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CommunicationNetworks(2ndEdition)Chapter3SolutionsSolutionstoChapter31.Supposethesizeofanuncompressedtextfileis1megabyte.Solutionsfollowquestions:a.Howlongdoesittaketodownloadthefileovera32kilobit/secondmodem?T32k=8(1024)(1024)/32000=262.144secondsb.Howlongdoesittaketotaketodownloadthefileovera1megabit/secondmodem?T1M=8(1024)(1024)bits/1x106bits/sec=8.38secondsc.Supposedatacompressionisappliedtothetextfile.Howmuchdothetransmissiontimesinparts(a)and(b)change?Ifweassumeamaximumcompressionratioof1:6,thenwehavethefollowingtimesforthe32kilobitand1megabitlinesrespectively:T32k=8(1024)(1024)/(32000x6)=43.69secT1M=8(1024)(1024)/(1x106x6)=1.4sec2.Ascannerhasaresolutionof600x600pixels/squareinch.Howmanybitsareproducedbyan8-inchx10-inchimageifscanninguses8bits/pixel?24bits/pixel?Solution:Thenumberofpixelsis600x600x8x10=28.8x106pixelsperpicture.With8bits/pixelrepresentation,wehave:28.8x106x8=230.4Mbitsperpicture.With24bits/pixelrepresentation,wehave:28.8x106x24=691.2Mbitsperpicture.3.Supposeacomputermonitorhasascreenresolutionof1200x800pixels.Howmanybitsarerequiredifeachpixeluses256colors?65,536colors?Solution:Thenumberofpixelsis1200x800=960000pixelsperscreen.With256colors,wehave:9.6x105xlog2256=9.6x105x8=7.68x106bitsperscreen.With65536colors,wehave:9.6x105xlog265536=9.6x105x16=15.36x106bitsperscreen.4.Explainthedifferencebetweenfacsimile,GIF,andJPEGcoding.Giveanexampleofanimagethatisappropriatetoeachofthesethreemethods.Solution:Facsimilescansablack-and-whiteimageintorowsofblackandwhitedots,whicharethencompressed.Thescanningprocessintroducesdistortioninthesensethatthescannedimageisnotthesameastheoriginalimage.GIFtakesimagedata,inbinaryform,andappliesalosslessdatacompressionscheme.JPEGinvolvesscanninganimageandapplyingalossycompressionschemethatisdesignedsothatthedistortionisnotvisible.Leon-Garcia/Widjaja1CommunicationNetworks(2ndEdition)Chapter3Solutions5.Adigitaltransmissionsystemhasabitrateof45megabits/second.HowmanyPCMvoicecallscanbecarriedbythesystem?Solution:PCMchannels=(45x106bits/sec)/(64x103bits/secchannel)=703channels.6.Supposeastoragedevicehasacapacityof1gigabyte.Howmany1-minutesongscanthedeviceholdusingconventionalCDformat?usingMP3coding?Solution:AstereoCDsignalhasabitrateof1.4megabitspersecond,or84megabitsperminute,whichisapproximately10megabytesperminute.Thereforea1gigabytestoragewillhold1gigabyte/10megabyte=100songs.AnMP3signalhasalowerbitratethanaCDsignalbyaboutafactorof14,so1gigabytestoragewillholdabout1400songs.7.Howmanyhigh-qualityaudiochannelscouldbetransmittedusinganHDTVchannel?Solution:Anaudiochannelisabout1.4MbpsandanHDTVchannelisabout38Mbps,soanHDTVchannelcancarryabout27suchaudiochannels.Thenumberofaudiochannelsincreasesbyafactorof10ifmorecompression(e.g.MP3)isappliedtotheaudiosignals.8.HowmanyHDTVchannelscanbetransmittedsimultaneouslyovertheopticalfibertransmissionsystemsinTable3.3?Solution:Supposethatanopticalfibercarries1600x109bps,andanHDTVchannelisabout38Mbps,thenthefibercancarryabout1600000/38=40,000HDTVchannels.9.Commentonthepropertiesofthesequenceofframeimagesandtheassociatedbitratesinthefollowingexamples.Solutionsfollowquestions:a.Achildren’scartoonprogram.Theframesconsistofrelativelysimpleobjectsandstaticbackgroundswithlittlefastmotion,sothedifferencesbetweenconsecutiveframesaresmall.Thereforethesesequencesarehighlycompressible.b.Amusicvideo.Theframesconsistofrelativelycompleximagesthatmayconsistoftheoverlay/combinationofmultipleimages,andtherecanbefastmotionandsuddenchangesinscenes,sothedifferencesbetweenconsecutiveframescanbehigh.Thereforethesesequencesarenothighlycompressible.c.Atennisgame;abasketballgame.Bothtennisandbasketballhavefastmotion.Intennistherearefewermovingobjectsthatinbasketball,andinbasketballthebackgroundcanbemorecomplex.Bothsequencesarenoteasytocompress.Leon-Garcia/Widjaja2CommunicationNetworks(2ndEdition)Chapter3Solutionsd.Adocumentaryonfamouspaintings.Thesequencesarerelativelyslowlychanging,withmuchpanningandzooming.Thedegreeofdetail/complexityoftheimagescanbehigh.Thebitratedependsonthedetailintheimages.10.Supposethatatagiventimeoftheday,inacitywithapopulationof1million,1%ofthepeopleareonthephone.a.WhatisthetotalbitrategeneratedbyallthesepeopleifeachvoicecallisencodedusingPCM?Thenumberofpeopleonthephoneatagiventimeis106x10–2=104,sothetotalbitrateis104x64x103=640megabitspersecond.b.WhatisthetotalbitrateifallofthetelephonesarereplacedbyH.261videoconferencingterminals?Ifthevideoconferencingbitrateis64kbps,thenthetotalbitrategeneratedbythecityisunchanged.Howeverifhigh-qualityvideoconferencingisusedandthebitrateisincreasedto1.5Mbps,thenthetotalbitrateincreasesto15Gbps.11.Considerananalogrepeatersysteminwhichthesignalhaspowerσx2andeachstageaddsnoisewithpowerσn2.Forsimplicityassumethateachrepeaterrecoverstheoriginalsignalwithoutdistortionbutthatthenoiseaccumulates.FindtheSNRafternrepeaterlinks.Writetheexpressionindecibels:SNRdB=10log10SNR.Solution:Afternstages,thesignalpowerisσx2andthenoisepowerisnσn2,sotheSNRis:SNRdB=10log10σx2/nσn2=10log10σx2/σn2+10log101/n=10log10σx2/σ