4signal and systemh系统是由若干相互作用和相互依赖事物组合而成具有特定功能整体

SignalandAsignalisafunctionofindependentvariablessuchastime,distance,position,temperature.forexample,speechandmusicsignalsrepresentairpressureasafunctionoftimeatapointinClassificationofContinuousversusDiscrete RealversusComplex Scalar[ˈskeɪlə(r)]数量，标量versusVectorOnedimensionalversusMulti-Dimensional DeterministicversusRandomInthiscase,signalscanbeclassifiedintocontinuous-timesignalsanddiscrete-time(sequenceofnumbers)Acontinuous-timesignalwithacontinuousamplitudeisusuallycalledanogsignal.Adiscrete-timesignalwithdiscrete-valuedamplitudesrepresentedbyafinitenumberofdigitsisreferredtoasthedigitalsignal.Adiscrete-timesignalwithcontinuousvaluedamplitudesiscalledasampled-datasignal.Adigitalsignalisthusazed['kwɒntɑɪzd]sampledatasignal.Acontinuous-timesignalwithdiscretevalueamplitudesisusuallycalledazedboxcarsignal(量化矩形信号)System:ismadebyanumberofinctiveandinterdependentthings binationwithaspecificfunctionasawhole.Thedifferencebetweensystemandcircuit:thesystemfocusontheoverallsituation,thecircuitconcernedaboutthelocal.Circuitysistofocusonstudydetails(suchastheloopcurrentandvoltage)fromthesystempointofview,onecanconsiderhowitmightconstituteadifferentialorintegralfunctiondevices(suchasarithmeticunit)Itinvestigatestheresponseofalinearandtime-invariantsystemtoanarbitraryinputsignalLinearitymeansthattherelationshipbetweentheinputandtheoutputofthesystemisamap:Ifinputproducesresponseandinputresponsethenthescaledandsummedinputproducesscaledandsummedresponsewhere arerealscalars.[ˈskeɪlə(r)]数量，标量TimeinvariancemeansthatwhetherweapplyaninputtothesystemnoworTsecondsfromnow,theoutputwillbeidenticalexceptforatimedelayoftheTseconds.Thatis,iftheoutputduetoinputis,thentheoutputdueinputis.Hence,thesystemistimeinvariantbecausetheoutputdoesnotdependontheparticulartimetheinputisapplied.ThefundamentalresultinLTIsystemtheoryisthatanyLTIsystemcanbecharacterizedentirelybyasinglefunctioncalledthesystem'simpulseresponse.Theoutputofthesystemissimplytheconvolutionoftheinputtothesystemwiththesystem'simpulseresponse.Thismethodof ysisisoftencalledthetime point-of-view.Thesameresultistrueofdiscrete-timelinearshift-invariantsystemsinwhichsignalsarediscrete-timesamples,andconvolutionisdefinedonRelationshipbetweentheandEquivalently,anyLTIsystemcanbecharacterizedinthefrequency bythesystem'stransferfunction,whichistheLacetransformofthesystem'simpulseresponse(orZtransforminthecaseofdiscrete-timesystems).Asaresultofthepropertiesofthesetransforms,theoutputofthesysteminthefrequency istheproductofthetransferfunctionandthetransformoftheinput.Inotherwords,convolutioninthetime isequivalenttomultiplicationinthefrequency ForallLTIsystems,theeigenfunctions,andthebasisfunctionsofthetransforms,arecomplexexponentials.Thisis,iftheinputtoasystemisthecomplexwaveformforsomecomplexamplitude andcomplexfrequency,theoutputwillbesomecomplexconstanttimestheinput,sayforsomenewcomplex .Theratioisthetransferfunctionatfrequency.Becausesinusoidsareasumofcomplexexponentialswithcomplex-conjugatefrequencies,iftheinputtothesystemisasinusoid,thentheoutputofthesystemwillalsobeasinusoid,perhapswithadifferentamplitudeandadifferentphase,butalwayswiththesamefrequency.LTIsystemscannotproducefrequencycomponentsthatarenotintheinput.LTIsystemtheoryisgoodatdescribingmanyimportantsystems.MostLTIsystemsareconsidered"easy"to