dsp第9章%20多采样率信号处理[1]

•fs•“”•••••“”1•x(n)D/Ax(t),A/Dx(t)D/AA/D•x(n)2•“”“”•“”“”•••DD-1D1.•xa(t),x(n),T1111Tfs=Dxd(n),T2fs2,DDffDTTss1212==t)(txan)(nxn)(nxd123TT=2↓D1/DD)(nxd)(nx↓D)(nxd)(nx•D•x(n)x(n)xp(n)D=x(n),⎩⎨⎧===nDkkDnnxnxp0),...(2,1,)()(1xp(n)∫-=pqqqp20)()()(21)(deXePeXwjjjwp∑∞-∞=-=⋅=kpkDnkDxnpnxnx)()()()()(d2p(n)•p(n)P(ejw).•p(n)P(k))2()(1)(10)2(∑-==DkknDjekPDnpp)3()()(10)2(∑-=-=DnknDjenpkPp)1()()(∑∞-∞=-=kkDnnpd∑∑∑-=--=-∞-∞==-=10)2(10)2()()()(DnknDjDnknDjkenekDnkPppdd130≤n≤D-1δ(n)1)(=kP•p(n)P(ejw).•p(n)•p(n)P(ejw)∑∑-=-=-=-=1010)(2)2()(2)(DksDkjwkwwDDkwkPDePdppdpP(ejw)P(k)ws=2π/D.3xp(n)xp(n)Xp(ejw)∑-=-=10)(2)(DksjwkwwDePdp∑-=-=*=10)()(1)()(21)(DkkwwjjwjwjwpseXDePeXeXp6X(ejw)Xp(ejw)Xd(ejw)xd(n)Xd(ejw)X(ejw).xp(n)x(n)D)()(Dnxnxd=)()(Dnxnxpd=)(npn)(nxn)(nxp0n)(nxdx(n)p(n))(nxp)(nxdXd(ejw):∑∑∞-∞=-∞-∞=-==kjwkpkjwkdjwdeDkxekxeX)()()(n=Dkk=n/D,∑-=DnDnjwpjwdenxeX)()(Xd(ejw):))(DwjpjwdeXeX=nD)()()(DwjpnDnjwpjwdeXenxeX==∑∞-∞=-0)(=nxp)(jweX0pp-jweP(pp-ww0)(1jwpeXhw-wp2-p2hwpp-hw-p2-p2hw11Dhw-sw-sw0wpp-hw-p2-p2hw11Dsw2sw2-)(2jwpeX)(jwdeXpp-whw-p2-p2hw:•(1)xp(n)xd(n)•(2)X(ejw)Xp(ejw)•3x(n)X(ejw)(0~π).•41•x(n)fsII•(I-1)(I-1)1:x(n)=xa(nT1)D/Axa(t)2xa(t)x1(n)=xa(nT2),T1=IT2•I11I•I1x(n)(I-1)2I2I↑Ix(n)I-1.x(n)xp(n),Ix1(n).↑I)(nx)(nxp)(1nx)(nh3=•⎪⎩⎪⎨⎧±±==nIInInxnxp02,,0()(•x1(n)(a)x(n)X(ejw))(jweXpp-wn)(nxx(n)000)(jwpeXpp-w0)(nxpn(b)0)(jwpeXpp-w0)(jwbeXpp-w(c)I/Dx(n)I/D.ID.x(n)1↑Ih1(n))(nxsf)(nxp)(1nxsIIff=)(2nhD↓)(1nxdDIffsId/=sf↑Ih(n)D↓)(nx)(1nxda)b)2⎪⎩⎪⎨⎧≤≤=wIDwIeHjw0),min(0)(pp••1x(n)7/2•2x(n)xa(t)(I=2)(D=7)x1d(n)xa(t)•FIR•1DFIR•9.1D•N••9.10a∑∞-∞=-==mDDemhmnxnhnxnx)()()(*)()(∑-=-=10)()(NnnznhzH9.10FIRD9.10b•••••••(0)h(1)h(2)h(1)hN-'↓•1z-1z-1z-1z-)(a)(nx)(nxd↓↓↓↓••••••••1z-1z-1z-1z-(0)h(1)h(2)h(1)hN-()xn()()ddxnxDnT=•)(bD••9.10bD∑-=-=10)()()(NmddmDnxmhnx)1(,),2(),1(),(+---NDnxDnxDnxDnxL∑-=-=10)()()(NmddmDnxmhnx•9.11••••••↓↓↓↓↓•••••↓↓↓↓↓1z-1z-1z-1z-1z-1z-1z-1z-1z-1z-1z-••••••(0)h(1)h(2)h(2)2Nh-(1)2Nh-)(nx)(nxd2FIR•9.5FIR9.129.12FIR9.13FIR•••••••(1)h(2)h(1)hN-•↑()xn1z-1z-1z-1z-()Ixn)(nxe••••••(1)h(2)h(1)hN-•1z-1z-1z-1z-()Ixn)(nxe9.14FIR•FIR9.15()xn()Ixn••••••••1z-1z-1z-1z-(0)h(1)h(2)h(1)hN-•↑↑↑↑3I/DFIR•••••••(1)h(2)h(1)hN-•,↑()xn1z-1z-1z-1z-()Ixn'9.16FIRFIR•H(z)•DnD∑∞-∞=-=nnznhzH)()(mrDn+=()1,2,1,0-=DmL∑∑-=∞-∞=+-+=10)()()(MmrmrDzmrDhzH∑∑∞-∞=--=-+=rrDDmmzmrDhz)(10••••1,,1,0,)()(-=+=∑∞-∞=-DmzmrDhzGrrmL)()(10DmDmmzGzzH∑-=-=)()(1zGzRmDm--=)(zGm)()(10)1(DmDmmDzRzzH∑-=---=9.17FIR9.18(b)••sf•••••1z-1z-1z-sfD)(nx)(nxd)(0zG)(1zG)(2zG)(1zGD-↓••↓sf•↓•↓•••1z-1z-1z-↓sfDsfD)(nx)(nxd)(0zG)(1zG)(2zG)(1zGD-sf1z-1z-1z-••sIf•••••0()um1()um2()um)(nx)(nxI)(0zR)(1zR)(2zR)(1zRD-)(1muD-↑sf1z-1z-1z-••sIf↑↑↑↑•••••sf0()um1()um2()um)(nx)(nxI)(0zR)(1zR)(2zR)(1zRD-)(1muD-I9.18I•••9.19∏==KiiDD1•↓•()a()xn()dxnsFsF/sFD•↓•()b()xn()dxnsFsF/sFD↓↓1/sFD12/()sFDD1D2DKD•()xnsF()c↓↓↓•()dxn/KsFFD=1()hn1D2()hn2D()KhnKD11/sFFD=212/()sFFDD=D•9.19DKDKiiiiDff1-=Ki,,2,1L=•••K•∏==KiiII1••()a()xn()IxnsFsIF••()b()xnsF1I•()xnsF()c•()Ixn1()hn2()hn()Jhn↑sIF↑↑1sIF↑2I12sIIF↑iIsIF()IxnsIF↑1I1sIF↑2I12sIIFJIsIFD