7(1)h(n)=2nu(-n)(4)h(n)=(—)wu(n)2(2)h(n)=-aMu(-n-l)(5)h(n)=—u(n)n(3)h(n)=0(6)h(n)=2"Ru(n)00/(1)=ºᙠn<0áh(n)=2"#0,ᦑÅklU=¼kl0000=ºS=2lh(n)|=Z2"I=l<8,ᦑÅkl»kl=-0077=0(2)=ºᙠnீ0áh(n)#0,ᦑÅklU=¼kl00-]00=ºS=£|h(n)|=ZIa"|=2a-",ᦑÅklÈᨵᙠ|a|>láé»kl=-00”=-00=00(3)=ºᙠnீ0áh(n)#0,ᦑÅklU=¼kl0000=ºS=Zlh(n)|=Z|J(n+n)|=l<00,ᦑÅkl»kl0?4=-<»”=-00(4)=ºᙠn<0áh(n)=0,ᦑÅkl=¼kl=ºS=£|h(n)|=£|(ê)"|<8,ᦑÅkl»kl(5)=ºᙠn<0áh(n)=,u(n)=0,ᦑÅkl=¼kln=ºS=X|h(n)|=y|-u(n)|-VL=8,ᦑÅklU»kl11=~coM=-OOn=0(6)=ºᙠnீ0áh(n)=O,ᦑÅkl=¼klooN-\=ºS=£|h(n)|=Z|2"|=2'T<8,ᦑÅkl»kl=co=02.9íîy(n)-2cospy(n-1)+y(n-2)=0,ïy(0)=0,y(1)=1,ð±y(n)=ᵫ("4)sin(3±½⚪òóôõᑖöḄᱯøöºa2-2cosp•a+1=0ùᱯøöð;ᱯø᪷a]=cosQ+jsineaücosQ-jsine~^óôõᑖöḄý/ºy(n)=c[a]”+c2a2=c1e/+c?e+,
8þᐭÿ ᩩy(0)=c+c=012y(l)=c,e7/?n+ce-j7?n=l2ᵫᑮ111-2sin£'02"-'sincτc2ᐭᨬᑮy(n)=c,e-+ce-=—?—(e+e-)="32'22sin/?sin£2.10!"y(n)+2ay(n-l)+0(n-2)=0,#y(0)=0,y(1)=3,y(2)=6,y(3)=36,$y(n)✌ᐜᵫ' ᩩ$()*+,ᦪab[y(2)+2ayপ+/(0)=6+6a=0ᵫ<[y(3)+2ay(2)+by(\)=36+12+3/?=02$(a=-l,b=-8345)*6y(n)-2y(n-l)-iy(n-2)=0ᵫᱯ8)*a2—2a—8=0$ᱯ8᪷a]=4,a=-22:;<ᑖ)*6y(n)=c,a1"+c2aM=cj4M+c(-2")22ᐭ' ᩩy(n)=c,a]+c2a=4a]+2a=322ᵫ>ᑮ11C]=?,c=——12222c1c2ᐭᨬᑮy(11)=0,aτ"+c2a2"=J14"-(-2)"]2.11ᵨᱯ8᪷B⌴DB$Eᑡ<ᑖ)*Gy(n)-y(n-D-y(n-2)=0,#y(0)=1,y(1)=1ᵫᱯ8)*a2—a-1=0$ᱯ8᪷
91+V51-V5a.=------a---12226y(n)=c,ai"+ca2ᐭ' ᩩc,+c=121+5/5C1(—y-)+c211+A/51-$(275ᨬᑮy(n)=c21+V5„_,I-A/5,+11+1V52>/52V52.12?,TḄ᪾WWP2.12ᡠZ[$\,TḄᓫ^_᪵abh(n)ᓫ^▤dabBᵫW2"y(n)=x(n)+£y(nT)6$ᓫ^_᪵abex(n)=b(n),34ᨵh(n)=8(n)+/7h(n-l)ᵫgᑮ"h=u(n)▤dab6
10y(n)=h(n)*u(n)=Z*“y(k)u(n-k)«=ol_0»iu(n)If2.13,-ᑡx(n)ḄᏝ01 ᣚX(e6'),'3ᑡᔜ-ᑡḄᏝ01 ᣚ(1)F[ax,(n)+bx(n)]=aX(e>u)+bX(e}H)2l2(2)F[x(n-k)]=e->x'X(e>)(3)F[eM"x(n)]=X[e"i)](4)F[x(-n)]=X(e->)মF[x*(n)]=X*(ef)(6)F[x*(-n)]=X*(ew)(7)(8)jIm[x(n)]=l[X(e>)-X*(e->)]2(9)8X(e)*X(e/w)27r/ஹdx(")(10)j—~~-dw2.14, ;<Ḅឋ !ᵫ3ᑡ>ᑖ?@ABy(n)--y(n-1)=x(n)+—x(n-1)22(1)'C!Ḅᓫ᪵h(n)(2)ᵨ(1)EᑮḄG<'(ᐭx(n)=e*"I!Ḅ(3)'!Ḅ⚣᳛7T7T(4)'!L(ᐭx(n)=cos(Nn+N)Ḅ24(1)eX(n)=8(n),ᑮh(n)-h(n-l)/2=8(n)+6(n-l)/2
11ᵫ34Ḅឋ,Tᦑᵫ(h(n)=h(n-l)/2+8(n)+6(n-l)/2,nNO⌴D(h(-l)=Oh(O)=h(-1)/2+6(0)=1h(l)=h(0)/2+l/2=lh(2)=h(l)/2=l/2h(3)=1h(2)=(1)2h(4)=1h(2)=(1)3h(n)=8(n)+(g)n"u(n-l)ᡈh(n)=(1)n[u(n)-u(n-l)]2<ᑖ)*ᵨᓫ^⊤Zᡂ(1-D)h(n)=(l+D)8(n)ᵫgᑮh(n)=[(l+D)/(l¤D)]6(n)=[1+D+1D2+(i)2D3+...+(-)k-'D3+...]622222=6(n)+8(n-l)+-8(n-2)+-6(n-3)+...+(-)k-18(n-l)+,,,222=8(n)+(1)nu(n-l)2)X()=e""'ᐭy()=x(n)*¥()ᑮ
121+-£>-b(n)]1--D21+-D=——2ߟe"1--D2¨1++"ᑅ2(1Y'-1£)ஹ+ +|—D"+••••_2প'(-1)^jJwn.c-eH---------21\+-e-JW=>wn_2----e12(3)ᵫ(2)(1\+-e-JW2(4)ᵫ(3)2",.1.1~J^W(wஹ1H—eH4=2=1I11-5,2■(,wY|0iri-j~argHrje2=arctan1+—e2-arctan1——e22J[2°,m=-2arctan—y()="(e"]c()sy«+^+arg[H(ey,')]ᦑG7171-cos—+---2arctan—24[22.15O;<ឋ !ᵫ3ᑡ>ᑖ?@AB
13y(n)-ay(n-1)=x(n)-bx(n-1)PQRST!ᡂᐰW!ḄbX(bWa),ᡠYᐰW!ᢣᐸ⚣᳛Ḅ\]⚣᳛^ᐵḄ`ᦪḄ!Gex(n)=6(n),ᑣh(n)=ah(n-l)=^(n)-b8(n-l)ᡈh(n)=ah(n-l)+®(n)-®(n-l),n^Oᵫ34ឋḄ,Tᦑ´⌴D(Gh(-l)=Oh(O)=lh(l)=ah(0)-b^(O)=a-b2h(2)=ah(l)=a--ab32h(3)=ah(2)=a-abh(n)=ah(n-l)=an-a"1b,n^:0h(n)=a"u(n)-anXbu(n-1)ᡈ,TḄ⚣᳛ᱯឋ6H©3)=24=_g[a11u(n)-a**-1bu(n-1)]=Zf=oane-i3_bEjanTe-j31bera=l-ae-iw°l-ae_iwl-be-^=l-ae-jw·¸Ḅᱯឋ¹)1-be+2|H@3)|2=l-ae-i^(lbe-j3)(ibej3)(l-ae-iw)(l-ae>w)=
14l-ber3-b23+|b2|=l-ae-jw-aejw+al2He-Fe^+l|b|2^-^——-----=l-ae-j3-ae-j3+|8|211º⌱_a=7ᡈb=/,ᑣᨵ|H(e/w)|2=|b|2,ᓽ¸½ab¾3¿⚣᳛abÀᐵḄÂᦪᦑ\,T6ᐰ,T2.16(1)?Äឋ,TḄᓫ^ÅÆab6h(n)=a"u(n),ᐸ+a6Èᦪ#OீaீlÊËᐭ6x(n)=B"u(n),Ì6Èᦪ#0<£<1.[ᑭᵨឋᔁÏ,TḄË(y(n),ÐÑᑏᡂEᑡÓy(n)=(ka"+k")u(n)12(2)ᑖÔx(n)ஹh(n)প+$Ḅy(n)ḄᏝÖ×ᣚX(e'“)ஹH(e)ஹY(e'"')ÐÚÛY(e>)=H(e>)X(e>)8(l)y(n)=Eh(k)x(n-k)k=-co=y^aku(k)J3'u(n-k)k=-cc>>|£ÝÞ)ஹ’àTaáâ]£i-ᶭ=O'p,n201-ᶭy(n)=(/T)u(n)1—01—0s1ফXO&L=-èéé=oi?HH(eê)=Xa:=—L-=o1aewaBY(ew)=g(———;᮱)1n=oa-Ba-B=—!—(ߟ--------)a-(3\-ae-]0>a-pe-1'0
15ᵫb—1-í-"_________1=X(e>)H(e>)(1—aefQ->rmᦑ(Y(eiw)=H(e)X(e)2.17ex(n)X(e7")ᑖÔ⊤Z?ÄîïðᐸᏝÖ×ᣚÚÛGZx(rt)x*(n)=—rX(eJH)X\eJKñ2ᐔ%g4òóôõ(Parseval)öᳮḄ?øÓÚÛGÚB?
16X(eJwn)=Z00X*(e)=(Zx*(N)ejwn)*Xx*(")eJwnn=-oon=-oo1X“)X*(e)dw271ᑍ001x(m)e-jwn][£X*(n)e/u]dw271n=—ooITஹ1tZX()ZX*()eJW(n-m)dwm=-co2ᐸ+717C—27C,♦ • mejw(n-m)dwjyv[n—nt)jw(n-in)--------=0,•…nwmnm130X(e)Xjw)dwZx(n)x*(H)2ûn=—ooÚB>:QOZX(n)x*(/?)n=-co£X()[ijw)e-jwndw]n--oo2n-n1XX(")[X(ej'')e'dw]1-Kn=-oo2711X*(e>H)Zx()e-jwndw2711-nn=—oo1ᑍX(ejw)X*(ejw)dw2n-712.18ý◤⌕ ▲ᵨᦪᘤP2.18ᡠT⊤ ᪵ᕜ!Ꮇ#T$%&'■)*+ᜫ-./X(t)ᑮy0(t)Ḅ;<=>ᦔᡂA;ᘤJI1(1)Bᦪᘤh(n)ḄE)⚣᳛>H'rad,-=10kHz,S;<=ḄE)⚣᳛T,USV8TᳮXYZᘤḄE)⚣᳛fe(2) =20kHz,[\(1)Ḅ]^T
177T_ᳮXYZᘤḄE)⚣᳛A(`a/c)ᢚᔠᡂᦪf⚣᳛gh(`a)ijᦪᘤh(n)ḄTTTITE)⚣᳛A(`a)⌕ᜧᦑ;<=ḄE)⚣᳛ᵫᦪᘤh(n)ḄE)⚣᳛A(`a)ᩭpqr88ᐸᣚ^ᡂu▭⚣᳛ᓽr£==10000Hzᐭ2A=?,|}ᑮ~=625HzTTTTᳮXYZᘤḄE)⚣᳛(`a/c)ᣚ^ᡂu▭⚣᳛}ᑮTᓽᵫᐵ=2f,}ᑮc,110000„f.=——=-----=500HzMM2T22.19SᑡᑡḄZᣚᦈf(1)8(n—m)ফ(“(”)(3)au(-nT)(4)(1)"[H(n)-M(n-10)](5)cos(a)n)u(n)[)_¡(1)X(z)=£6(/-m)zn=znm1¢m>0x(n)¥¦Bᑡᦈfg0<|zlW8,«¬g0(m▤)°¢m<0'x(n)¥⌮¦Bᑡᦈfg0WIzIW8,¬g0(m▤)«°¢m=0,X(z)=l,ᦈfgOWIzIW8,´«¬µ«ফXফ=X(£fu(n)z”=f(JZ7)=—]—n=-oo\)n=0\J11-2ZX(n)¥¹ºᑡiḄZᣚḄᦈf¥»¼gR¾ḄᙊḄÁÂfÃÄx(n+1)_1Rஹ=lim“TOOx()2T(n)Ç¥¦BᑡÈ'ᨵIzI=8,ᦑᦈfgIz|Ê8¬g0,2
18X(n)Ç¥¦BᑡÈ'ᨵIzI=8,ᦑᦈfgË<|zI<0°o¬g0,gÍ(3)228—00x(z)=ZDz"=Z("Z1)"n=oon=-\—008,=£(Jz)"Í3“)"=1"=Tτ=-i=\az\-aznnX(n)¥ÏºᑡiḄZᣚḄᦈf¥»¼Ð&+ḄᙊḄᑁÁÂfÃÄ&+8 1x(-(n+1))LUf1Q-+Dl=ldx()Ç¥⌮¦BᑡÈ'ᨵlzl=0,ᦑᦈfgOMzIMal¬g0,gÓ(4)X(z)=£-j[u(n)-u(n-10)]znn="ooÕÖA×-(2z)7°-SI2JZ-1—(2z)TX(n)¥ᨵ▲ÙᑡÚiḄZᣚÛᨵÜÝ⚗ᦑᦈfg00M(5)X(z)=Ecos0o)i/5)z=S-----------------z/I=-00n=ooZ001001=oZ«=oD111__(--------H---------)=21-eJW°zl-e~JW°z1--Icosw01A2z"cosw+z-20x()¥¹ºᑡiḄZᣚḄᦈf¥»¼gâ-ḄᙊḄÁÂfÃÄ
19%(+1)¾Icos[w(H+l)]0HPX(n)=1å1cos(ᔩç=1x(n)Ç¥¦BᑡÈ'ᨵτZ1=00,ᦑᦈfg14ZK8,¬g(JCOSW,ojwAoÓ"ogeeo2.20SᑡᑡḄZᣚᦈf¬ᑖë(1)x(n)=alHl,02011—X nᑡḄZᣚḄᦈ RḄᙊḄ!"#$Xx(+l)R_=lime°XX-»ooX(71)I_τeii/e+x,n-.ᑡ/0ᨵ14=°0,ᦑᦈ eீ4W867 0,7 e00X(z)=£Ar"COS(G0+*)"()[-"71=-0000----------------------------zߟ"H=0nApjv>oo?0-j=2,——£+———£(re…z2=02=oAe"]Ae-"]21-reMJ21-re~i(0°z~x-j(co-(O)./(6?-69)\-1.-i(pAren+rez)z+e~21-rz-1(eK+e-*)+r2z-2cos(p-rz~1cos(&)-(p)()=A1-2rzcosco+rznQߟX nᑡḄZᣚḄᦈ /?3—ḄᙊḄ!"#$Arecos[69(n+1)+]..x(n+1)0Rxlim--------------=lim-8x(n)”faA,”COS(69+9)015-.JKᑡ/0ᨵ|z|=8,ᦑᦈ |H21Y1—nᔞZx(z)="—U(")z=Z-----(4)=R°°”Yn=0n!-11-21-31-n=1+Z+~2TZ+3"]Z+...+-^Z+...1xRX(n)ᑡḄZᣚḄᦈ _ḄᙊḄ!"#$x{n+1)RY_=limlim=0An-»oox(n)7?—>00X(n).JKᑡ/0ᨵZ=8,ᦑᦈ 022sin°+sin(%ROz~ll-2cos+2R,x()ᑡ,ḄZᣚᦈ 4ḄᙊḄ!m",#$x(+l)sin[w(n+1)+0]07?=lim-lim——-——P------r——-=10…n…sin(wJ0/j+x().JKᑡ,ᜧᦑᦈ 1<ম<8.67 0Us"pq,7 sincos%+jsinwUcosw-jsinw.0002.21ᵨstuvwxᑡZᓄḄ⌮ᣚ(1)X(Z)=ߟ{—,|z|<-14z-I22(2)X(Z)=-Q2_||>-(Z,31_2l+-z+-z248(3)X(Z)=>l|Z|>|a-'|Z-'-a|(1)}ᵨ~ᦪvᵫᦈXI(n)ᑡJ limX1(z)=l ᨵ▲ᡠ0X|(n)Xfoo⌮JKᑡᵨ◀vX1(z)ᡂᦪᓽXτ(z)—{=2z-4z2+8z3-16z4+21z5+...+(-1l21"+…=£(-1l2ᨌ"=£-(-2)"1n=
23=]ᨬᑮX](n)=~2(-2)~n,n=T,-2,-3...X](n)=_(_{)(-R1)ᡈ
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25/()=Res[x^z)z'-',1]=(l-a-1z)z"-1(a2-l)a-n-',n>0±n=0²¯®°ᦪᙠ¬¶ᑁᨵ©¹7z=Uz=0,Jºx=Re"বz"R¾+Res[X3(z)z“T,0]3=(ߟ£)11+¿—(1—ci~)ci—a=—a',zt—0±n<0²J ÂÃ11ᙠ¬¶c7ÄX3(Z)Z"Tᙠz=ooᜐᨵl-n)2▤7ᡠ0ᨵÇ()=0,n<0ᨬ|☢-1)ᨌ"-|,>0x(n)=<-a~',n=030,n<0ᦑX3(n)=(a22.22wxᑡZᣚḄ⌮ᣚ(2)X(z)=,0.5<|z|<2(l-0.5z-1)(l-0.5z)বX(z)=τ2lz|>e"z-|—I—IxZ(4)X(z)=Z(2z—“—b),|a|<|z|<|b|(z-a)(z-b)|(4)}ᵨ!ᑖᑖvX4(z)=,
26᪷Ëᦈl0(l-0.5z)z=0.5/|z|<2ÍÎÓR¹⌮JKᑡᓽn20²x(n)=0;n<0²¯®°ᦪᙠ¬ᨵ1¹72,Äᑖ×Ø⚗Ḅ▤ÚᑖÛØ⚗Ḅ▤Ü2—(n+1)=l-n>2,ᦑx(7i)=-Res[X(z)z,_|,2]55(z-5)z"=-2"+,n<0"0.5n-1ᨬᑮ-6Þß0%()=«-2,,=+l,n<0ᡈ%()=-}ᵨᶇᦪᳮv¯®°ᦪc~'znX,(z)z"Tz-c~r᪷Ëᦈlzl>c"/0´⍝ÍÎḄᑡR¹JKᑡᓽn<0²ᙠx()=0²ᙠ20²¯
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541H('X(z)l-2rcos6,z-1+r2z-'____________1__________~(rz-l-e-J0)(rz-'-ej0)ᵫd1ç`¾&=re1° Z2=re~16éêH¾ᵫᡠḄéêᑏ 5ØW(z)=X(z)=(rsin6)z'Y(z)+(rcos'W(z)জK(z)=(rsinO)z-Wফ+(rcos8)zTy(z)ঝû1জ551/33/4Z-1/8(2)cdney()(3)\ὶex(ri)c------>——c-----------►-----------•------->----------•------->----------c----------->----------•------->-------9y(n)-\-\uZMZ0--------------<-------9------->-----------------------------------1/41/31/2g ᦪᑏᡂ1+9]"ব=ߟ7—Xߟk—42(4)^ὶex(n)-7/3y(n)C----------->----------C----------►----------C-------------->----------C------->----------C--------->----------3-1-z--------------<------------v1/4u10/3
561/2g ᦪᑏᡂlᑖᑖ S -7/310/3”(z)=-i--i-1&oTJ/4.4ᵨcdτe/cdneq᪀stuF ᦪ;-5+2z--0"2পH(z)=1+3k+3o+oফH(x)=0.2^+2?+2Z+58z+4j+3z+2f(D᪷| ᦪᑏRHᑖJK)Y()+3y(-1)+3y(&2)+y(n-3)=&5x()+2x(-1)-0.5x(&2)cdIeq᪀0᪷| ᦪᡈHᑖJK ᑮYXᡠy(n)gcdIeq᪀?\ὶ Ḅᣚ,^ḕᔣ23Ḅ?ᓫᘤY ᑮFXᡠḄcdHeq᪀x()y()
57-32-3-0.5z~}-1(2)ᵫ ᦪᑏRHᑖJK2y()+3y(-1)+4y(-2)+y(n-3)=4x()+1.6x(&1)+1.6x(-2)+2Ax(n-3)ᡈ)Y()+1.5y(-1)+2y(&2)+0.5y(/?-3)=2x(n)+0.8x(-1)+0.8x(&2)+1.2x(-3)᪷| ᦪᡈHᑖJK ᑮFXᡠḄcdIeq᪀ḄUVWKXx(n)2y(n)C---------►--------(>--------------1J--------->-------------(>---------(Z-'z-10.8-1.5rQz-1,,Z-10.8-2$Qz~''[T1.2-0.5j---->----()(1---------iᣚcdieq᪀?\ὶ ḄY^3?ᘤᐳᵨY ᑮFXᡠḄcdneq᪀ḄUVWKXx&yrz~]-1.50.8*(<>---------------------(1---->------4>
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5912.346x()yW-3.9780.5-3.5661.2728-4.858-0.814.6P¬®FIR±²ᘤḄ³´µ¶ᐹᨵZ¸ឋ¹Yᓽh(n)=-h(N-l-n)Yᐸ8ᐹᨵᑖ¾BឋḄឋ¹,ᓽ/\/N—1ஹ71=&(-----)+&ᐹᨵ(1)®N¨ᦪY±²ᘤḄÁµ¶¨(N-l)/2H(co)=Zc(Y2)sin(/H)"=iN—l(N-1)ᐸYc(n)=2(-------)Y"1,2,•••,--------22(2)®N¨ᏔᦪY±²ᘤḄÁµ¶¨N/2τH(co)=Zd()sin3(Ä——)]n=\2NNᐸYd(n)=2/i(----ri),n=l,2,—,&22Z[uÆÇÈYÁµ¶/8µ¶ÉBXP4.6ᡠË()ft??«N-1K%111n
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700.91ll8”“(s)=N3tlDDU(sF(T)k=00.47483nb—G+sQs+s"]k=O__________________________________0.4748________________________________"(r-0.3556.v+0.83)Gv2-1.01245+0.83)(.v2-1.5155+0.83)(?-1.7872.V+0.83)___________________________________0.4748_________________________________-s8+4.67?+10.90556+16.536?+17.754+13.715?+7.515?+2.67h+0.475(5)ᵨû⊤"ïðñᦪH“(s)᪷þ⊤[ᑮ8▤ÿ ᓄᱯᘤḄᦪ”(s),1“মߟ8+5.1258i713.137h6+21,8462i5+25.6884/+21.8462i3+5.12585+15'(s)(sᵨ*•=-./0(s)1Q,0.9111"Hব=________________________________04748________________________________“§-58+4.67.y710.905.y6+16.536.V5+17.7.V4+13.71553+7.515.v2+2.67Is+0.475<(4)=>?@4.13BᵨCDឋFᣚHIJ KᱯLMᘤᎷO-᪵⚣᳛£=1.5kzᜐ⊦XYZ12dB]'^/•_f`ᣚᡂᦪb⚣᳛%_gTO,/=2f^/=2^x1000=2000iOr=2fk=2fx1500=3000f11T=10^f10xl03a%—TCl-10^*x2000f=0.2fpcu-TQ7.=104x3000f=0.3ir(2)oᘤḄ▤ᦪN_ᱯrsLMᘤḄ3dBtu⚣᳛Q.-T=l,'ᦪb⚣᳛v_=⚜ᶚF/0⚜ᶚFyḄ._Q
712জp,,10.2fQ=tan=2tan=2tan(O.l^)=0.649841PT222co0.3fQT=tanT=2tan=2tan(0.15i)=1.01905371T22z{/rsLMᘤḄᢣ᪗~20 |=201g|H.649841 |>-1.8<201ghk201g0190537 -12ᵫᱯᘤḄᦪ0201g|//(jQ)|=-101gl+A2Wঝa'ঝ.ᐭজ/0201gH(j%)|=—101g1+("-L8ঞ201g-101g1+(10°537>,ট12ὶo]ঞ_ট/0NNI?"=47305515=3.7389420.649841-0.19538998J.0190537J-N=4'N=4ᑖ.ᐭঞ_ট/0__1_Q,>0.649841(10°1X18-1)^=a=0.7063rl__1_Q,<1.0190537(10°1x12-l)-^=Q,2=0.7274-5=gg“+Q,2)=0-7168¡¢£¤¥ᵨ¦ᩭoN_Q,,¨©ª«/¬CDឋFᣚHᩭ/¦(Ḅ_®¯⚜ᶚFyḄ°3o”.sḄ²Sk=³´/0.7168/%µ,k=0,l,...,7ᐸ(/·¸s☢Ḅ²~.5%=0.7168J?"=—0.2743+J0.6623(%+º)»=0.7168/8,=-0.6623+70.27435=*=-0.6623-jO.274325|$3=%*=-0.2743-.6623
724oᦪH“sHa(s)=Q---------------=n---------------¿Gf)DU(f)GFk=0_0.264“[$2 6+sj)s+.%.%*]k=0_____________________0.264___________________—(§2+0.5486s+0.5139)($2+1.3246s+0.5139)=_________________0.264_________________-s4+18732d+1.7545/+Q9626s+0.264(5)ᵨÄ⊤Hoᦪ”“(s)᪷Ç⊤0ᑮ4▤É ᱯᘤḄᦪHspa“"মߟ54+2.6131.?+3.4142.r+2.61315+1'""'G(ḄsᵨÌ-./00.7168H(s)=________________________-_______________________1/+2.6131Q/+3.4142Q2?+2.6131Q3s+Q4cccc__________________________________0.264~/+2.6131x0.7168?+3.4142X0.7168253+2.6231X0.716835+0.71684=_________________0.264_________________-54+1.8731?+1,754252+0.9624s+0.264<(4)Ḅ=>ÎÏ?Ð4.14ᵨCDឋFᣚHIJ KᦪbᑗÒÓÔLMᘤ/ᔜᢣÖ<⚪4.13?@]4.15MØ⚣᳛FᣚHIJ KᦪbᑗÒÓÔÙMᘤ/rsᑮᦪbḄ`ᣚÚᵨCDឋFᣚH/ᎷI-᪵⚣᳛~2.4kHz/ᙠ⚣᳛160Hzᜐ⊦XYᜧZ3dB,ᙠ40Hzᜐ⊦XYZ48dB]1'ÙMᦪbᘤḄ⚣᳛ᢣ᪗_fᢚᔠᡂᦪb⚣᳛T2_2^x160_2"”=TQ/,ßf~152400s.^fr.2fx40_71(Dj=TC1=T240030
73IT=2,ᢥ᯿CDឋFᣚH/'ÙMᦪbᘤḄᦪbâ⚣᳛`ᣚ~ÙMrsᘤḄ⚣᳛2%12fQ-ß—tan—=tan(—x——0.2126pT22152co17TஹTzQT--tan—=tan(—x—)=0.0524iT2230'ÙrsᘤḄ⚣᳛ᢣ᪗æᡂrsL@ᘤḄ⚣᳛ᢣ᪗114.7040%Q/-0212611Q=19.0840çߟ005242᪷ÇrsL@ᘤḄᢣ᪗o_N£2=10,_]=io°lx3-l=0.9953ᡈ£=0.9977Q,=Q,=4.7040,Qp4.7040…/uk=—=-------=0.2465Q19.0840z1O01"-11in01x3-1-1=1——í*—7^-]2=3.9717x10-3-1100|x48-larch1-arch1N>d-3.9717x103arcdarchLk0.2465525L7814_2994]tzrc/i4.0568-N=33orsLMᘤḄᦪð/'ᐸ.ᐭ3▤ᑗÒÓÔñ⚗Ḅ(4.7040=0.2126Qᓃ2(%)=[%(4X2-3)]2=16x6-24x4+9x2=16(0.21260)6-24(0.2126Q)4+9(0.2126Q)2=0.00148Q6—0.049"+0.4068Q2z{/3▤ᑗÒÓÔrsLMᘤḄᦪ~1õl+e2V2(Q/Q)3r
74_______________________1_____________________-1+0.9953(0.00148Q6-0.049Q4+0.4068Q2)___________________1__________________-0,00147Q6-0.0488Q4+0.4048Q2+1(4)orsLMᘤḄᦪ'= 1.ᐭ(4)÷/0___________________1_________________--0.0014756-0.0488/-0.404852+1ᵫøoùH“(s)H“(-s)Ḅ²5=-0.701+J4.25170=-1.4047^=^•=-0.701-74.2517S=0.701-J-4.25143S4=1.4047S5=.%*=0.701+74.2517ᐸ(s0,»_S2¯·¸s☢Ḅ3K²/ᵫûü᪀ᡂ KþOḄ3▤ᑗÒÓÔrsLMᘤ/ᐸᦪ~Haম=-------“B-------(S-S|)(S-SO)(S-S2)_________B_________(S-Si)(S-So)(S-So*)_______________B_____________(s-s)[?-Go+5*)5+55*]t000_________________B_______________"(5+1.4047)[52+1.4025+18.5684]zN=3~ᦪᡠ”"(0)=1,B=H(0)x1.4047x18.5684=26.083aᨬ„,ஹ26.083H(s)=---------------------------------"(5+1,4047)[52+1.4025+18.5684]26.083d+2.8067.V2+20.53855+26.083
75ᘤḄᦪᙠ s ☢Ḅ3 !"#ᵨ%&'(:s,——asin(-----1---k)+bQcost------1----k),k=0,l,…,2N-1kc2NN'2NNᐸ,-.a/bᵨ%ᑡ1&23a-e'x+Je"+1=0.9977,Vo.9977-2+1=2.4182τ1_11a^-{aN-aw)=0.5(2.41823-2.41823=0.5(1.3422-0.7451)=0.2986i_Lb=-(aN+aN)=0.5(1.3422+0.7451)=1.04374.=0.2986x4.7040=1.4046aQ=1.0437x4.7040=4.90967“Q,/bQ,Ḅ89ᐭ23!Ḅ1& s ☢Ḅ!%<7TTT5--1.4O46sin(-)+;4.9096cos(--)o2x32x3=-0.7023+J4.2518-i.4046sin(—+-)+74.9096cos(—+-)=-1.4046=2x332x33S2=s()*=-0.7023-J4.2518?@ḄABCD☢Ḅᦪ8EFGH(5)7ᘤIᣚᡂLᘤᵨ1/s9ᣚᘤḄᦪ,Ḅs,ᑮLᘤḄᦪNஹ23.083.V2H(s)=---------------------------------------“1+2.80675+20.5385525+26.08353r(6)ᵨOPឋRᣚS7LᘤUᡂᦪVLᘤWT=275=—'9ᐭLᘤḄᦪ1+Z-'26.083(Z )3H(z)=-------------------[------------------------------------------1—7-1—7—1--171+2.8067+20.5385(^^)2+26.083(^^)3i+r1i+z-1i+z-10.5172(1-3Z-,+3Z-2-Z-3)l-1.0293z-1+1.14821N0.1458z-3
764.16W%`bcN ᏔefgᑡN=8,jkP4.16`ab/%`bc4`bḄo!pqrsᓽub=u`"N4bb,/?6`b`1b'(x`bḄDFTCpḄDFT|}Ḅᐵᓽ|,`b|C42`Gs4`C`b|}Ḅᐵ`2bᵫ4`b/`b#᪀ᡂ FIRᦪVᘤPឋGsᦪVᘤᔩTT`3bB"`beN ¡⚣᳛¤ḄᘤkP4.16`bbᡠ¦§¨"`b"eN2TT ¡⚣᳛NḄᘤᔠᳮᔩ2kP4.16«`1b¬ShZg-l-/?b/x2`b=x2`%-1Nbᡠ³N=8,ᨵNT3_.2µ7_.23¶"|`Ab=Z%`b¸+Z"`be,8"w=0n=0M=432ᐗ.7.2zr,=£ub¼½+£u7-bM=0n=4-j—nk-j— 7-nk=Z45bÀe8+e8Án=oV",-j—nkj— n+\k=Z%`bÀeg+e&Án=0d-j->nk,.j2—TT.5+1 .¤"2`Q=WX`bÀe8+e8In=0ᵫ/%`b=/i2`3-bn=0,1,2,3
77ᡠ32K..2".v■ߟ~J—nkj—"i(%)=Z%2(3-)[e8+e8]n=0-j-(3-n)kj—8(4~n)k=£u)[&+e]n=0-j—4kj^^(n+\)k-j^-nk=e8Zᑘ()[e8+e81=o="Ï"(%)(2)4()/%()cᐹᨵefឋÑᡠcPឋGsᦪVᘤ=(N-l)/2=3.5(3)ᵫ(1)ḄABÒ⍝%()/%()ḄÔÕÖG×ᡠ#¨(¬)"eN ¡⚣᳛n/2Ḅᘤ4.17ᵨØÙÚW2N PឋGsLᘤᐸ,n-(o<(o")=[0,ᐸìWN=21,'h(n)Ḅ⊤â&ᐸᦪ8«7ᳮíᘤḄ¡⚣᳛ᣚ3ᡂᦪVî⚣᳛2^x1259=TQ,=2ß"=0.25ß1000ᳮíPឋGsᦪVᘤḄ⚣᳛ᱯឋ|^|<0.25)0.25ßீHWëÖḄᓫsò᪵Ö1M1(4).25ᐔ()=FLÛ(*)*"=£
78sin[0.25^(n-a)]_sin[0.25^(/?-10)]7r(n-a)%(N10)᪷û⌕'æçÚḄýÕN=2a+1=21,ᡠ⌕W2ḄFIRPឋGsᦪVᘤḄᓫsò᪵Ösin[O25"(-10)]x()=ß(N10)ᐸ,⚚)ᦪTT")=0.54-0.46cos(—)0<7i<20ᵫ!"ḄRR%&ᦪ'()ᘤᐹᨵ-ឋ/0ᡠ2h(n)ᐵa=73=10Ꮤ;<Ḅ>22020sin[0.25^(n-10)]"(z)=@(6"=ZGHF"=0"=0E(F10)202>$I'n=Osin[0.25)KLᔆ/L”/PஹஹL,,LLᦑa=------------0.54-0.46cos(—n)],0<<20—10)10ᑭᵨVWX"YZ!"ḄFIR()ᘤḄ]ᦪF_a-%()=0.00254648()4=~0.00256375=Q|8=0%==0.00866936a=a=0.02110671416a=a=0.024308545X5°6=%4=°a—=0.060799957g="i2~0.14517283e=41=0.22001165a=0.2510fgh5.1ijklmḄᙳoḄ-ឋឋpᓽW(5.16)rW(5.17)iE(%+y,„)=K(X+y)P%%(%xm)dxdy
79yVz5%(□ᐘMdx‘ᐸzdXp(x,n,y,m)dy=x—(x,n,y,m)J-8x“Jv$”Jzaa_ji_8'"“CmPw”@ym)Jᵫp(x,n,,m)=[xFF=)%.()'ᨬE[x„+y„,]=[xp(x,n)dx+[”)•“(>m)=E[x]+E[y„]xn(F☢ᨵE[ax]=Kaxp(x,n)dx=aKxp(x,n)dx=aE[x]J-8-nJ-00nᦑjklmḄᙳoᐹᨵ-ឋឋp5.2x(n)ry(n)/ᐵḄ¡jk¢£¤¥Ḅ¦ᑖ¨crªr«¬w(n)=x(n)+y(n)Ḅ¦᪷®jk¢£ḄᙳoḄ-ឋឋpᑮm-£*[&()]=E[x(n)+y(n)]=E[x(n)]+E[y(n)]=m+mxxy=£[(«(«)-m)2]=E{[x(n)+y()-m-m]2}a)xy=E{[x()+y(±2-2[x(n)+y(/i)](m+m)+(m+mj2}vyxஹ,ᵫx(n)rE{[x(n)+y(n)]-}-2(m+m)E[x(n)+y(n)]+(m+myxyxy=E[x2(»)]+f[.y2(n)]+2E[x(n)y(n)]~2(w+m){£[x(n)]+E[y(n)]}+(%+m)2tvyy(n)/ᐵḄ¡jk¢£ᡠ2ᙠVᑡᨬF¡W¹=mmxy>º
80crj=E[x2()]+E[y2()]+2mM-2(%+m)2+(m+m)2yyxy=£[x2(n)]+£[y2(n)]-/n^-mJ=E[x2(n)-m1]+E[y2(n)-mj]=E[(x(n)=z,»]+E[(y(n)~m)2]y2o5.3!ᨵ3¡¼½¾¿ᑡX](n)ஹX2(n)rX3S),¤¥ᑖ¨ᙠÁÂ(-q,0)ஹ(-q/2,q/2)r(0,2%)VᕈᙳᒴᑖÆ(1)ÇZ¤¥Ḅᭆ᳛ÈÉᦪÊË(2)"Y¤¥ᔜÍḄᙳo(3)"Y¤¥ᔜÍḄ¦Îপ%()ஹ-(")r/()Ḅᭆ᳛ÈÉᦪᑖ¨F,Fq81fp£x)iin02P(2)Ò()ஹX2()rÓ()Ḅᙳo=E[xJ=£xp(x)dxXi=LKMx='x2|ÕqL,2qr2=E[X]^]Öp*(x)dx2£xdx=Ø2=0q4g2qk&=Ú᳝]=/p*(x)dx=-^—fxdx=Ö•x1IQ,T=ᐔ2P4P°(3)᳝()ஹÜ2()rÝ3()Ḅ¦_=Ú(ᓰFßà]=[_(X-ßàp,,(X)dxá=E[(x-mJ2]-K(x—m)2(x)dx2X2=-[2x2dx=-xi^2=—L23qT212b=Ú(ÓF%)2]=K(x-%fp(x)dxx)=^—[(X-7T)2dx-(X-7rY2%16%35.4jk¢£x(n)=cos(4n+)ᐸâ⚣᳛gäᦪå/”ᙠÁÂ(0,24)ᙳᒴᑖÆḄjklm¬x(n)ḄᙳorÍ/ᐵ¿ᑡæᑨ¨x(n)ᔲéêëjkìíx(n)Ḅᙳom=E[x(n)]x=],x()p«(e)d
821Að=——cos(6y7?2+0)cos(cotn+0)d0=O0o2%ñRmQn,n)=E[x(m)x(n)]1=——Icos(ry7?2+0)cos(69m+0)d30024ñ11=——I—{cosf®(“Fó)]+cos[g(+[)+26]2ᐔA2=^cos[(y(n-??/)]0=^-cos[«y
83-m\]0>/r(?,)ðôõÂö÷nøᐵ/?,.(?,)ùôú¦In-mlᨵᐵᡠ2x(n)éêëjkìí5.5iF¡üýjk¢£ôF¡ôᐸ/ᐵḄ¼½¾¿ᑡ/þlᡂ ᑡ x(n),ᑡ e(n),Ḅy(n)=x(n)e(n),ᑡe(n)Ḅ ᐵᑡ R{n,n+tri)-E[e(n)e
84+m)=cr2?@Aᑏᡂ??“(,+m)=E[x(n)x
85+m)D+/”)]=&ஹ•())&”")=o-2/?(m)cr(/M):My(n)+(vvᑡ5.6QᔊឋTUV+WXḄ)WXTUV+QᔊឋḄ)YZ[\D]ᔩ_ `a_5.7ᨵdex,Ḅᙳg m,ஹ,- cr*hixḄNkegx,(i=0,…,N-1)+p< ᐵḄ,YqkegḄrsWᙳgt)u 2᪵ᙳg(1)v⛳Ḅxyg(2)vzஹ.Ḅ,-1N-\5.8|?⚪~=?Z12᪵,-N,=o
86(1)r2᪵,-ḄxygE[3*]xyg1N-]]=ᓃ()—)1NT=77X{a—()]+E[,h*]-2E[x^mJ)NMiNTiNTNT2MNT=.X)()]+QXXEWi)x())QXXMi)")]N=oNi=0j=0Ni=oJ=owiN-liN-lN-l=.Z/()]—-zZ|x(i)x())]N=oNj=()j()=iN-IiN-\N7N-1=ᯅZ)()]Q{ZEMপ]+ZZE[x(i)x(j)]}Nn=0N,=o/=o)=01N2-N=E[x72(n)]--E[x72(i)]kMi)x(/)]NNN—lN—1=-—^[x72—(92a)]-E[X()/])NNN—l2=N(x-m)2x1ফ£x+¤¥de)ᓽḄᭆ᳛©ª«ᦪ p,e2CT'v2᪵,-6±Ḅ,-v(x)=V^CT`Var[(T^]=E[(d--ᑖᑡḄ,-
87CT*=2()]ᵨ*=E[d2()]=2[Rq(0)R\,প]x(n)Ḅ¸᳛¹ S.a(i)=fR“(Me3J=-X_QOOP=&ஹ(())+2>Ò(Ó)/5+£Õ(Ó)Ö.m=-\m=l=&ஹ(0)+£&*-/)/Ó+£×Ó//:=1i=l=&ஹ(O)+£R,@Ùᔬ+e"1=1=R"(0)+£2R(m)cos(mo)XXm=\?@AÜ Ꮤ«ᦪS"(eW)ḄᏝßàáᦪâã@)áᦪḄÂZäᦪᑖå &@°)=*[S*,(/)do;R“(l)=*fS.(i)cosç02"2)’ᐔᵫéê;<1ᓃëì)Sஹx(e"")=0,ᡠ>Õপ=*[5*"")cos4cosS*dí?@(—cosgPS(*)da)=cosaR(0)=(1—2sin?ð)&r(0)>(1-2(ðñ)òஹ(0):Móxxccc2ëô.22Õ(1)2(1õÕ(0)ᓽÕ(0)—Õপ4öÕ(0)ᡈE[d2(n)]<^E[x2(n)]5.10x(n)+ᙳg µ),- O■:ḄWX)úᵨéûüýt h(n)ḄÿឋḄᐭᑮy(n)(1)x(n)y(n)Ḅ ᐵ ᑡᙠ!"#$m=0#Ḅ(᪵*R,(0)(.9012ឋḄy(n)ᐭx(n)ᨵ5ᐵ00y(n)=y^h(k)x(n-k)k=-oo
88678).(0)=9x()y()]=E[x()£//(A)x("-%)]k=-co=^h(k)E[x(n)x(n-k>)]=ᑍh(k)Rᨌk)jk= »&=-ooᐸER.a(A)Gᙳ*IJஹLMIb1ḄOPQRSx(n)ḄT ᐵ ᑡᨵ/?.(.)=E[x(n)x(n+k)]=<73(A)ᡠY%>()=ᓃয=ᡈ^(0)A=-00(2)y(n)ḄLMb`016Ix(n)Ḅᙳ*IJᡠYy(n)Ḅᙳ*aIJ67bj=E[y2(n)]=E[(f//(A)x(i—f))(£h(k)x(j—Q)]A=-<»k=-PC88=£2(6h/(—@+XZh\k)E[x{i-k)x(j-k)]jt=—001=—00j=-00iwj"i000co=E*(k)R".(o)+£)A=-00/=-00J=-00Hjpiᵫrx(n)Gstᙳ*IJஹLMIb`ḄOPQRSᡠYu,()=ᡈR""j)=oiwj67ᡈ£620k=-89R(m)=E[x(n)x(n+m)]xxp=E[x(n)(-^ax(n+m-k)+u(n+m))]kk=\p=-4Y+sᦇ)]+E[x(n)w(n+m)]«=ip-4RKm+k)+E[x(n)u(n+m)]k=\(1)~(1)⚗8E[x(n)u(n+m)]=E{h(l)u(n-l)]u(n+in)]1=0Z(/)9(s1)(+/??)]=y^/?(/)cr2ey(m+/)=(y2h{-ni)l=Q1=0(2)ᵫrh(n)G6ᓽᩩh(-m)=0(m>0),ᡠY~(2)ᡂI20),=0E[x(n)u(n+m)]=<¡1ব0,m>0£⚪¥MᑖLy¦§ᦪk=l᪷©ª*«ᳮᨵ(o)=lim"(z)=lim-----------1(4)PZTOOZToo1+£]k=l¯~(4)°ᐭ~(3),a',in-0E[x(n)u(n+m)]=<মO,m>Q¯~(5)°ᐭ~(1),ᨬ"Pa2,m=0§j)+£(1¨▾5-ª=,k=\0,wi>0²³Gx(n)ḄT ᐵ ´U/?„.(/»)¸ḄLy~.2/%ஹsin(ߟn)25.12ᨵs2ឋᐸᓫº»¼½¸Ih(n)=!——¥0,ᙠᐭᵨstᦣ71n0,n=0
