数字信号处理—基于计算机的方法第3章答案

3-2(a)SketchthenaturallysampledPAMwaveformthatresultsfromsamplinga1-kHzsinewaveata4-kHzrate.(b)Repeatpart(a)forthecaseofaflat-toppedPAMwaveform.Solution:3-4(a)Showthatananalogoutputwaveform(whichisproportionaltotheoriginalinputanalogwaveform)mayberecoveredfromanaturallysampledPAMwaveformbyusingthedemodulationtechniqueshowedinFig.3-4.(b)FindtheconstantofproportionalityC,thatisobtainedwiththisdemodulationtechnique,wherew(t)istheoriqinalwaveformandCw(t)istherecoveredwaveform.NotethatCisafunctionofn,wheretheoscillatorfrequencyisnfs.Solution:afterLPF:3-7InabinaryPCMsystem,ifthequantizingnoiseisnottoexceedpercentofthepeak-to-peakanaloglevel,showthatthenumberofbitsineachPCMwordneedstobe(Hint:LookatFig.3-8c.)Solution:BinaryPCMM=levelsforWeneed3-8TheinformationinananalogvoltagewaveformistobetransmittedoveraPCMsystemwitha0.1%accuracy(fullscale).Theanalogwaveformhasanabsolutebandwidthof100Hzandanamplituderangeof–10to+10V.(a)Determinetheminimumsamplingrateneeded.(b)DeterminethenumberofbitsneededineachPCMword.(c)DeterminetheminimumbitraterequiredinthePCMsignal.(d)DeterminetheminimumabsolutechannelbandwidthrequiredfortransmissionofthisPCMsignal.Solution:(a)Determinetheminimumsamplingrateneeded.(b)DeterminethenumberofbitsneededineachPCMword.Usingtheresultsgiveninprob.3-7.(c)DeterminetheminimumbitraterequiredinthePCMsignal.(d)DeterminetheminimumabsolutechannelbandwidthrequiredfortransmissionofthisPCMsignal.ForbinaryPCMD=R3-9An850-MbyteharddiskisusedtostorePCMdata.Supposethatavoice-frequency(VF)signalissampledat8ksamples/sandtheencodedPCMistohaveanaverageSNRofatleast30dB.HowmanyminutesofVFconversation(i.e.,PCMdata)canbestoredontheharddisk?Solution:3-10Ananalogsignalwithabandwidthof4.2MHzistobeconvertedintobinaryPCMandtransmittedoverachannel,Thepeak-signalquantizingnoiseratioatthereceiveroutputmustbeatleast55dB.(a)IfweassumethatandthatthereisnoISI,whatwillbethewordlengthandthenumberofquantizingstepsneeded?(b)Whatwillbetheequivalentbitrate?(c)Whatwillbethechannelnullbandwidthrequiredifrectangularpulseshapesareused?Solution:(a)IfweassumethatandthatthereisnoISI,whatwillbethewordlengthandthenum-berofquantizingstepsneeded?Using(3-18),(b)ForrectangularpulseshapeGivenanaudiosignalwithspectralcomponentsinthefrequencyband300to3000Hz,assumethatasamplingrateof7KHzwillbeusedtogenerateaPCMsignal.DesignanappropriatePCMsystemasfollows:DrawablockdiagramofthePCMsystem,includingthetransmitter,channel,receiver.Specifythenumberofuniformquantizationstepsneededandthechannelnullbandwidthrequired,assumethatthepeaksignal-to-noiseratioatthereceiveroutputneedstobeatleast30dBandthatpolarNRZsignalingisused.Discusshownonuniformquantizationcanbeusedtoimprovetheperformanceofthesystem.Solution:(a)略(b)(c)uniformquantizing:forallsamples,thequantizingnoisepoweristhesameuniformquantizingisnotgoodforsmallsignal.Nonuniformquantizing:samplesarenonlinearprocessed,Smallsignalisamplified(orsmallsignal---usingsmallstepsize)InaPCMsystem,thebitserrorrateduetochannelnoiseis10-4.Assumethatpeaksignal-to-noiseratioonthereceivedanalogsignalneededtobeatleast30dB.FindtheminimumnumberofquantizingstepsthatcanbeusedtoencodetheanalogsignalintoaPCMsignal.Iftheoriginalanalogsignalhadanabsolutebandwidthof2.7kHz,whatisthenullbandwidthofPCMsignalforthepolarNRZsignalingcase.Solution:(a)3-17Fora4bitPCMsystem,calculateandsketchaplotoftheoutputSNR(indecibels)asafunctionoftherelativeinputlevel,for(a)APCMsystemthatuseslawcompanding(b)APCMsystemthatusesuniformquantizationWhichofthesesystemisbettertouseinpractice?Why?Solution:n=4bits----aPCMword(a)(b)3-19Amultileveldigitalcommunicationsystemsendsoneof16possiblelevelsoverthechannelevery0.8ms.