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1、Chapter2ProblemAnswers2.1Twosequencesandare,respectively,givenbyand.Findthesequenceofthesample-addedsumoftwosequences.Solution:Thesample-addedsumisgivenby.2.2Findthesample-accumulatedsequenceofagivensequence.Solution:For,thesample-accumulatedsequenceisgiv
2、enby.For,wehave.Thus,thesample-accumulatedsequenceis.2.3Assumethatasequenceisthesameasthatinproblem2.2.Determinethefirst-orderforwardandbackwarddifferencesequencesof,respectively.Solution:Thefirst-orderforwarddifferencesequenceisgivenby,andthefirst-orderb
3、ackwarddifferencesequenceisgivenby.2.4Determinewhetherornoteachoffollowingsignalsisperiodic.Ifasignal,inthecase,isperiodic,specifyitsfundamentalperiod.(1)(2)(3)(4)Solution:(1)Considering,andtaking,weseethatthesequenceisperiodicwithperiod.Solution:(2)Thiss
4、equenceisperiodic.Since,wecantakeandobtaintheperiodofthesequenceas.Solution:(3)Considering,andtaking,weseethattheperiodofthesequenceis.Solution:(4)Since,isnotanintegerforanyintegervalueof.Thus,thegivensequenceisnonperiodic.2.10Foreachofthefollowingsystems
5、,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，和（E）无记忆。(1)(2)(3)(4)(5)(6)(7)Solution:(1)Thesystemisdefinedby.(a)Consideraninputwhichisboundedby,thesystemresponsetothisinputis
6、determinedas(考虑一个输入x(n)=u(n)这是有界的x(n)
7、
8、<=B=1,系统响应这个输入是确定).Becausethesystemisunstable.系统不稳定(b)Sincethesystemoutputvalueatpresenttime,doesnotdependonanyfuturevalueoftheinput,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)Consideringthatthesys
9、temislinear.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)Becausethesystemoutputatpresenttimedependsonthepresentandpasttimevaluesoftheinp
10、ut,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
