Analogchannel
ThebandwidthoftheanalogchannelW=f2-f1wheref1isthelowestfrequencythatthechannelcanpass,andf2isthehighestfrequencythatthechannelcanpass.BotharedeterminedbythechannelDeterminedbyphysicalcharacteristics.Whenthecircuitsthatmakeupthechannelaremade,thebandwidthofthechannelisdetermined.Inordertomakethesignaltransmissionlessdistortion,thechannelmusthaveenoughbandwidth.
Digitalchannel
Digitalchannelisadiscretechannel,whichcanonlytransmitdigitalsignalsofdiscretevalues.Thebandwidthofthechanneldeterminesthehighestpossibleundistortedtransmissionpulsesequenceinthechannelrate.
Adigitalpulseiscalledasymbol,andweusethesymbolratetorepresentthenumberofsignalwaveformtransformationsperunittime,thatis,thenumberofsymbolstransmittedthroughthechannelinaunittime.IfthesignalsymbolwidthisTseconds,thesymbolrateB=1/T.Theunitofsymbolrateiscalledbaud(Baud),sothesymbolrateisalsocalledbaudrate.Asearlyas1924,HenryNyquist,aresearcheratBellLaboratories,deducedthelimitbaudrateofanoiselesschannelwithlimitedbandwidth,whichiscalledtheNyquisttheorem.IfthechannelbandwidthisW,theNyquisttheoremstatesthatthemaximumsymbolrateisB=2W(Baud).ThechannelcapacityspecifiedbytheNyquisttheoremisalsocalledtheNyquistlimit,whichisdeterminedbythephysicalcharacteristicsofthechannel..ItisimpossibletotransmitpulsesignalsbeyondtheNyquistlimit,sothechannelbandwidthmustbeimprovedtofurtherincreasethebaudrate.
Theamountofinformationcarriedbythecodeelementisdeterminedbythenumberofdiscretevaluestakenbythecodeelement.Ifthesymboltakestwodiscretevalues,onesymbolcarries1bitofinformation.Ifthesymbolcantakefourdiscretevalues,onesymbolcarries2bitsofinformation.Thatis,theamountofinformationn(bit)carriedbyasymbolhasthefollowingrelationshipwiththenumberoftypesofsymbolsN:n=log2N
Theamountofinformation(numberofbits)transmittedonthechannelperunittimeiscalledthedatarate.Thewaytoincreasetherateatacertainbaudrateistouseonesymboltorepresentmorebits.Iftwobitsareencodedintoonesymbol,thedataratecanbedoubled.
Forthis,wehavetheformula:
R=Blog2N=2Wlog2N(b/s)
whereRrepresentsthedatarateandtheunitispersecondBit,abbreviatedasbpsorb/s
Datarateandbaudratearetwodifferentconcepts.Thetwoareequalonlywhenthesymboltakestwodiscretevalues.Forordinarytelephonelines,thebandwidthis3000HZandthehighestbaudrateis6000Baud.Themaximumdataratecantakedifferentvaluesdependingontheencodingmethod.Thesearethelimitvaluesunderidealconditionswithoutnoise.Theactualchannelwillbeinterferedbyvariousnoises,soitisfarfromreachingthedatatransferratecalculatedaccordingtotheNyquisttheorem.Shannon'sresearchshowsthatthelimitdataratewithnoisecanbecalculatedbythefollowingformula:
C=Wlog2(1+s/n)
ThisformulaiscalledShannon'stheorem,WhereWisthechannelbandwidth,Sistheaveragepowerofthesignal,Nistheaveragepowerofthenoise,ands/niscalledthesignal-to-noiseratio.SincetheratioofStoNistoolargeinactualuse,itisoftentakenindecibels(db).Therelationshipbetweendecibelsandsignal-to-noiseratiois:db=10lgs/n
Forexample,whens/nis1000,thesignal-to-noiseratiois30db.Thisformulahasnothingtodowiththediscretevalueofthesignal,thatistosay,nomatterwhatmethodisusedformodulation,aslongasthesignal-to-noiseratioisgiven,themaximumamountofinformationtransmissionperunittimeisdetermined.Forexample,ifthechannelbandwidthis3000HZandthesignal-to-noiseratiois30db,themaximumdatarateis
C=3000log2(1+1000)≈3000×9.97≈30000b/s
ThisisthelimitValuehasonlytheoreticalmeaning.Infact,itisverygoodthatthedataratecanreach9600b/sonatelephonelinewithabandwidthof3000HZ.
Tosumup,wehavetwoconceptsofbandwidth.Intheanalogchannel,thebandwidthiscalculatedaccordingtotheformulaW=f2-f1.Forexample,thebandwidthofaCATVcableis600HZor1000HZ;thebandwidthofadigitalchannelisthechannelThemaximumdataratethatcanbeachieved,forexample,thebandwidthofEthernetis10MB/Sor100MB/S,andthetwocanbeconvertedtoeachotherbyShannon'stheorem.
Relateddifferences
Channelbandwidth
Thefrequencybandbandwidthisthestandardforsendingwirelesssignals.Inthecommonlyused2.4-2.4835GHzfrequencyband,thefrequencybandbandwidthofeachchannelis20MHz;theformerworkswithb/g/nprotocols,andthelatterhasac/a/n.
Thehigherthefrequency,theeasieritistobedistorted.Inthecaseof11n,20MHzcanreachabandwidthof144Mbps(howtocalculate?).Ithasbetterpenetrationandalongtransmissiondistance(about100meters);40MHzInthecaseof11n,itcanreachabandwidthof300Mbps,withaslightlypoorerpenetrationandashorttransmissiondistance(about50meters).
Signalbandwidth
Signalbandwidthreferstoelectromagneticwavesintheradiofrequencybandthatpropagateinfreespace(includingairandvacuum).
Electromagneticwavesincludemanytypes,arrangedintheorderoffrequencyfromlowtohigh:radiowaves,infraredrays,visiblelight,ultravioletrays,X-raysandgammarays.Radiowavesaredistributedinthefrequencyrangeof3Hzto3000GHz.Inthisspectrum,itcanbedividedinto12bands.Thelowerthefrequency,thesmallerthepropagationloss,thelongerthecoveragedistance,andthestrongerthediffractionability.However,thefrequencyresourcesofthelowfrequencybandaretight,andthesystemcapacityislimited.Therefore,theradiowavesofthelowfrequencybandaremainlyusedinsystemssuchasbroadcasting,television,andpaging.
Thehighfrequencybandisrichinfrequencyresourcesandthesystemcapacityislarge.Butthehigherthefrequency,thegreaterthepropagationloss,thecloserthecoveragedistance,andtheweakerthediffractionability.Inaddition,thehigherthefrequency,thegreaterthetechnicaldifficultyandthecorrespondingincreaseinthecostofthesystem.