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1、Chapter2ProblemAnswers2.1Twosequencesandare,respectively,givenbyand.Findthesequenceofthesample-addedsumoftwosequences.Solution:Thesample-addedsumisgivenby.2.2Findthesample-accumulatedsequenceofagivensequence.Solution:For,thesample-accumulatedsequenceisgivenby.For,wehave.Thus,thesample-a
2、ccumulatedsequenceis.2.3Assumethatasequenceisthesameasthatinproblem2.2.Determinethefirst-orderforwardandbackwarddifferencesequencesof,respectively.Solution:Thefirst-orderforwarddifferencesequenceisgivenby,andthefirst-orderbackwarddifferencesequenceisgivenby.2.4Determinewhetherornoteacho
3、ffollowingsignalsisperiodic.Ifasignal,inthecase,isperiodic,specifyitsfundamentalperiod.(1)(2)(3)(4)Solution:(1)Considering,andtaking,weseethatthesequenceisperiodicwithperiod.Solution:(2)Thissequenceisperiodic.Since,wecantakeandobtaintheperiodofthesequenceas.Solution:(3)Considering,andta
4、king,weseethattheperiodofthesequenceis.Solution:(4)Since,isnotanintegerforanyintegervalueof.Thus,thegivensequenceisnonperiodic.2.10Foreachofthefollowingsystems,determinewhetherthesystemis(a)stable,(b)causal,(c)linear,(d)timeinvariant,and(e)memoryless.下列系统，确定系统是否(a)稳定，（b）因果，（C）线性，（D）时不变，
5、和（E）无记忆。(1)(2)(3)(4)(5)(6)(7)Solution:(1)Thesystemisdefinedby.(a)Consideraninputwhichisboundedby,thesystemresponsetothisinputisdeterminedas(考虑一个输入x(n)=u(n)这是有界的x(n)
6、
7、<=B=1,系统响应这个输入是确定).Becausethesystemisunstable.系统不稳定(b)Sincethesystemoutputvalueatpresenttime,doesnotdependonanyfuturevalu
8、eoftheinput,thesystemiscausal.因为系统输出值y(n)目前时间n,并不依赖于任何未来值的输入x(n),系统是因果。(c)Consideringthatthesystemislinear.该系统是线性的(d)Assumethatanewinputis.Thesystemresponsetothisnewsignalisgivenby假设一个新的输入。系统对这个新的信号产生的响应为.Thisimpliesthat.Thus,thesystemistime-invariant.这意味着。因此,该系统是时不变的(e)Becausethesystem
9、outputatpresenttimedependsonthepresentandpasttimevaluesoftheinput,thesystemisdynamic.因为系统输出当前时间取决于当前和过去的时间值的输入,系统是动态的。Solution:(2)Thesystemisdefinedby.(a)Foranyboundedinputsatisfying,wehaveThereforethesystemisstable.(b)Becausetheoutputvalueatpresenttimedoesnotdependonanyfuturev