(a)Whatisthenumberofbitscorrespondingtoeachlevel?(b)Whatisthebaudrate?(c)Whatisthebitrate?Solution:(a)Whatisthenumberofbitscorrespondingtoeachlevel?(b)Whatisthebaudrate?(c)Whatisthebitrate?3-20Amultileveldigitalcommunicationsystemistooperateatadatarateof9,600bits/s.(a)If4-bitwordsareencodedintoeachlevelfortransmissionoverthechannel,whatistheminimumrequiredbandwidthforthechannel?(b)Repeatpart(a)forthecaseof8-bitencodingintoeachlevel.Solution:(a)If4-bitwordsareencodedintoeachlevelfortransmissionoverthechannel.Whatisthemin-imumrequiredbandwidthforthechannel?(b)Repeatpart(a)forthecaseof8-bitencodingintoeachlevel.3-24Considerarandomdatapatternconsistingofbinary1’sand0’s,wheretheprobabilityofobtainingeitherabinary1orabinary0is.CalculatethePSDforthefollowingtypesofsignalingformatsasafunctionof,thetimeneededtosend1bitofdata:(a)PolarRZsignalingwherethepulsewidthis.(b)ManchesterRZsignalingwherethepulsewidthis.Whatisthefirstnullbandwidthofthesesignals?Whatisthespectralefficiencyforeachofthesesignalingcases?Solution:PolarRZsignalingwherethepulsewidthis.andthedataareindependentfrombittobitThefirst-nullbandwidthisandthebandwidthefficiencyis(b)ManchesterRZsignalingwherethepulsewidthis.Whatisthefirstnullband-widthofthesesignals?Whatisthespectralefficiencyforeachofthesesignalingcases?Equation(3-36)canalsobeusedtoevaluatethePSDforRZManchestersignalingwherethepulseshapeisshowninthefigure.Using(3-40)and(3-36),thePSDforManchestersignalingisIf,thisbecomesThefirst-nullbandwidthisandthespectralefficiencyis(bits/sec)/Hz.3-29Thedatastream01101000101appearsattheinputofadifferentialencoder.Dependingontheinitialstart-upconditionoftheencoder,findouttwopossibledifferentialencodeddatastreamsthatcanappearattheoutput.Solution:3-30Createapracticalblockdiagramforadifferentialencodingsystem.Explainhowthesystemworkbyshowingtheencodinganddecodingforthesequence001111010001.Assumethatthereferencedigitisabinary1.Showthaterrorpropagationcannotoccur.Solution:3-34TheinformationinananalogwaveformisfirstencodedintobinaryPCMandthenconvertedtoamultilevelsignalfortransmissionoverthechannel.Thenumberofmultilevelsiseight.Assumethattheanalogsignahasabandwidthof2700Hzandistobereproducedatthereceiveroutputwithanaccuracyof(fullscall).(a)DeterminetheminimumbitrateofthePCMsignal.(b)Determinetheminimumbaudrateofthemultilevelsignal.(c)DeterminetheminimumabsolutechannelbandwidthrequiredfortransmissionofthisPCMsignal.Solution:3-35Abinarywaveformof9600bits/sisconvertedintoanoctal(Multilevel)waveformthatispassthroughachannelwitharaisedcosine-rolloffNyquistfiltercharacteristic.Thechannelhasaconditioned(equalized)phaseresponseoutto2.4kHz.(a)Whatisthebaudrateofthemultilevelsignal?