英文资料1.docx
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英文资料1.docx
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英文资料1
DigitalTelephony
Analogtelephonyisalmostdead.
InthePSTN,thefamousLastMileisthefinalremainingpieceofthetelephonenetworkstillusingtechnologypioneeredwelloverahundredyearsago.[1]
Oneoftheprimarychallengeswhentransmittinganalogsignalsisthatallsortsofthingscaninterferewiththosesignals,causinglowvolume,static,andallmannerofotherundesiredeffects.Insteadoftryingtopreserveananalogwaveformoverdistancesthatmayspanthousandsofmiles,whynotsimplymeasurethecharacteristicsoftheoriginalsoundandsendthatinformationtothefarend?
Theoriginalwaveformwouldn’tgetthere,butalltheinformationneededtoreconstructitwould.
Thisistheprincipleofalldigitalaudio(includingtelephony):
samplethecharacteristicsofthesourcewaveform,storethemeasuredinformation,andsendthatdatatothefarend.Then,atthefarend,usethetransmittedinformationtogenerateacompletelynewaudiosignalthathasthesamecharacteristicsastheoriginal.Thereproductionissogoodthatthehumanearcan’ttellthedifference.
Theprincipleadvantageofdigitalaudioisthatthesampleddatacanbemathematicallycheckedforerrorsallalongtheroutetoitsdestination,ensuringthataperfectduplicateoftheoriginalarrivesatthefarend.Distancenolongeraffectsquality,andinterferencecanbedetectedandeliminated.
Pulse-CodeModulation
Thereareseveralwaystodigitallyencodeaudio,butthemostcommonmethod(andtheoneusedintelephonysystems)isknownasPulse-CodeModulation(PCM).Toillustratehowthisworks,let’sgothroughafewexamples.
Digitallyencodingananalogwaveform
TheprincipleofPCMisthattheamplitude[2]oftheanalogwaveformissampledatspecificintervalssothatitcanlaterbere-created.Theamountofdetailthatiscapturedisdependentbothonthebitresolutionofeachsampleandonhowfrequentlythesamplesaretaken.Ahigherbitresolutionandahighersamplingratewillprovidegreateraccuracy,butmorebandwidthwillberequiredtotransmitthismoredetailedinformation.
TogetabetterideaofhowPCMworks,considerthewaveformdisplayedinFigure7.2,“Asimplesinusoidal(sine)wave”.
Todigitallyencodethewave,itmustbesampledonaregularbasis,andtheamplitudeofthewaveateachmomentintimemustbemeasured.Theprocessofslicingupawaveformintomomentsintimeandmeasuringtheenergyateachmomentiscalledquantization,orsampling.
Thesampleswillneedtobetakenfrequentlyenoughandwillneedtocaptureenoughinformationtoensurethatthefarendcanre-createasufficientlysimilarwaveform.Toachieveamoreaccuratesample,morebitswillberequired.Toexplainthisconcept,wewillstartwithaverylowresolution,usingfourbitstorepresentouramplitude.Thiswillmakeiteasiertovisualizeboththequantizationprocessitselfandtheeffectthatresolutionhasonquality.
Figure7.3,“Sampleoursinewaveusingfourbits”showstheinformationthatwillbecapturedwhenwesampleoursinewaveatfour-bitresolution.
Figure 7.2. Asimplesinusoidal(sine)wave
Figure 7.3. Samplingoursinewaveusingfourbits
Ateachtimeinterval,wemeasuretheamplitudeofthewaveandrecordthecorrespondingintensity—inotherwords,wesampleit.Youwillnoticethatthefour-bitresolutionlimitsouraccuracy.Thefirstsamplehastoberoundedto0011,andthenextquantizationyieldsasampleof0101.Thencomes0100,followedby1001,1011,andsoforth.Intotal,wehave14samples(inreality,severalthousandsamplesmustbetakenpersecond).
Ifwestringtogetherallthevalues,wecansendthemtotheothersideas:
00110101010010011011101110100001010101010000110011001010
Onthewire,thiscodemightlooksomethinglikeFigure7.4,“PCMencodedwaveform”.
Figure 7.4. PCMencodedwaveform
Whenthefarend’sdigital-to-analog(D/A)converterreceivesthissignal,itcanusetheinformationtoplotthesamples,asshowninFigure 7.5,“PlottedPCMsignal”.
.
Figure 7.5. PlottedPCMsignal
Fromthisinformation,thewaveformcanbereconstructed(seeFigure 7.6, “Delineatedsignal”.)
Figure 7.6. Delineatedsignal
AsyoucanseeifyoucompareFigure7.2,“Asimplesinusoidal(sine)wave”withFigure 7.6, “Delineatedsignal”,thisreconstructionofthewaveformisnotveryaccurate.Thiswasdoneintentionally,todemonstrateanimportantpoint:
thequalityofthedigitallyencodedwaveformisaffectedbytheresolutionandrateatwhichitissampled.Attoolowasamplingrate,andwithtoolowasampleresolution,theaudioqualitywillnotbeacceptable.
Increasingthesamplingresolutionandrate
Let’stakeanotherlookatouroriginalwaveform,thistimeusingfivebitstodefineourquantizationintervals(Figure 7.7. “Thesamewaveform,onahigher-resolutionoverlay”).