yze,atleastcomparedtothetime-varyingand/ornonlinearcase.AnysystemthatcanbemodeledasahomogeneousdifferentialequationwithconstantcoefficientsisanLTIsystem.Examplesofsuchsystemsareelectricalcircuitsmadeupofresistors,inductors,andcapacitors(RLCcircuits).Idealspring–mass–dampersystemsarealsoLTIsystems,andaremathematicallyequivalenttoRLCcircuits.impulseInsignalprocessing,theimpulseresponse,orimpulseresponsefunction(IRF),ofadynamicsystemisitsoutputwhenpresentedwithabriefinputsignal,calledanimpulse.(Mathematically,howtheimpulseisdescribeddependsonwhethersystemismodeledindiscreteorcontinuoustime.TheimpulsecanbemodeledasaDiracdeltafunctionforcontinuous-timesystems,orastheKroneckerdeltafordiscrete-timesystems.transferAtransferfunction(alsoknownasthesystemfunction[1ornetworkfunctionandwhenplottedasagraph,transfercurve)isamathematicalrepresentation,intermsofspatialortemporal(空间或时间)frequency,oftherelationbetweentheinputandoutputofalineartime-invariantsystemwithzeroinitialconditionsandzero-pointtransferfunctionistheLacetransformofthesystem'simpulseresponse(orZtransforminthecaseofdiscrete-timesystems).inthestudyofsignalsandsystems,theeigenfunctionofasystemisthesignalwheninputintothesystem,producesaresponsewiththecomplexconstantBIBOInsignalprocessing,specificallycontroltheory,BIBOstabilityisaofstabilityforlinearsignalsandsystemsthattakeinputs.BIBOstandsforBounded-InputBounded-Output.IfasystemisBIBOstable,thentheoutputwillbeboundedforeveryinputtothesystemthatisbounded.Asignalisboundedifthereisafinitevaluesuchthatthesignalmagnitudeneverexceeds,thatisfordiscrete-timesignals,orforcontinuous-timesignals.Continuous-timenecessaryandsufficientForacontinuoustimelineartimeinvariant(LTI)system,theconditionforBIBOstabilityisthattheimpulseresponsebeabsolu yintegrable,i.e.,itsL1normexist.Discrete-timesufficientForadiscretetimeLTIsystem,theconditionforBIBOstabilityisthattheimpulseresponsebeabsolu ysummable,i.e.,itsnormexist.Forarationalandcontinuous-timesystem,theconditionforstabilityisthattheregionofconvergence(ROC)oftheLacetransformincludestheimaginaryaxis.Whenthesystemiscausal,theROCistheopenregiontotherightofaverticallinewhoseabscissaistherealpartofthe"largestpole",orthepolethathasthegreatestrealpartofanypoleinthesystem.TherealpartofthelargestpoledefiningtheROCiscalledtheabscissa[æbˈsɪsə]ofconvergence.Therefore,allpolesofthesystemmustbeinthestrictlefthalfofthes-neforBIBOstability.Thisstabilityconditioncanbederivedfromtheabove conditionasfollowswhereandTheregionofconvergencemustthereforeincludetheimaginaryDiscrete-timeForarationalanddiscretetimesystem,theconditionforstabilityisthattheregionofconvergence(ROC)ofthez-transformincludestheunitcircle.Whenthesystemiscausal,theROCistheopenregionoutsideacirclewhoseradiusisthemagnitudeofthepolewithmagnitude.Therefore,allpolesofthesystemmustbeinsidetheunitcircleinthez-neforBIBOstability.Thisstabilityconditioncanbederivedinasimilarfashiontothecontinuous-timewhereandTheregionofconvergencemustthereforeincludetheunitAsystemiscausaliftheoutputdependsonlyonpresentandpast,butnotfutureinputs.Anecessaryandsufficientconditionforcausalityiswhereistheimpulseresponse.ItisnotpossibleingeneraltodeterminecausalityfromtheLacetransform,becausetheinversetransformisnotunique.Whenaregionofconvergenceisspecified,thencausalitycanbedetermined.Inelectronics,controlsystemsengineering,andstatistics,thefrequency referstotheysisofmathematicalfunctionsorsignalswithrespecttofrequency,ratherthantime.