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课件16.6 物理可实现性佩利维纳准则（1）时域时域因果性因果性（2）频域）频域有界有界 能量可积能量可积 频带内不为零频带内不为零0)(,0thtdjH21)(lndjH2)(0)(jH限制了衰减速度课件2LCCLR)(1tv)(2tv?)(th222322332)(ccccjjH)0()23sin(32)()(21ttejHFTthctcc)(thcc2由实际电路组成从t=0开始，物理可实现例：课件3高斯幅频特性是否物理可实现？2)(ejH2lim2(2limlim11111)ln(1)(ln11222222BBtgBtgdddedjHBBBBB发散的，物理不可实现课件4例：延时TT1tdt)()(ty)(txTTT,?)(ty)()()()()()()(1)()1(111)1)()()1(1)()()()()(2TtuTtTtuttutttuTtyeeeTssTesXsYessXtututxTssTssTs课件5T)()()()1(tutttuT)()()()()2(TtuTtTtuTt)2()1()(tyTTTTT1T1T1T1T1TTT课件66.7可实现的典型滤波函数巴特沃兹逼近(与切比雪夫逼近)011011.)()()(bsbsbasasasBsAsHnnnnmmmm滤波器特性取决于系数滤波器特性取决于系数 a,b取决于分母多项式的阶次取决于分母多项式的阶次 nn 与元器件的数目有关与元器件的数目有关课件7一一、巴特沃兹逼近(Butterworth)(Butterworth)()(11)(202jHjHjHn0)(21)(1max)0(000jHjHjH 通带内最平坦滤波器通带内最平坦滤波器课件8为什么“巴特沃兹滤波器”最大平坦二项式定理.12835165832111)(806040202/120nnnnnjH在在 点，点，它的前它的前 阶导数都为阶导数都为零，所以说在零，所以说在 点附近一段范围内最点附近一段范围内最平。平。012 n0课件9巴特沃兹滤波器的极零点分布nnjsnssH20202)1(1111)(oddneSnkjk,220evenneSnkjk,2)12(0evennoddnsn1120课件104011)(1,2ssHn47454341,jjjjkeeeeS)()()(2sHsHsH41je43je45je47je取左半平面极点给H(s)121)(1)(1)(245432ssesessBsHjj)(1)(sBsHn对于n 阶参见P506表6-1课件11巴特沃兹低通滤波器的设计 Low Pass Analogical Filter(AF)(p)(sps0)(p)(sps通带最大衰减阻带最小衰减通带截止频率阻带下限频率222)(1lg10)()(lg10)(jHjYjX)1(ppor0课件12）22)(1lg(10)(1lg10)(jKjHnjK2010)(2110)(11010)(20pnp11010)(20sns?nspspnlg110110lg10)(10)()()(11)(202jHjHjHn课件13例：按下列技术指标设计一个模拟低通滤波器dbsradkdbsradkLPAFsspp30/103/5:设计：03ppdb521lg32lglg110110lg10)(10)(spspn)()(11)(522jHjHjHp课件1455kjpkeSoddnoddneSnkjk,2201S2S3S4S5S6S7S8S9S7,6,5,4,3ktake)()()()()(57565554535jjjjjpejejejejejjH)()(11)(522jHjHjHp0S课件15巴特沃兹高通滤波器 置换0001001010100000000111)(11)(ssssnjH20211)(njH20211)(课件16巴特沃兹带通滤波器01001031213slsh低通带通 2213220220132221321322222222)()(课件17013222)(nnjH22021111)(nnnjH2132222202)(111111)(变量置换得到带通课件18巴特沃兹带阻滤波器nnnjH2222132202)(111111)(频率取倒数为带阻课件19二、二、切比雪夫逼近切比雪夫逼近(Chebyshev)(Chebyshev)（简要介绍）（简要介绍）通带等起伏（等纹波）特性滤波器通带等起伏（等纹波）特性滤波器 02211)(nTjH纹波系数)1()()1()(coscos()(11xxnchchxxnxTnn=4n=511211010p课件20作业作业 设计一个巴特沃兹低通滤波器，技术要求如下：dbsradkdbsradkLPAFsspp35/153/6:
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