Figure 7.7. Thesamewaveform,onahigher-resolutionoverlay
Tip
Inreality,thereisnosuchthingasfive-bitPCM.Inthetelephonenetwork,PCMsamplesareencodedusingeightbits.[3]
We’llalsodoubleoursamplingfrequency.ThepointsplottedthistimeareshowninFigure 7.8. “Thesamewaveformatdoubletheresolution”
.Figure 7.8. Thesamewaveformatdoubletheresolution
Wenowhavetwicethenumberofsamples,attwicetheresolution.Heretheyare:
001110100001001010010100000101101101100011001110011100010111
101001000100010001110100101010010010011100000110001101011010
11001110001011010001
Whenreceivedattheotherend,thatinformationcannowbeplottedasshowninFigure 7.9. “Five-bitplottedPCMsignal”
Figure 7.9. Five-bitplottedPCMsignal
Fromthisinformation,thewaveformshowninFigure 7.10. “Waveformdelineatedfromfive-bitPCM”canthenbegenerated.
Asyoucansee,theresultantwaveformisafarmoreaccuraterepresentationoftheoriginal.However,youcanalsoseethatthereisstillroomforimprovement.
Tip
Notethat40bitswererequiredtoencodethewaveformat4-bitresolution,while156bitswereneededtosendthesamewaveformusing5-bitresolution(andalsodoublingthesamplingrate).Thepointis,thereisatradeoff:
thehigherthequalityofaudioyouwishtoencode,themorebitsrequiredtodoit,andthemorebitsyouwishtosend(inrealtime,naturally),themorebandwidthyouwillneedtoconsume.
Figure 7.10. Waveformdelineatedfromfive-bitPCM
Nyquist’sTheorem
Sohowmuchsamplingisenough?
Thatverysamequestionwasconsideredinthe1920sbyanelectricalengineer(andAT&T/Bellemployee)namedHarryNyquist.Nyquist’sTheoremstates:
“Whensamplingasignal,thesamplingfrequencymustbegreaterthantwicethebandwidthoftheinputsignalinordertobeabletoreconstructtheoriginalperfectlyfromthesampledversion.”[4]
Inessence,whatthismeansisthattoaccuratelyencodeananalogsignalyouhavetosampleittwiceasoftenasthetotalbandwidthyouwishtoreproduce.Sincethetelephonenetworkwillnotcarryfrequenciesbelow300Hzandabove4,000Hz,asamplingfrequencyof8,000samplespersecondwillbesufficienttoreproduceanyfrequencywithinthebandwidthofananalogtelephone.Keepthat8,000samplespersecondinmind;we’regoingtotalkaboutitmorelater.
Logarithmiccompanding
So,we’vegoneoverthebasicsofquantization,andwe’vediscussedthefactthatmorequantizationintervals(i.e.,ahighersamplingrate)givebetterqualitybutalsorequiremorebandwidth.Lastly,we’vediscussedtheminimumsamplerateneededtoaccuratelymeasuretherangeoffrequencieswewishtobeabletotransmit(inthecaseofthetelephone,it’s8,000Hz).Thisisallstartingtoadduptoafairbitofdatabeingsentonthewire,sowe’regoingtowanttotalkaboutcompanding.
Compandingisamethodofimprovingthedynamicrangeofasamplingmethodwithoutlosingimportantaccuracy.Itworksbyquantizinghigheramplitudesinamuchcoarserfashionthanloweramplitudes.Inotherwords,ifyouyellintoyourphone,youwillnotbesampledascleanlyasyouwillbewhenspeakingnormally.Yellingisalsonotgoodforyourbloodpressure,soit’sbesttoavoidit.
Twocompandingmethodsarecommonlyemployed:
μlaw[5]inNorthAmerica,andalawintherestoftheworld.Theyoperateonthesameprinciplesbutareotherwisenotcompatiblewitheachother.
Compandingdividesthewaveformintocords,eachofwhichhasseveralsteps.Quantizationinvolvesmatchingthemeasuredamplitudetoanappropriatestepwithinacord.Thevalueofthebandandcordnumbers(aswellasthesign—positiveornegative)becomesthesignal.Thefollowingdiagramswillgiveyouavisualideaofwhatcompandingdoes.Theyarenotbasedonanystandard,butratherweremadeupforthepurposeofillustration(again,inthetelephonenetwork,compandingwillbedoneataneight-bit,notfive-bit,resolution).
Figure 7.11. “Five-bitcompanding”illustratesfive-bitcompanding.Asyoucansee,amplitudesnearthezero-crossingpointwillbesampledfarmoreaccuratelythanhigheramplitudes(eitherpositiveornegative).However,sincethehumanear,thetransmitter,andthereceiverwillalsotendtodistortloudsignals,thisisn’treallyaproblem.
Figure 7.11. Five-bitcompanding
AquantizedsamplemightlooklikeFigure 7.12.“ Quantizedandcompandedat5-bitresolution”.Ityieldsthefollowingbitstream:
Figure 7.12. Quantizedandcompandedat5-bitresolution
000001001110100101010110100001000111101000010000010100010011
101001010000101001000010110101100111000100011000010000010100
100101010101101101000010111010001000000001000
Aliasing
Ifyou’veeverwatchedthewheelsonawagonturnbackwardinanoldWesternmovie,you’veseentheeffectsofa
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