[1]Putsimply,a graphshowshowasignalchangesovertime,whereas graphshowshowmuchofthesignallieswithineachgivenfrequencybandoverarangeoffrequencies.Afrequency- representationcanalsoincludeinformationonthephaseshiftthatmustbeappliedtoeachsinusoidinordertobeableto binethefrequencycomponentstorecovertheoriginaltimesignal.Agivenfunctionorsignalcanbeconvertedbetweenthetimeandfrequency swithapairofmathematicaloperatorscalledatransform.AnexampleistheFouriertransform,whichposesafunctionintothesumofa(potentiallyinfinite)numberofsinewavefrequencycomponents.The'spectrum'offrequencycomponentsisthefrequency ofthesignal.TheinverseFouriertransformconvertsthefrequency functionbacktoatimefunction.Aspectrum yzeristhetoolcommonlyusedtovisualizereal-worldsignalsinthefrequency MagnitudeandInusingtheLace,Z-,orFouriertransforms,thefrequencyspectrumiscomplex,describingthemagnitudeandphaseofasignal,oroftheresponseofasystem,asafunctionoffrequency.Inmanyapplications,phaseinformationisnotimportant.Bydiscardingthephaseinformationitispossibletosimplifytheinformationinafrequencyrepresentationtogenerateafrequencyspectrumorspectraldensity.Aspectrumyzerisadevicethatdisysthespectrum,whilethetimefrequencycanbeseenonanoscilloscope.[əˈsɪləskəʊp]Thepowerspectraldensity功率谱密度isafrequency-descriptionthatcanbeappliedtoalargeclassofsignalsthatareneitherperiodicnorsquare-integrable(平方可积);tohaveapowerspectraldensity,asignalneedsonlytobetheoutputofawide-sensestationaryrandomprocess广义平稳随机过程.DifferentfrequencyAlthough"the"frequencyisspokenofinthesingular,thereareanumberofdifferentmathematicaltransformswhichareusedtoyzetimefunctionsandarereferredtoas"frequency"methods.Thesearethemostcommontransforms,andthefieldsinwhichtheyareused:Fourierseriesrepetitivesignalsoscillating[asə'leɪtɪŋ]systemsFouriertransform–nonrepetitivesignals,transients[t'rænzɪənts]瞬变Lacetransform–electroniccircuitsandcontrolZtransform–discretesignals,digitalsignalMoregenerally,onecanspeakofthetransformwithrespecttoanytransform.Theabovetransformscanbeinterpretedascapturingsomeformoffrequency,andhencethetransformisreferredtoasafrequency.DiscretefrequencyTheFouriertransformofaperiodicsignalonlyhasenergyatabasefrequencyanditsharmonics.Anotherwayofsayingthisisthataperiodicsignalcanbeyzedusingadiscretefrequency.Dually,adiscrete-timesignalgivesrisetoaperiodicfrequencyspectrum.Combiningthesetwo,ifwestartwithatimesignalwhichisbothdiscreteandperiodic,wegetafrequencyspectrumwhichisbothperiodicanddiscrete.ThisistheusualcontextforadiscreteFouriertransform.FourierInmathematics,aFourierseries