电子科大-信号与系统chap2ppt课件

.,1,Chapter2,LinearTime-invariantSystems,.,2,Consideralineartime-invariantsystem,Example1anLTIsystem,.,3,2.1Discrete-timeLTISystems:TheConvolutionSum（卷积和）,2.1.1TheRepresentationofDiscrete-TimeSignalsinTermsofimpulses,SiftingProperty,离散时间信号的冲激表示,.,4,2.1.2TheDiscrete-TimeUnitImpulseResponsesandtheConvolution-SumRepresentationofLTISystems,TheUnitImpulseResponses单位冲激响应,Let,Let,.,5,2.Convolution-Sum（卷积和）,TimeInvariant,Scaling,Additivity,Convolution-Sum（卷积和）,系统在n时刻的输出包含所有时刻输入脉冲的影响,k时刻的脉冲在n时刻的响应,.,6,3.卷积和的计算,图解法,例2.3,图解法步骤：,求乘积,对每一个n求和,.,7,Example2.4,Determinetheoutputsignal,Solution,(a)n0微分n0积分,.,28,.,29,Example,Solution1,.,30,.,31,ExampleConsidertheconvolutionofthetwosignals,.,32,6几种典型系统,恒等系统,微分器,积分器,延迟器,累加器,.,33,2.3.4LTISystemswithandwithoutMemory,1.Discrete-timeSystem,Itismemoryless,AnLTIsystemwithoutmemory,2.Continuous-timeSystem,AnLTIsystemwithoutmemory,.,34,2.3.5InvertibilityofLTISystemsLTI系统的可逆性,.,35,2.3.6CausalityforLTISystemsLTI系统的因果性,1.Discrete-timeSystem,Causalsystem,2.Continuous-timeSystem,.,36,Consideralinearsystem,Foranytimet0,2.3.7StabilityforLTISystems(稳定性）,1.Discrete-timeSystem,.,37,2.Continuous-timeSystem,absolutelySummable绝对可加,Thesystemisstable.,absolutelyIntegrable绝对可积,Thesystemisnotstable.,.,38,2.3.8TheUnitStepResponseofanLTISystemsLTI系统的单位阶跃响应,Discrete-timeSystem,Continuous-timeSystem,UnitStepResponse,UnitStepResponse,.,39,2.4SingularityFunctions(奇异函数）,2.4.1TheUnitImpulseasanIdealizedShortPulse,.,40,Example2.16,.,41,Example2.17,.,42,2.4.2DefiningtheUnitImpulsethroughConvolution单位冲激的卷积定义,Foranyx(t),Foranynormal,whichiscontinuousattimet=0.,Lett=0,SiftingProperty,Theunitimpulsehasunitarea,.,43,2.4.3UnitDoubletsandOtherSingularityFunctions单位冲激偶和其它奇异函数,1.,Ingeneral,.,44,.,45,3.PropertiesofUnitDoublets（冲激偶的性质）,2.Defining,Forany,.,46,Ingeneral,Derivativesofdifferentordersoftheunitimpulse单位冲激的各阶积分,.,47,2.5CausalLTISystemsdescribedbyDifferentialandDifferenceEquations用微分方程和差分方程描述的因果LTI系统,2.5.1LinearConstant-coefficientDifferentialEquations线性常系数微分方程,一经典解法,1.Homogeneoussolution齐次解,特征方程,.,48,特征方程有N个不同的单根,特征方程有1个r阶重根，其余N-r个根各不相同,HomogeneousSolutionNaturalResponse齐次解自然响应,2.ParticularSolutionForcedResponse特解受迫响应,的函数形式取决于输入的函数形式,.,49,不是特征单根是特征单根,或,.,50,齐次解：,特解：,全响应：,.,51,若初始条件不为零，,若初始条件不跃变，,代入,全响应,N阶系统，初始松弛：,初始松弛条件下：,.,52,二零输入、零状态解法,全响应：,1.零输入响应：,具有齐次解的形式；,假定特征方程含有N个不同的单根,2.零状态响应：,.,53,由初始状态唯一决定,由零初始状态及输入共同决定,由初始状态及输入决定,函数形式由输入信号决定,1.零输入零状态解法,2.经典解法,三两种响应分解形式的关系,.,54,Zero-inputresponse,Zero-stateresponse,3.Fullresponse,.,55,2.5.2LinearConstant-coefficientDifferenceEquations线性常系数差分方程,Nthorder,RecursiveSolution递推算法,RecursiveEquation递归方程,.,56,ParticularlyN=0,NonrecursiveEquation非递归方程,Unitimpulseresponse,Finiteimpulseresponse(FIR)system,Example2.15,.,57,.,58,.,59,2.差分方程的经典解法,FullHomogeneousParticular,Homogeneoussolution,Eigenequation特征方程,(a)特征方程有N个不同的单根,(b)特征方程有1个r阶重根1其余N-r个根各不相同,.,60,Particularsolution(ForcedResponse),不是特征单根是特征单根,或,.,61,3.零输入、零状态解法,FullZero-inputZero-state,零输入响应：,具有齐次解的形式；,零状态响应：,假定特征方程含有N个不同的单根,.,62,由初始状态唯一决定,由零初始状态及输入共同决定,由初始状态及输入决定,函数形式由输入信号决定,4.两种响应分解形式的关系,.,63,Solution1,HomogeneousSolution,ParticularSolution,FullSolution,.,64,InitialState:,FullSolution,Solution2,Zero-inputSolution,.,65,Zero-stateSolution,FullSolution,Zero-inputresponse,Zero-stateresponse,Naturalresponse,Forcedresponse,.,66,2.5.3BlockDiagramRepresentationsofFirst-OrderSystem一阶系统的方框图表示,1.Discrete-timesystems,Addition,Multiplicationbyacoefficient,Delay,RecursiveEquation,.,67,2.Continuous-ti