(b)Whatistherollofffactorofthefiltercharacteristic?Solution:3-37Abinarycommunicationsystemusespolarsignal.Theoverallimpulseresponseisdesignedtobeofthetype,asgivenbyEq(3-67),sothattherewillbenoISI.Thebitrateis.(a)Whatisthebaudrateofthepolarsignal?(b)Plotthewaveformofpolarsignalatthesystemoutputwhentheinputbinarydatais01100101.Canyoudiscernthedatabylookingatthispolarwaveform?Solution:(b)3-43Usingtheresultsofprob.3-42,demonstratethatthefollowingfiltercharacteristicsdoordonotsatisfyNyquist’scriterionforeliminatingISI().Solution:3-45AnanalogsignalistobeconvertedintoaPCMsignalthatisabinarypolarNRZlinecode.Thesignalistransmittedoverachannelthatisabsolutelybandlimitedto4kHz.AssumethatthePCMquantizerhas16stepsandthattheoverallequivalentsystemtransferfunctionisoftheraisedcosine-rollofftypewithr=0.5.(a)FindthemaximumPCMbitratethatcanbesupportedbythissystemwithoutintroducingISI.(b)Findthemaximumbandwidththatcanbepermittedfortheanalogsignal.Solution:3-47Multileveldatawithanequivalentbitrateof2,400bits/sissentoverachannelusingafour-levellinecodethathasarectangularpulseshapeattheoutputofthetransmitter.Theoveralltransmissionsystem(i.e.,thetransmitter,channel,andreceiver)hasanr=0.5raisedcosine-rolloffNyquistfiltercharacteristic.(a)Findthebaudrateofthereceivedsignal.(b)Findthe6-dBbandwidthforthistransmissionsystem.(c)Findtheabsolutebandwidthforthesystem.Solution:(a)Findthebaudrateofthereceivedsignal.(b)Findthe6-dBbandwidthforthistransmissionsystem.(c)Findtheabsolutebandwidthforthesystem.3-54Oneanalogwaveformw1(t)isbandlimitedto3kHz,andanother,w2(t),isbandlimitedto9kHz.ThesetwosignalsaretobesentbyTDMoveraPAM-typesystem.(a)Determinetheminimumsamplingfrequencyforeachsignal,anddesignaTDMcommutatoranddecommutatortoaccommodatethesignals.(b)Drawsometypicalwaveformsforw1(t)andw2(t),andsketchthecorrespondingTDMPAMwaveform.Solution:(a)Determinetheminimumsamplingfrequencyforeachsignal,anddesignaTDMcommutatoranddecommutatortoaccommodatethesignals.TDMDrawsometypicalwaveformsforw1(t)andw2(t),andsketchthecorrespondingTDMPAMwaveform.3-56Twenty-threeanalogsignals,eachwithabandwidthof3.4kHz,aresampledatan8-kHzrateandmultiplexedtogetherwithasynchronizationchannel(8kHz)intoaTDMPAMsignal.ThisTDMsignalispassedthroughachannelwithanoverallraisedcosine-rolloffNyquistfiltercharacteristicofr=0.75.(a)Drawablockdiagramforthesystem,indicatingthefcofthecommutatorandtheoverallpulserateoftheTDMPAMsignal.(b)Evaluatetheabsolutebandwidthrequiredforthechannel.Solution:3-58ReworkProb.3-56foraTDMpulsecodemodulationsysteminwitchan8-bitquantizerisusedtogeneratethePCMwordsforeachoftheanaloginputsandan8-bitsynchronizationwordisusedinthesynchronizationchannel.Solution:3-59DesignaTDMPCMsystemthatwillaccommodatefour300-bit/s(synchronous)digitalinputsandoneanaloginputthathasabandwidthof500Hz.Assumethattheanalogsampleswillbeencodedinto4-bitPCMword.Drawablockdiagramforyourdesign,analogoustoFig.3-39,indicatingthedataratesatthevariouspointsonthediagram.Explainhowyourdesignworks.Solution:3-60DesignaTDMPCMsystemthatwillaccommodatetwo2400-bit/ssynchronousdigitalinputsandananaloginputthathasabandwidthof2700Hz.Assumethattheanaloginputissampledat1.11111timestheNyquistrateandconvertedinto4-bitPCMword.Drawablockdiagramforyourdesign,andindicatethedataratesatthevariouspointsonyourdiagram.ExplainhowyourTDMschemeworks.Solution: