Chapte2 Poblm nswers2.1 Twosequeces and are, resctvey, given byand .Find thesquence of the saple-ded sumofto seuncs.Soltion: Thesampl-adde smis give .2 Finthesmpl-aumulated seuene of a genquence.Soltion： For ,th ampl-cumuat suence i given b or ， w have.Tus， the samleaccumated sqencis.2.3uth a equence s e ae s that in problem2.2. Dermine the first-order forwrdan barddiference equencesof , repectivelySolution: The firs-order forwarddfference unce i given by，n th fs-ordard difrence squenc is en .4 Deermi whethr r noteh of folowing sigalss periodic. Ifa sgl,in h ae， is erioi, speifys undamtal perid.()（)(3) (4) Sltio: （1) Conideig,and taking ,we see thtthe seque isperdic with prio .Sluti: (2)Thissquece i iodic Sc，wecnak andoba he p of th sequenc a .olution： (3) Conidering,ntaking,we eethatth perod of the equce is Solin: (4） Snce, isnot integ fo ay iteger alue of. hu, thegieneuen s nopeidic.2.10For eh of he flowing sytems, dtrmine whether he sstem is (a) stable， (b) causal, () linear， （d） timeinvarian, and (e） emorlss.下列系统,确定系统是否(a)稳定，(b）因果,()线性,(）时不变,和（E)无记忆。 (1)（) （3） () （5） (6) (7)Sluton： （) Th systm isfinedby .(a) Cnider aninput icbounded by , the systemspnse o ti inpu is detrmined as(考虑一个输入x（n)=u(n)这是有界的x(n) = B = 1,系统响应这个输入是确定).ecauseth syem s usble. 系统不稳定() Sin he systemouput alu at presen time, does not depend on n fturvalue f the inpt , e ssmis cusal.因为系统输出值y(n)目前时间,并不依赖于任何未来值的输入(n),系统是因果。 (c) onidring thathe se liner.该系统是线性的 (d) Asue ata w put s . Thesstem resose othis newsial s gven 假设一个新的输入。系统对这个新的信号产生的响应为 .Tis imls ha . Tu, tsystem istime-ivriant.这意味着。因此，该系统是时不变的(e） Becausesystem oututat pesen tm depndso the pesent and pas ie vlues ofthe nut, the sysem is dynam.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。Solutn: (2) e sysem is efined by .(a) or anyboue iutsisfyg,we aeThereforthe ys is stable(b) Bcase the otpt vaueat prsent ime doesnodend on an futurevlueofthe inu,thesystem i usal.() Cnidrng tatth smis olinea.（d) Let he sytem respose tothis nw signal s v bywhich satisis . Thus,th system s timnvan.(e) Bause te een outpuae ees only o thepesent alue of the nt, the system is mmorylesSolu: (） The sseis fined y .(a)If anip saisies ,thn.Tereoe thsstemis tabl.(b) ecase the presnuput value is unate to anfure ipt ale, th systems causal.（c) onsirig thaWe see htthe syte is line.() . The ystem respone tohis ne gl is gvey.hismeas ht Tus， the systemis time-varing.(e) inc te resentoutput alue epends nly onthepresnt vaue f e inpt， te system is moyless.Sotion: () osierg thathe systeis dned y .（a）Letteiput of te system be wic is undd y . Fr and , thsstmrespns to thsit i dtermined asor both case, havThushe yem sunstab(b) A h defiitn f the sytem,weaways assum tat. Therfor the prsenouuvaue does ot eend onany fuure valueof te nput This means tha theysem s causl.() Becauseth sytem sline.(d) Let .Thessem reone otis ew sgnals gve by.euse, the sym is timevayig（e） Genall, hprsnt output vale is late to th inut vaue t other me. Terore, theyse is dynamc.Souion:(5) Cosderintht the system i ined (） For bouninpt whichsatisies , we hae.Therefo,i , he . This ws hat theytem is tbe.() Bease he peset output valueisunlated toyfuurevalueof heiput, th sysem is usal.(c) CondringhtWe tht hestems inar() Le . he systmrespose t ts e ignal s given y.Bcase, the syem is ime-vaing.（e）Since he pesetotp aue deped only onthepreetinptvle， thstem is mryes.Solio： ()onsierngthat te ystem is efiney (a） If, then.Thus， thsystem istale.(b) f, hen heprset output alue sunretd o the utureinput valu. Ths the syst i ausal. therwise, the system inoncausal.(c) Becasete systm is lear() Ltting, e v.T,the syemsis meinvarit.（) If , he the ouuval depends nlyo th esent nput value，i.e., t