《信号与线性系统分析基础 》 课件 第 1 章 信号与系统的基本概念

信号与系统SignalsandSystems吉林大学FundamentalConceptsofSignalsFundamentalConceptsofsignals1.Definition:AnalyticrepresentationAsignalisareal-valuedorscalar-valuedfunctionofthetimevariable.2.Description:GraphicalrepresentationFrequency-domainanalysisFundamentalConceptsofsignalsTime-domainrepresentationAnalyticrepresentationGraphicalrepresentationFrequency-domainrepresentationFundamentalConceptsofsignals3.Classification:DeterminatesignalRandomsignal(1)One-dimensionalsignalMulti-dimensionalsignal(2)PeriodicsignalAperiodicsignal(3)EnergysignalPowersignal(4)FundamentalConceptsofsignalsSampledsignalContinuous-timesignal(5)Discrete-timesignalAnaloguesignalPiecewise-continuoussignalDigitalsignalDecompositionmethodFundamentalConceptsofsignals4.Signalsprocessing:(1)DirectcurrentcomponentAlternatingcurrentcomponent(2)EvensignalOddsignalFundamentalConceptsofsignals(3)PulsesStepfunctions(4)RealcomponentImaginarycomponent(5)FundamentalConceptsofsignalsOrthogonalfunctions(6)SuchasIffunctionsandareintegrableontheinterval,andsatisfythenthetwofunctionsandaresaidtobeorthogonalontheinterval.信号与系统SignalsandSystems吉林大学FundamentalConceptsofSystemsFundamentalconceptsofsystems1.Definition:Asystemisaninterconnectionofcomponentswithterminalsoraccessportsthroughwhichmatter,energy,orinformationcanbeappliedorextracted.Asystemisamathematicalmodelforaphysicalprocessthatrelatestheinputtotheoutput.Fundamentalconceptsofsystems2.Blockdiagramrepresentation:ScalarmultiplierUnit-delayelementFundamentalconceptsofsystemsSummator/adder/subtracterIntegratorFundamentalconceptsofsystems3.Classification:(1)CausalsystemNoncausalsystem(2)Continuous-timesystemDiscrete-timesystem---Describedbyalgebraicequationsordifferentialequations.---Describedbydifferenceequations.Fundamentalconceptsofsystems(3)Time-varyingsystemTime-invariantsystem---Describedbydifferentialequationswithvariablecoefficients.---Describedbydifferentialequationswithconstantcoefficients.Fundamentalconceptsofsystems---Describedbyordinarydifferentialequations.---Describedbypartialdifferentialequations.Distributedparametersystem(5)Lumpedparametersystem(6)StablesystemUnstablesystem(Boundedinputboundedoutput,BIBO)(4)InstantaneoussystemDynamicsystem---Describedbyalgebraicequations.---Describedbydifferentialequations.Fundamentalconceptsofsystems(b)Superposition/Additivity(a)Homogeneity(c)Decomposition(8)LinearsystemNonlinearsystem(7)ReversiblesystemIrreversiblesystemInitialcondition信号与系统SignalsandSystems吉林大学DeterminationofSystemCharacteristicsDeterminationofsystemcharacteristics[Example]Determineifthesystemdescribedbyislinear,time-invariant,causalandstable.Linearornonlinear?(1)Time-invariantortime-varying?(2)Let?Determinati