1、2*()()()aaaHjHjHj( )()aasjHs Hs h(t)是實函數(shù)2()aHj( )aHs()()aaHjHj 將左半平面的的極點歸( )aHs將以虛軸為對稱軸的對稱零點的任一半作為 的零點，虛軸上的零點一半歸( )aHs( )aHs( )()aaHs Hs()aHj( )aHs( )aHs2()( )aaHjHs由確定的方法2222216(25) ()( )(49)(36)aaHjHs已知幅度平方函數(shù)：，求系統(tǒng)函數(shù)例：解：222222216(25)( )()()(49)(36)aaassHs HsHjss 7, 6ss 極點：零點： （二階）5sj 零點：5sj 7, 6ss

2、的極點：( )aHs設(shè)增益常數(shù)為K020(25)( )(7)(6)aKsHsss000( )()4asaHsHjK由，得2224(25)4100( )(7)(6)1342assHsssss221()1aNcHj2()1/2acHj時c1( 0)20lg3()aacHjdBHjc為截止頻率221()1aNcHj20()1aHj (1)21()1/23caHjdB (2)c 通帶內(nèi)有最大平坦的幅度特性，單調(diào)減小 (3)c 過渡帶及阻帶內(nèi)快速單調(diào)減小 (4)22/1()( )()1aaaNs jcHjHs Hssj1211222( 1)1,2,.,2kjNNkccsjekN 2）幅度平方特性的極點分

3、布：221()1aNcHj 極點在s平面呈象限對稱，分布在Buttterworth圓上，共2N點 極點間的角度間隔為/ N rad 極點不落在虛軸上 N為奇數(shù)，實軸上有極點，N為偶數(shù)，實軸上無極點121221,2,.,kjNkcsekN 1( )()NcaNkkHsss1)0(aH將左半平面極點給Ha(s)1 /ccrrad s 為歸一化系統(tǒng)的系統(tǒng)函數(shù)( )anHs去歸一化，得( )( )crcaanssHsHscrancsH當(dāng)1( )()NcaNkkHsss由于濾波器的頻率范由于濾波器的頻率范圍取決于設(shè)計者的實圍取決于設(shè)計者的實際應(yīng)用目的，必然千際應(yīng)用目的，必然千差萬別。差萬別。ccr 幅度

4、平方特性：221()1aNcHj1( )()NcaNkkHsss221()1apNpcHj120.10.1101101spk12ps120lg()apHj 120.1110Npc220.1110NscsspplglgspspkN 120.10.1101101Nps( )anHs( )aancsHsHc110.12101Ncp 210.12101Ncs 120.1110Npc220.1110Nsc0.20.3/0.2 /ppTrad s /0.3 /ssTrad s 0.2 prad0.3 srad11dB215dB11dB215dB/1.5spsp 120.10.11010.092101spk

5、lg/lg5.8846spspNkN 取110.121010.7032/Ncprad s 121221,2,.,6kjNkcsek 661( )()cakkHsss234561( )1 3.86377.46419.14167.46413.8637anHsssssss654320.1209( )2.7163.6913.1791.8250.1210.1209aancsHsHssssss( )aHs1( )NkakkAHsss11( )1kNks TkTAH zez1112120.2871 0.44662.1428 1.14541 0.12970.69491 1.06910.3699zzzzzz11

6、21.85580.63041 0.99720.2570zzz變換成Butterworth數(shù)字濾波器：20.65 /2pptgrad sT 21.019 /2sstgrad sT 0.2 prad0.3 srad11dB215dB11dB215dB1Ts選/1.568spsp 120.10.11010.092101spklg/lg5.3066spspNkN 取210.121010.7662/Ncsrad s 121221,2,.,6kjNkcsek 661( )()cakkHsss234561( )1 3.86377.46419.14167.46413.8637anHsssssss2220.20240.3960.58711.0830.58711.4800.5871ssssss( )aancsHsH112 11( )( )azsTzH zHs121211(1