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96Rjmp=R³ஹmTp=´SKjQWdQz1{2|$~☢᪷vSmRW{ḄGHᨵzrfsᨌ/p*ஹdজফ2|1|z1{⊤ᡂ▲ᑖcBᐸᑖᙠI27/TḄᓽ/?=z?{=1K2A+1 ”"cT—XI5\4%¶·¸z3{2|ߟhk-lWJTxxK=-0O24!ᣚfQ^Q+—Z:,z3{ᓄITR.…cᓃz4+¡¢/£…¤z4{DRk=-8'¥ᣚ^BaᑖḄ¦@ὃ⇋ᑮ©ᡠᨵᦪkBmᨵ=1,liz4{ᓄI/?3°z?{=DES,z/Q+®WdQz5{C=⁐³ᐭz5{,3Tµ3z¶{=11·2z¸+/¹º»idz6{L7i¾¿Tc;TTz6{az2{᯿3S.uze""{=f+JÂÃ{z7{1—001/18245ᡈ^O^{=-EUO^+J—Ä/—001z3{IÅÆᜫÈᙢᵫ$"e”"{3ᑮ5ËzÌ1{5{z/£1{ÎÏÐÑÒᩩÔÕ277,efÖz7{ᡈz8{ØÙÚS,xze“{ 52z/{Ḅᕜ)ÛÜᕜ)IÝ=liÞÏÐᩩÔSßzjO{=0,11·â/TᑣSA"{åæᕜ)ÛÜ ÆçèéêëᜫÈlìíîÆᜫÈᙢᵫᐔz/"{3ᑮ.z/Q{,ᓽᨵ5/{="ᐸᓩ3K%
975.16óôõöX”(t)ḄC᳛DøP5.I6ᡠ'ᕜ)TXপ/◞1᪵3ᑮ5ᦣõöx(n)=X"(nT)প^x(n)Ḅ=>ᐵ@ᑡR*(m)&,(?)=R¹º="f(4)ú7ef24û=——'ߟsin(fVnT)2"LQ7rmT(2)IÅüx(n) ý⁐õö@ᑡÎþ⌱ T?JT7=2ᦇkᦪᑣᓄQ°sin()%()=-------;----=—d(m)7imk7rn⁐ ᑡḄ!"ᐵ ᑡḄ$&'(⌕*᪵ᕜ-T/0Ḅᦪ/01x(n)2⁐ ᑡ5.17Ꮇ45678 9:xপḄ<᳛>@P5.17ᡠBCD5.16⚪x(n)Ḅ!"ᐵ ᑡ
98=£[x(H)x(/i+m)]=£{1(Q)(RS/(+TR4)+(J+m)]k=\p=~/aE[x(n)x(n+VR%)]+E[x{n}u{n+m)](1)jkk=]P=RZak(VRᜧ)+ETM+m)]k=\(1)\]^_⚗a`+V)]=a[h(l)u(»R/)](+?)}/=o0000=/?(/)E[w(n-l)w(n+m)]=(g+/)(2)1=01=0=(y2h(-in)ᵫjh(n)&lmnᓽpqᩩsh(-m)=0(m>0),ᡠa(2)ᡂc/ஹ/M/z(0)V={E[x(n)w(«+m)j=<(3)0,m>0ᵫ⚪ᑖmnᦪH(z)=-1+"1k=\᪷ᳮᨵ/?(0)=lim//(z)=lim-----?-----=1(4)1+24Zk=\(4)ᐭ(3),2a~,in=0E[x(n)u(nm)]=ீ(5)0,m>0(5)ᐭ(1),ᨬஹஹ~—0&*(m)+4&(ᵨR¡={’n77?0,V>02x(n)Ḅ!"ᐵ ᑡR"(m)¥pqḄ5.18⚪5.16©⚪5.17ª«ᑮR®¯45678 9:x“পḄ<᳛>S^(t),´x(t)a¶7a88◞T0*᪵ᑮ¸ᦣ78 ᑡx(n)ºx(n)⁐ ᑡ»¼S,প©T0¥pq½1ᩩs¾q5.194ᙳÁஹb?ḄÃÄ ᑡu(n)ÆᵨjRÇÈÉᦪH^=Yb^'kḄÊឋÌÍÎmMAk=0
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100S.d)=a2H(eja>)H(ejm)=a215")I2(3)MAMAq-mM,=1…q(4)þÿ ᐵᑡᑖR,(m)=/-*)*+,k=Oh(k)=b[u(k)-u(k-q-I)]k-.u(k)⊤1ᓫ3▤5ᑡ67q-m.9):+;<…w“q(4)0,/?2>(7+1BC(4)DᐭC(2),,q-m¼(ஹ½+“,ᑘ=0,1,…q4.r(;)=jM0,zn>4-15.20LᙳNOPஹOcy2ḄTUVᑡx(n)XᵨZ[\]^_ᦪOH(Z)=[J-----ḄbឋdeAKk=lfgh,ᑮ^jklmnx(n)(1)ᑏjghḄᑖ!LghḄ^ᐭp^jmnḄZfᣚᑖsOUফpX(z),ZwX(z)=U(Z)"y=[)প1+t&Z*=1ᵫ~C,X(z)+£4Z“X(Z)=U(Z)k=\⌮Zfᣚ,ghḄᑖPx(n)+^ax(n-k)=u(n)(1)kk=\ᡈpx(n)=[1%)([2)+()k=l
101p[£4)(;[)+/;=0k=l(2)x(n)Ḅ ᐵᑡᑖR„(m)=Pஹ&=i!BC(2)Dᐭx(n) ᐵᑡC,R(tn)=E[x(n)x(n+m)]xxp-E{x(n)[-^4(+m—%)+(+m)]}k=l=aE[x(n)x(n+m-k)]+E[x(n)u(n+m)]kk=l=-fakR-k)+R/m)k=\LghḄᓫ3᪵Oh(n),ᑣghḄ^jO0Q%()=#(/)(-/)/=067,C(3)<Ḅ(;)OR(m)=E[x(n)u(n+m)]xu=£{£(/)([/)(+l)}1=000=Z//(/)£1[(-/)(+;)](4)1=08=2(/)&(l+/)1=0=a2h(-m)ᵫZghw6ghᨵh(m)=0(mv0)ᡈh(-m)=0(m>0),ᡠ*C(4))ᑏᡂ2#(0),?=()R,"(;)=<(5)0,m>0ᐸ8U--.,i+Z3k=l67C(5)ᓄOcr2,m-0“(")='(6)0,/n>0BC(6)DᐭC(3),ᨬ,
102p[Z4R_M(;[)+2m=k=\RQn)=0kxxk=lqzw5.21LbឋdefghḄ]^_ᦪOHARMA¯Z°=-------⚪5.20k=\
