FIR滤波器设计(本科).ppt

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1、FIR滤波器设计滤波器设计(本科本科)( )01h nnN10( )( )NnnH zh n z()()jjH ee ( )dd 0( ) ( ) 10()( )Njj nnH eh n e()( )jHe ()()jjH ee 10()( )Njj nnH eh n e( ) ()jjH ee 10() coscosNjnH eh nn 10() sinsinNjnH eh nn 1010sinsincoscosNnNnh nntgh nn 1100sincoscossin0NNnnh nnh nn 10sin0Nnh nn( ) ( )(1)01h nh NnnN 12N 10sin0Nn

2、h nn0( ) ( )(1)01h nh NnnN 12N0/2 1100( )( )(1)NNnnnnH zh n zh Nn z 1(1)0( )NNmmh m z (1)1()NzH z 1mNn 令( )(1)01h nh NnnN 由1(1)0( )NNmmzh m z (1)11 ( )( )()2NH zH zzH z得11(1)001( )( )2NNnNnnnh n zzh n z1(1)01( )2NnNnnh nzzz11122120( )2NNnnNNnzzzh n (1)1 ()NH zzH z 由11221cos 221sin 2jNNnnz eNnzzNjn 1

3、1122120( )2NNnnNNnzzH zzh n112011201( )cos2()( )1( )sin2jNNjnjz eNNjnNeh nnH eH zNjeh nn cos2jxjxeex( )(1)h nh Nn 11201()( )( )cos2jNNjjz enNH eH zeh nn12N1( )2N ( )(1)h nh Nn 11201()( )( )sin2jNNjjz enNH eH zjeh nn12N112201( )sin2NNjjnNeh nn0/21( )22N 11cos(1)cos22NNNnn 11cos22NNn对呈偶对称101( )( )cos2

4、NnNHh nn1cos2Nn-32011( )2 ( )cos22NnNNHhh nn121112cos()22NmNNhhmm12Nnm令120( )( )cos()NnHa nn1(0)2Nah11,.,2Nn1( )22Na nhn120( )( )cos()NnHa nn1(0)2Nah11,.,2Nn1( )22Na nhn( )0, , 2 H对呈偶对称cos()0, 2 n对，呈偶对称120( )( )cos()NnHa nn12012 ( )cos2NnNh nn101( )( )cos2NnNHh nn2112cos22NmNhmm2Nnm令/211( )( )cos2Nn

5、Hb nn( )22Nb nhn1,.,2Nn 1201( )2 ( )cos2NnNHh nn/211( )( )cos2NnHb nn( )22Nb nhn1,.,2Nn ( )H对呈奇对称( )01Hz 则是零点1 cos02n时1z 为零点( )0, 2H对呈偶对称/211( )( )cos2NnHb nn11sin(1)sin22NNNnn 11sin22NNn对呈奇对称101( )( )sin2NnNHh nn幅度函数：1sin2Nn -3201( )2 ( )sin2NnNHh nn12112sin()2NmNhmm12Nnm令121( )( )sin()NnHc nn1( )2

6、2Nc nhn11,.,2Nn其中：1( )02Nh nNh奇对称且 为奇数121( )( )sin()NnHc nn1( )22Nc nhn11,.,2Nn其中：( )0, 2H故对， 呈奇对称( )01Hz 则是零点0, , 2 sin()0n时121( )( )sin()NnHc nnsin()0, 2 n因对，呈奇对称101( )( )sin2NnNHh nn幅度函数：12012 ( )sin2NnNh nn1201( )2 ( )sin2NnNHh nn2112sin22NmNhmm2Nnm令/211( )( )sin2NnHd nn( )22Nd nhn1,.,2Nn /211(

7、)( )sin2NnHd nn( )22Nd nhn1,.,2Nn ( )01Hz 则是零点10, 2 sin02n时( )0, 2H对呈奇对称( )H对呈偶对称/211( )( )sin2NnHd nn( )0iH z*, 1/iizz即 也是零点(1)1( )()NH zzH z (1)1()( )0NiiiH zzH z 11( )(1)(1)iijjiiiH zrezrez111111iijjiiezezrr1222112 cosiiiirzr zr2122 cosiiirrzz1522NN10ijiiiizrer 或1）11iiiijjjjiiiirereeerr零点：12221(

8、)12 cosiiiiiH zrzr zr2122 cosiiirrzz11( )11iijjiH zezez1212 cosirzz 1312NN10ijiiiizrer 或2） ，即零点在单位圆上iijjee零点：111( )11iiiH zrzzr1211iirzzr 1312NN i负实轴上 0 i正实轴上10ijiiiizrer 或3） ，即零点在实轴上1iirr零点：1( )(1)iH zz11222NN 1 01iizz 10ijiiiizrer 或4）即零点既在实轴上，又在单位圆上1零点：10()( )()Njj njdnH eh n eHe1( )2jj nddh nHeed

9、( )( )( )dh nw n h nw(n)：窗函数序列要选择合适的形状和长度()0,jjccdcceHe 1sin()( )2()ccjj nccdcnh needn( )( )Nw nRn 1sin201 120cccNnnNh nNnn其它( )01( )( ) ( )0ddh nnNh nh n w nn其它12Nsin()( )()ccdcnh nn1()2jjjdH eHeW ed 1120sin2()( )sin2NNjjj nRnNW ew n ee( )( ) ( )dh nh n w nsin2 ( )sin2RNW其幅度函数： 12()( )NjjddHeHe11()

10、221()( )()2NNjjjdRH eHeWed 121( )()2NjdReHWd1( )0cdcH 1( )()2dRHHWd其幅度函数：(0)( )RHW近似于的全部积分面积()0.5(0)cHH2cHN为最大值，正肩峰2cHN为最小值，负肩峰( )H随，绕零值波动( )(0)HH随，绕波动0c2cN2cN2cN2cN1( )( )()2dRHHWd幅度函数：2cNsinsinsin22 ( )sin22RNNxWNNxN幅度函数：( )( )Nw nRn4N 1120()( )NNjjj nRRnWew n eWesin2( )sin2RNW幅度函数： 21012( )212112

11、nNnNw nnNnNN8N 12()NjjW eWe2sin24( )sin2NWN幅度函数： 1N 12( )1 cos( )21Nnw nRnN8N22( )0.5( )0.25RRRWWWWNN幅度函数： 1N 2( )0.540.46cos( )1Nnw nRnN8N22( )0.54( )0.23RRRWWWWNN幅度函数： 1N 0.54Hamming)(jeW0.2324( )0.420.5cos0.08cos( )11Nnnw nRnNN12N22( )0.42( )0.25RRRWWWWNN440.04RRWWNN幅度函数： 1N Blackman0.420.250.04)

12、(jeW0( )I 2002111( )( )nINw nI01nN改变 可同时调整主瓣 宽度和旁瓣幅度 旁瓣幅度 但主瓣宽度/ 2 / N/ 2 / N7.865阻带最小衰减只由窗形状决定过渡带宽则与窗形状和窗宽N都有关()jdHe2,( )dh n( )w n()jH e/NA( )( )( )dh nh nw n()jdHe( )dh n, ( )( )dMMNh nhn当时1( )2jj nddh nHeed( )()Mdrhnh nrM计算其IFFT，得：()jdHe2()jkMdHe/2/0.2ppspsf /2/0.4ststsstsf 250dB421.5 10 (/sec)s

13、rad 321.5 10 (/sec)prad 323 10 (/sec)strad ()0,jjccdcceHe ccsf()11( )22ccjj njndh needed1sin()()ccnnnn12N1/220.3psts 2( )0.540.46cos( )1Nnw nRnN20.2stps 6.6330.2AN1162N250dB3）选择窗函数：由 确定海明窗（-53dB）6.6N海明窗带宽：( )( ) ( )dh nh n w n33sin 0.3160.540.46cos( )1616nnRnn()jH e若不满足，则改变N或窗形状重新设计()()1( )2ccjnjndh

14、 neded1sinsin()1()ccnnnnn()=()cc高通滤波器全通滤波器低通滤波器12N()0jjcdeHe其它理想高通的频响：1221()()1( )2jnjndh neded21211sinsin1nnnnn1221(,)=()() 带通滤波器低通滤波器低通滤波器120()0jjdeHe其它12N2112()()()1( )2jnjnjndh nededed12121sinsinsin1nnnnnn12N120,()0jjdeHe 其它1221()=()()带阻滤波器，高通滤波器+低通滤波器对理想频率响应等间隔抽样 作为实际FIR数字滤波器的频率特性的抽样值2( )( )()j

15、ddkNH kHkHe0,1,.,1kN( )h n( )H z()jH e10()( )()Njj njdnH eh n eHe1( )()2jj nddh nHeed( )( )( )dh nw n h n窗函数设计法：1101( )( )1NNkkNzH kH zNWz 102NjkH eH kkN12sin12( )sin2NjNeN 11(1)20sin21sin2kNNjNjjNkkNNH eeH kekNN内插公式： 12NjjH eHe( )(2)HH 2kjkjNkH kH eH ekN kHH1 2112kNkkNN 2kN12()( )NjjH eHe( )(2)HH 2

16、kjkjNkH kH eH ekN kHH 11kkN 2kN2、频率抽样的两种方法、频率抽样的两种方法 2jddkNH kHkHe0,1,.,1kN1101( )( )1NNkkNzH kH zNWz 1120sin12sin2kNNjjjNkNH eeH k ekNN 2jdkNNH kHe0,1,.,1kN 1210121( )1N NjkkNH kzH zNez 121120cos21sin22jkNNNjjkNH k eH eeNjkN *H kHNk又线性相位：12jNe kNk H kH Nk2N 2110,.,22211,.,122NNkkNkNNNkkNN 210,.,122

17、02211 ,.,122NNkkNNkkNNNkkNN 21221210,.,21,.,12NjkNNjN kNNH k ekH kNH Nk ekN 2122120,.,12021 ,.,12NjkNNjN kNNH k ekNH kkNH Nk ekN12(0) sin2sin2NjjNHH eeN 1sinsin22sinsin22MkkkNNH kNNkkNNN12NM12NM *( )(1)H kHNk 又线性相位：12jNe ( )(1)kNk ( )(1)H kH Nk 12N 2110,.,1222211,.,1222NNkkNkNNNkkNN 21130,.,22210221

18、11,.,1222NNkkNNkkNNNkkNN 21122211220,.,121,.,12NjkNNjN kNNH k ekH kNH Nk ekN 211222112230,.,2112211,.,12NjkNNjN kNNH k ekNNH kHkNH Nk ekN 121cos22cos2NNNHHN 121021sin221sin22NMjjNkNkH kNH eeHNkN1sin221sin22NkNkN32NM当N为偶数时： 120NH12NM 102NjkH eH kkN220dB 240 54dB 260 75dB 280 95dB 102NjkH eH kkN2 / Nc/N110Int824( )10Int191622ccNNkH kNNk 100cjdHe理想低通频率特性其它按第一种频率抽样方式，N=33，得抽样点816133sin 33sin 33sin233233233sin33sin33sin2233233jjkkkH eekk2 /334 /336 /65