posesperiodicfunctionsorperiodicsignalsintothesumofa(possiblyinfinite)setofsimpleoscillatingfunctions,namelysinesandcosines(orcomplexFourierTheFouriertransform,namedafterJosephFourier,isamathematicaltransformwithmanyapplicationsinphysicsandengineering.Verycommonlyittransformsamathematicalfunctionoftime,f(t),intoanewfunction,sometimesdenotedbyorF,whoseargumentisfrequencywithunitsofcycles/s(hertz)orradianspersecond.LaceInmathematicsandsignalprocessing,theZ-transformconvertsatimesignal,whichisasequenceofrealorcomplexnumbers,intoacomplexfrequencyrepresentation.Abandlimitedfunctioncanbeperfectlyreconstructedfromacountablesequenceofsamplesifthebandlimit,B,isnogreaterthanhalfthesamplingrate(samplespersecond)Thissubjectpresentsthetheoreticalbasisforsystemysisandgivesstudtsskillsinusingthetechniquestodesigncomponentsofreal systems.Thederivationofmodelsfromreal-worlddevicesthroughmeasurementandthecomparisonofmodelpredictionswithexperimentalresultsisemphasisedinthelaboratorycomponentofthecourse.Agroupprojectthatrequiresthedesignandimplementationofpartofa municationsystemallowsstudentstoapplytheirknowledgetoareal-lifeproblem.Topicsinclude:signaltypesandtheirrepresentationinthetimeandfrequencys;odellingsysteswithdifferentialordifferenceequationsandtransforoftheequations;signaloperationsandprocessing;therelationshipbetweendiscreteandcontinuoustiesandthemathematicaltechniquesapplicabletoeach;theeffectsoffeedback;timeandfrequencyperformanceofsystems;systemstability;andcontroldesigntechniquesandsimplecommunicationsystems.Signal:manifestationofthemessage,themessageisthespecificcontentofthesignal.Inthecommunicationsystem,thegenerallanguage,text,imagesordataarecollectivelyreferredtoasmessage信号分类：周期信号：依一定时间间隔周而复始，且是无始无终的信号（Periodicsignals:againandagainaccordingtoacertaintimeinterval,andiswithoutbeginningandwithoutendsignal(expressionoff(t)=f(t+T)n=0,±1...)Non-periodicsignal:timecyclecharacteristics(thecyclesignalcycleTtendstoinfinityand enon-periodicsignal)Continuous-timesignalsanddiscrete-timesignalcanbedividedbasedonthecontinuityofthefunctionvaluesanddiscreteContinuous-timesignal:inagiventimeinterval,inadditiontothenumberofconsecutivepoints(breakpoints),thevalueofanytimecanbegiventodeterminethefunctionvalue,timeandamplitudearecontinuoussignalsogogsignals,thepracticalapplicationdoesnotdistinguishbetween ogsignalandcontinuous-timesignals.(SineDiscrete-timesignal:timediscretefunctionvalueisgivenonlyinsomeofcontinuous,instantaneous,intheothertimeisundefined（Randomsignals:discretesignalatime-discreteamplitudecontinuous(nottobelimitedtocertainvalues,bothpositiveandnegative)(populationstatisticsbymonthnumber)Digitalsignals:discretesignalsatimevalue(limitedtocertaindiscretevalues,suchas0,1)arediscreteDeterminethesignal:thesignalisexpressedasadefinitefunctionoftime(sinewave)Randomsignal:theactualtransmissionofthesignalwithunforeseenOne-dimensionalsignals:voicesignalisafunctionoftime-varyingsoundMultidimensionalsignals:electromagneticwavepropagationinthree-dimensionalspaceSystem:ismadebyanumberofinctiveandinterdependentbinationwithaspecificfunctionasaThedifferencebetweensystemandcircuit:thesystemfocusontheoverallsituation,thecircuitconcernedaboutthelocal.Circuitysistofocusonstudydetails(suchastheloopcurrentandvoltage)fromthesystempointofview,onecanconsiderhowitmightconstituteadifferentialorintegralfunctiondevices(suchasarithmeticunit)离散时间信号（RLC电路）Systems:continuous-timesystems:thesysteminputsandoutputsarecontinuous-timesignal,anditsinternalnorconvertedtodiscrete-timesignal(RLCcircuit)Discrete-timesystem:thesysteminputandoutputsarediscrete-timesignal(digitalcomputer,thethirdsymboldoesnotexistbetweentwoadjacentsymbols,noothervaluesuchas0110)andthetwooftenmix,knownasmixedTime-varyingsystem:Thesystemparameterschangeovertime(dailytemperature)Time-invariantsystem(ConstantSystems):Theparametersofthesystemdoesnotchangeovertime,strictlyspeaking,doesnotexist,canonlysaythatwithinacertaintimeconstantLinearsystem:superpositionandhomogeneity(ie,homogeneity,Superposition:whenseveralexcitationsignalatthesametimeactingonthesystem,thetotaloutputresponseequaltotheresponsegeneratedbytheindividualroleofeachincentive;Uniformity:TheinputsignalismultipliedbyaconstantresponsetimestakethesameconstantNonlinearsystems:doesnotmeettheoverlayandtheuniformityofthe线性时不变系统特性（LineartimeinvariantLIT）Superpositionandhomogeneity;time-invariante(t)r(t)de(t)/dt时，dr(t)/dt.Differentialcharacteristics:Ifthesystemundertheactionoftheexcitatione(t)responser(t)de(t)/dt,whentheexcitation,theresponsetothedr(t)/dt.（causalityt0时刻的响应只与t=t0和t<t0时刻的输入有关，r(t)=e(t+1)r(t)=e(t)是因果系统Causality(causality):referstotheresponseofthesystemattimet0t=t0andt<t0,timeinput,thatisincentivetoproducetheresponseinresponsetotheincentiveconsequences.r(t)=e(t-1)isnotacausalsystem,r(t)=e(t+1)andr(t)=e(t)isacausalCommonlyusedsignals:theindexsignal:theimportantcharacteristicsofthedifferentialandintegralofitstimeisstillexponential(expressionsandSinusoidalsignal:thetimedifferentialandintegralremainsthesamefrequencysinusoidalsignal(expressedwiththelegend)Complexexponentialsignal:infact,cannotproducethecomplexexponentialsignal(forillustrations)（（信号基本运算：移位：波形在tSignalofthebasicoperations:shift:thewaveformmoveoverallinthet-t=0Fold:foldoverthewaveformatt0

Scale:thetimelineforthe arkcompress1)orextended(coefficientDifferential(infinitesubdivision):theedgeofthegraphicssilhouette;tomakethegraphicsclearer积分（无限求和：图形更加平滑，可削弱信号中的毛刺（噪声）响Integral(infinitesum):smoothergraphics,canweakenimpactoftheglitchinthesignal阶跃信号（单位阶跃t=0时，对某一电路接入单位电源，并且无限持特性：单边性，即信号在某接入时刻t0Stepsignal(unitstep):thephysicalbackground:att=0,thepowerofacircuitaccessunit,andunlimitedcontinues(meaning,arectangularCharacteristics:unilal,thatisthesignalamplitudeofaaccesstimet0iszeroImpulsesignal(unitimpulse):Physicalbackground:theimpactofphysicalphenomenaneedtouseaveryshorttime,butthevalueofagreatmodeltodescribethe(rectangular)f(tf(-Features:dualfunction,f(t)=f(-Pulse->impulsesignal:theareatomaintaintherectangularpulse,whenthepulsewidthtendsto0,theamplitudetendstoinfinity,thislimitistheunitimpulsefunctionStepandimpulsecontact:theintegraloftheimpulsesignalfunctionisequaltothestepsignalfunction;stepsignalfunctionofthedifferentialisequaltotheimpulsesignalfunctionThezero-inputresponse:theroleofexternalexcitationsignalnoresponse,onlytheinitialstate(startingtimeofenergystoragesystem);Thezerostateresponse:donotconsiderthemomenttheroleoftheenergystoragesystem(theinitialstateisequaltozero),plustheresponsegeneratedbytheexcitationsignalbythesystem;（Theexpandedfunctionf(t)satisfytheDirichletWeekperiod,ifthereisdiscontinuitypoint,thenstoppedthenumberofpointsislimitedWeekperiod,thenumberof umandminimumvaluesisInInaweekperiod,thesignalis