5-3-第5章数字滤波器的基本结构

1、2021/3/271 2021/3/272 2021/3/273 1 0 ( )( )() N k y nh kx nk 1 z h(0)h(1)h(2)h(3) h(N-1) h(N-2) 1 z 1 z 1 z 2021/3/274 1 z 1 z 1 z 1 z 2021/3/275 21 12 012 01 ( )()( ) N N n kkk nk H zzzh nz 2 N 2021/3/276 1 z 1 z 1 z 1 z 1 z 1 z 01 11 21 22 12 02 0() 2 N 1() 2 N 2() 2 N 012 (,) iii 2021/3/277 () ()

2、( ) jj H eHe ( )H 2021/3/278 (01)nN ( )(1)h nh Nn 2021/3/279 1 1 2 00 2 ( )( )( )( ) N NN nnn N nn n H zh nzh nzh nz 11 22 (1) 00 ( )( )(1) NN nNm nm H zh nzh Nmz 1 2 (1) 0 ( )( ) N nNn n H zh nzz 2021/3/2710 1 0 ( )( ) N n n H zh nz 1 1 1 1 2 2 1 0 1 2 1 ( )()( ) 2 N N N nn N n n N h nzhzh nz 11 11

3、 1 22 (1) 2 00 1 ( )( )()( ) 2 NN N nNm nm N H zh nzhzh mz 2021/3/2711 1 1 1 2 (1) 2 0 1 ( )( ) () 2 N N nNn n N H zh nzzhz 1 ( )(1),()0 2 N h nh Nnh 故 2021/3/2712 1 z (2)h (2) 2 N h(1)h 1 z 1 z 1 z 1 z 1 z 1 z 1 1 1 1 (0)h (1) 2 N h 2021/3/2713 1 z (0)h (1)h 1 z 1 z 1 z 1 z 1 z 1 z 1 z 1 111 1 1 ()

4、 2 N h 1 (1) 2 N h (2)h 1 (2) 2 N h 2021/3/2714 11 00 ( )( )(1) NN nn nn H zh nzh Nnz 1 (1) 0 ( )() N Nm m H zh mz 1 (1)(1)1 0 ()() N NmN m zh mzzH z 2021/3/2715 (1)1 ( )() N H zzH z 1(1) ()( )0 N iii H zzH z *1 () ii zzzz 和 2021/3/2716 * 11 * 11 11 ,zz zz * 33 ,zz 2 2 1 ,z z 2021/3/2717 Im( )jz Re(

5、 ) z 1 z 4 z 3 z 1 z 1 1 z 2 z 2 1 z 3 z 1 1 z 2021/3/2718 ( )H k 1 1 0 1( ) ( )(1) 1 N N k k N H k H zz NWz 2021/3/2719 ( )1 N C Hzz 1 ( ) ( ) 1 K k N H k Hz Wz 1 0 ( )( ) N CK k HzHz 和 1 0 1 ( )( )( ) N CK k H zHzHz N 2021/3/2720 2 ,0,1,2,1 k j k N kN zeWkN ()1 ()2 sin() 2 jj N C j C Hee N He 2021

6、/3/2721 1 N W (1)N N W 0 N W () j C He 2021/3/2722 2 () k k N ()( ) k j H eH k 2021/3/2723 1 z 1 z 1 z N z 1 N W 0 N W (1)N N W 1 N (0)H 2021/3/2724 2021/3/27251r 2021/3/2726 1 1 0 ( )1 ( )(1) 1 N NN r k k N Hk H zr z NrWz 1r ( )( ) r H kH k 2 ,0,1,2,1 k j N r ekN 2021/3/2727 * ( )()H kHNk ()kN k NN

7、 WW 2 ,0,1,2,1 k j N r ekN 2 ()2 () () N kk jj N kk NN N WeeW N kk zz 2021/3/2728 1()1 11 1 01 122 ( )() ( ) 11 ( )( ) 11() 2 1 2cos() k kN k NN kk NN kk H kH Nk Hz r Wzr Wz H kHk r Wzr Wz aaz k rzrz N 0 2Re( ) k aH k 1 2Re( ) k kN ar H kW 2021/3/2729 1 z 0k a 1k a 1 z 2 r 2 2 cos() k r N 2021/3/273

8、0 1 1 2 01 11 122 1 () 1(0) 2 ( )(1) 2 11 1 2 cos() N NN kk k N H aa zH H zr z k Nr zr z rzr z N 1 1 2 01 1 122 1 1(0) ( )(1) 2 1 1 2 cos() N NN kk k aa zH H zr z k Nr z rzr z N 2021/3/2731 NN r z 1 z 1 z 1 N 1 2 ( ) N Hz () 2 N H 2021/3/2732 2021/3/2733 2021/3/2734 2021/3/2735 11 11 ( )( )(1) ( )(

9、)(1) llll llll e nenrnK r nenKrn 1 11 1 11 ( )( )( ) ( )( )( ) LLLL LLLL EzEzKzRz RzEzKRzz l k l k l e 1l r 1l e l r 1 z 2021/3/2736 1 1 1 1 ( )( )1 ( )( ) ll l lll E zEzkz R zRzkz 111 0 11 111 011 ( )( )111 ( )( ) N NN NNN EzEzkzkzkz RzR zkzkzkz 1 1 1 ( )11 ( )1010( ) ( )1 N i i NN i Ezk z Y zX z R

10、zkz 2021/3/2737 1 z 2 k 1 k 2 e 1 z 1N e 1 z 1 k 1 e 1 r 0 e 00 re 2 k 2 r 1 z N k N k 1N k 1N k 1N r 2021/3/2738 1 1 1 11 ( ) ( )10 1( ) i i N i k zY z H z X zkz 12 11 ( )1 42 H zzz 11 21 11 21 111 ( )10 1 k zk z H z kzkz 1212 1122 11 1()1 42 kk kzk zzz 2021/3/2739 112 12 2 1 11 4 , 122 2 kk k kk k l k l k l e 1l r 1l e l r 1 z 2021/3/2740 1 11 1 11 ( )( )( ) ( )( )( ) llll llll EzE zkzRz R zKEzzRz 1 1 1 1 ( )( )1 ( )( ) ll