Object:mathematicaltoolstodescribeandanalyzethesignalsFourierseriesandtransformImportantfunction:Diracdeltafunction,rectangularfunction,periodicfunctionandsincfunctionandtheirFouriertransformsfrequencyanalyze(timefunctionandhisspectrum)somepropertiesofsignal(DCvalue,rootmeansquarevalue,…)powerspectraldensityandautocorrelationfunctionlinearsystems:lineartime-invariantsystems,impulseresponse,transferfunction,distortionlesstransmissionbandwidthconcept:baseband,passbandandbandlimitedsignalsandnoise*samplingtheorem(dimensionalitytheorem)summarySignal:desiredpartofwaveforms;Noise:undesiredpartElectricsignal’sform:voltagev(t)orcurrenti(t)(timefunction)Inthischapter,allsignalsaredeterministic.Butincommunicationsystems,wewillbefacethestochasticwaveformsDeterministicresultsstochasticresultsbyanalogySignalanalysis:firstimportanceNonzerovaluesoverafinitetimeintervalnonzerovaluesoverafinitefrequencyintervalacontinuoustimefunctionafinitepeakvalueonlyrealvaluesIngeneral,thewaveformisdenotedbyw(t)Whent→±∞,wehavew(t)→0,butw(t)isdefinedover(+∞,-∞)Themathmodelofwaveformcanviolatesomeorallaboveconditions.Ex.w(t)=sinωt,physicallythiswaveformcannotbeexisted.Waveforms:signalornoisedigitaloranalogdeterministicornondeterministic(stochastic)physicallyrealizableornonphysicallyrealizablepowertypeorenergytypeperiodicornonperiodicPowertype:theaveragepowerofthewaveformisfinite(mathmodel)Energytype:theaverageenergyofthewaveformisfinite(allphysicallyrealizablesignal)Timeaverageoperator:dc(directcurrent)valueoftimefunctionDefinition:thetimeaverageoperationisgivenby:〈[·]〉=lim1/T-T/2∫T/2[·]dt〈[·]〉istimeaverageoperator.Theoperatorislinear.(Why?)Definition:w(t)isperiodicwithperiodT0ifw(t)=w(t+T0)foralltwhereT0issmallestpositivenumberthatsatisfiesaboverelationship.Theorem:ifw(t)isperiodic,thetimeaverageoperationcanbereducedto〈[·]〉=1/T-T/2-a∫T/2+a[·]dtwhereTisperiodofw(t)Definition:thedcvalueofw(t)isgivenbyitstimeaverage,〈w(t)〉.Wdc=〈w(t)〉=lim1/T-T/2∫T/2w(t)dtorWdc