七年级上册英语unit8公开课课件

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1、3.51T{&[川一ad[n-R}=H{e^)=I-ae~^R.Leta=

2、a0”.ThentlieniaxiinimivahofH(eJ(d)is1+aandtheminimumvalueisI-a.ThereareRpeaksofH(ejcy)locatedato)=2nk/R.0

3、itheaboveplotsthatHA)isaliiglipassfilter,whereasHs3®)isalowpassfilter.(b)Hc(e^)=HB(e^)=円仆川")).(3.47)4.3(町Now,theCTFTofV](Z)isgivenbyFj(jQ)=—Ga(jCl)®Ga(jQ.)where■2kGa(jCl)denotestheCTFTof^a(t)and©denotesthefrequency・doinaiiiconvolution.TheliighestfiequencypresentinVj(Z)isthereforetwicethatof^

4、a(t)andhence,theNyquistfrequencyofVi(Z)is2Q(b)TheCTFTofV2(0isgivenby迨(丿°)=Jdt—co=3Jga(T)«一丿•八=3Ga(J3Q).Thehighestfrequencypresentin(/)is—CCthereforeone-thirdofthatof仃)andhence,theNyquistfrequencyof匕仃)is心/3・OQ(c)TheCTFTof旳⑴isgivenby^(JQ)=jga(3t)e~^tdt-CO二一jga(T)e~J工■山=_Ga(j—)・Thelugliestfiequ

5、encypresentinis—GOthereforethreetimesofthatofg“(/)andhence,theNyquistfiequencyofis3%(d)TheCTFTofy^(t)isgivenbyGO■"1f"■丫4(丿0)=JJga"-T)ga(T)〃Te~jCltdt=jga(T)jga(t~dtdx-00-CO-00—00=f^(T)^~yQTGa(JQ)^T=G«(Jn)lga(^e~jQXdx=Ga(J^)Ga(J^The-co-00highestfiequencypresentinV4(Z)isthereforethesameasthatof

6、gd(f)andhence,theNyquistfiequencyofy4(r)isQm.(e)Nowga(')=—[Gq(丿0)2°1/£1Differentiatingbothsidesofthisequation2兀—COweget『丿GGq(丿Hence,itfollowsthattheCTFTof-—co了5(『)=驚⑴issimplyJQGa(jQ).Thehighestfiequencypresentin门⑴isthereforethesameasthatofga(t)andhence,theNyquistfrequencyofy5(Z)is(4.3)4.1One

7、possiblesetofvaluesforthefiequenciespresentinya(f)are:F-350HzFi=575Hz,心=815Hz.and=9650Hz.Anotherpossiblesetofvaluesforthefrequenciespresentinya(t)are:斤=350Hz,=575Hz.=815Hz.and耳=10575HzHence,thesolutionisnotunique・(4.7)4.15Gq(s)=——・Thus,Ga(jCl)=.andhence,s+ajC+a

8、Cn(jQ)

9、2=Ga(jO)Ga(-jQ)=——AsQi

10、ncreasesfrom1丿G+a-丿G+aq2+«29themagnitudefiinction0tos,itcanbeseenthatthesquare-magiiinidefiinctionG°(andhence,Ga(/Q)

11、二/Gincreasesmonotonicallyfiom--cGf/(yO)=0to=1.LetQcdenotethe3-clBcutofffiequency.TlienG<7(/Qc)

12、*_二2笃=_，whichimpliesQc=a.(4」2)4.26lO