lukiska isyarat jalur asas itu. (0 markah) 8/-

18 - 8 - [EEE 377] (iii) Lakarka purata ketumpata kuasa terormal spektra G PSK ( f ) da tujukka 90% ad 95% kuasa dalam julat. (0 markah) () Ada aka merekaetuk satu sistem komuikasi PSK jalus lulus dega keperlua erikut; Ketepata adalah 90% Salura jalur lulus dega f 00 khz ad f 300 khz Komuikasi sepatutya megguaka lear jalur sepeuhya Frekuesi pemawa adalah f c 00 khz. Turuta. Lakarka rajah sistem komuikasi terseut (dega peghatar da peerima) da tujukka dalam rajah perkara erikut; salura - spektra jalur lulus, iari data, isyarat yag dihatar S PSK ( t) (tujukka haya symol ii sahaja), kadar peghatara (perlu dikira). (0 markah) (ii) Sekiraya ketepata ditukar kepada 95%, kiraka kadar peghatara da eri kome tetag perezaa ilai yag diperolehi. (0 markah) 9/-

19 - 9 - [EEE 377] (c) Seuah sistem komuikasi PSK system meghatar r 00,000its / sec megguaka isyarat pucak yag amplitudya adalah 0.V. Bila isyarat ii sampai di peerima, voltaya adalah haya 40% dari yag telah dihatar. Higar pada kemasuka di peerima adalah higar Gaussia dega purata kuasa teromal ketumpata spektra adalah ditujukka dalam Rajah 3 di maa ilai tetap N o kesempuraa segerak; 9 volts.6 0. Aggapka sistem ii mempuyai Hz Bicagka sama ada peerima ii adalah peerima simetri atau asimetri. Tujukka lagkah yag memawa kepada kesimpula. (0 markah) (ii) Kiraka kearagkalia ralat it utuk peerima ii. (0 markah) Rajah 3 : Purata kuasa terormal ketumpata spektra agi higar pada kemasuka peerima 4. (a) Diketahui ahawa jarak miimum Hammig adalah sama dega erat miimum Hammig. Adakah ada setuju dega keyataa ii, da jika ya icagka seaya. (0 markah) 0/-

20 - 0 - [EEE 377] () Nyataka pemahama ada tetag Geerator Matrix da teragka kaedah implemetasiya di dalam kod. Guaka (7,4) Kod Hammig seagai cotoh. (0 markah) (c) Satu pemodulata kod deyut pemeza meghasilka kata 4-it seagai keluara, yag aka dilidugi daripada satu ralat rawak. Tetuka ilaga it kesetarafa yag diperluka jika kod lok diguaka. (0 markah) (ii) Tetuka matrix pejaa da matrix kesetarafa. (40 markah) (iii) Bia matrix semaka kesetarafa, H. (0 markah) 5. (a) Satu pejaa matrix agi mejaa kod liear adalah seperti erikut: Tetuka pajag mesej agi pejaa kod ii da pajag kod. (0 markah) (ii) Tetuka katakod agi mesej yag erkaita. (30 markah) (iii) Tetuka jarak miimum. (5 markah) /-

21 - - [EEE 377] () Daripada pejaa matrix di Q5 (a), tetuka matriks semaka kesetarafa. Jika kod diterima adalah 000, carika mesej yag etul. (45 markah) 6. (a) Satu pemodulat delta suai ketika mempuyai saiz lagkah secara ekspoe, i.e. jika peramal tidak mampu utuk megesa kemasuka, maka saiz lagkah aka digadaka. Oleh itu, lagkah yag terhasil mempuyai ilai seperti s, di maa,, 3,, 0. Tetuka etropi agi pejaa lagkah ii jika kearagkalia agi lagkah,, s adalah P(s ) /s agi,,, 9 da P(s 0 ) P(s 9 ). (40 markah) () Satu jurusa data digital dikod dega (5, ) kod lok Hammig yag mempuyai keoleha memetulka semua ralat tuggal. Data yag telah dikod aka dimodulasika dega PSK da dihatar melalui satu lalua AWGN. Tetuka matriks pejaa dega megguaka persamaa semaka kesetarafa. (50 markah) (ii) Satu kata mesej ersedia utuk dihatar, tetuka katakod yag etul di keluara. (0 markah) ooo0ooo

22 APPENDI LAMPIRAN (EEE 377). Fourier Series (Trigoometric form) S ( t) a + ( a cos( πf t) si( πf t) ) f t 0 + T 0 a s( t)dt T 0 T a t T T t0 s( t) cos( πf t)dt s( t) si( πf t)dt 0 t0 t T T t0. Fourier Series (Oe-sided form) S 0 ( t) + cos( π f t φ ) a 0 a + φ ta a 3. Fourier Series (Doule-sided form) s ( ) t c e jπf o t c T t o + T t o s ( t) e j πf o t dt 4. Coversio etwee -sided to -sides Fourier Series > 0 c ( a j ) c 0 c o ao o ( a j ) c * c c + c φ c c φ

23 APPENDI LAMPIRAN (EEE 377) 5. Fourier Trasform ad Iverse Fourier Trasform s j f t ( t) S( f ) e π jπ f t df S( f ) s( t) e dt 6. Parseval s Theorems t + T 0 Parseval s Power Theorem P s ( t) Parseval s Eergy Theorem s E s T t0 dt + time domai frequecy domai s 0 ( t) dt S( f ) df time domai frequecy domai 7. Normalized eergy spectral desity Ψ ( f ) S( f ) volts Hz or volts Hz sec 8. Raised-cosie shape pulse with roll-off factor α

24 APPENDI LAMPIRAN (EEE 377) 9. Average ormalized power spectral desity ( ( f )) G for PAM sigal 3

25 APPENDI (EEE 377) LAMPIRAN 0. Stochastic Relatios i. Proaility Distriutio Fuctio ( ) { } ( )dx x f a P a F a ii. Proaility Desity Fuctio ( ) ( ) x F dx d x f iii. Gaussia proaility Desity fuctio ( ) ( ) σ µ π σ x e x f iv. Other Relatioships { } { } { } ( ) ( ) ( )dx x f a F F a P P a P a < { } { } ( ) ( ) ( ) ( )dx x f dx x f dx x f c F c P c P c c >. Receiver desig Sample ad hold receiver ( ) ) ( 0 T T i t + σ µ γa Q P Optimum receiver ( 0 ) it t Symmetric 0 N E Q P ( ) ( ) ( )dt t s df f S E it T i γ γ ( ) 0 N T A Q P γ Coheret receiver Asymmetric N 0 E Q P d ( ) ( ) ( ) dt t s t s E it T i d γ ( ) 0 4N T A Q P γ Coheret receiver 4

26 APPENDI LAMPIRAN (EEE 377) The Q Fuctio (Gaussia distriutio with

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MST 561 Statistical Inference [Pentaabiran Statistik] UNIVERSITI SAINS MALAYSIA Secod Semester Examiatio 05/06 Academic Sessio Jue 06 MST 56 Statistical Ierece [Petaabira Statistik] Duratio : 3 hours [Masa : 3 jam] Please check that this examiatio paper cosists