yintegrable,Fouriertransform:transformandinversetransform变换的基本性质：线性（叠加性之和ThebasicpropertiesoftheFouriertransformof:linear(superposition),thesumofthespectrumofthesignalisequaltothespectrumofeachindividualsignal：时移特性()信号f(t)在时域中沿时间轴右移(延时)t0等效于在频域中频谱乘以因子：Shift:(formula)signalf(t)isshiftedtotherightalongthetimelineinthe (delay)t0,equivalentmultipliedbythefactorinthe spectrum,Whichmeansthatthesignalisshiftedtotheright,theamplitudespectrumofthesame,whilethephasespectrumtoproduceadditionalchangesScalechangesincharacteristics:LegendSymmetry,thatisanevenfunction,thespectrumoftherectangularpulsefunctionSa,Sa-shapedpulsespectrumoftherectangularfunctionPhasespectrum:thephasefunctionofthespectralfunction,indicatingthatthephaserelationshipbetweenthevariousfrequencycomponentsinthesignalF的绝对Amplitudespectrum:isthefunctionofthemagnitudeofthespectrumfunction,indicatingthatthemagnitudeofrelationshipsbetweenthevariousfrequencycomponentsinthesignal,representedbytheabsolutevalueofFFourierseriesisequivalenttotheFouriertransformintheperiodicsignalinaspecialformofexpressionFourierseriesandFouriertransformoftheperiodicrectangularpulsef(tFj是的实函数；f(tFj是f(t是非奇非Fj是Functionandcharacteristicsofthespectrum:Ifthefunctionisevenfunction,itsspectraldensityfunctionisarealfunction;ifthefunctionisanoddfunction,itsspectraldensityfunctionisavirtualfunction;ifthefunctionisnon-oddnon-dualfunction,itsspectraldensityfunctionisacomplexfunction.（1）Periodicsignalspectrumischaracterizedbyadiscretespectrum,whiletheaperiodicsignalspectrumischaracterizedbyacontinuousspectrumThespectrumoftheperiodicsignalamplitudespectrumandphaseThecharacteristicsoftheperiodicsignalspectrumincludingdiscreteThesamecycleofthepulse,adjacentlinesintervalthesame;thenarrowerthepulsewidth,thewiderthewidthofthespectrum,theband Frequencybandwidthofasinglerectangularpulseanditspulsewidthτ,τisthegreater,thenthebandwidthismorenarrow.周期性矩形脉冲信号的频谱，脉冲周期TPeriodicrectangularpulsesignalspectrum,thepulseperiodTisthelongertheintervalthesmallerlines.TheTheexpansionofthesignalinthe correspondingtoitsspectruminthe

Cyclepulseofthepulsewidth,periodTgreatertheintervallines,thespectrumismoredense;magnitudesThesamecycleofthepulseintervaladjacentlinesthesame;thenarrowerthepulsewidth,themorethenumberofspectrallinesbetweentwozero,containedinthebandcomponentmorePeriodicsignalbandwidthandthepulsewidthisinverselyproportionalto.Fn2倍。Fouriertransformoftheperiodicsignal(orthespectraldensityfunction)consistsofaninfinitenumberofimpulsefunction,itsstrengthis2timesthecorrespondingamplitudeSignalofconvergenceshowsthatthesignalenergyisconcentratedinthelowfrequencyband.WelearneddifferentkindsofsignalanddifferentkindsofsystemsinthisAsignalisasetofinformation.HerewetalkaboutsignalsthatarefunctionsofSignalpowerandWedefinethesignalenergyThesignalenergymustbefiniteforittobeameaningfulmeasureofthesignalsize.Thatis,thesignalamplitude→0as|t|P25)Ifnot,amoremeaningfulmeasureisthetimeaverageofenergy,wecallit[f(t)=tisneitherapowernoraenergyAsignalwithfiniteenergyisanenergysignal,andasignalwithfiniteandnonzeropowerisapowersignal.Asignalwithfiniteenergyhaszeropower,Asignalwithfinitepowerhasinfiniteenergy.Continuous-time,discrete-time,og,anddigitalsinalContinuous-timesignalisspecifiedforeveryvalueoftimet.Discrete-timeisspecifiedonlyatdiscretevaluesoft.ogsignalcantake