模拟滤波器的设计-》模拟系统函数H(s)aP1772019-5-9Digital Signal Processing-12-
2019-5-9 Digital Signal Processing -12- ( ) H a s P177
根据幅度平方函数确定系统函数A(2) = |Ha(j2)2= H.(s)Ha(-s)s=i如何由A2()确定H(s)?P1782019-5-9Digital SignalProcessing-13-
2019-5-9 Digital Signal Processing -13- 2 2 ( ) ( ) ( ) ( ) a a a s j A H j H s H s W W = W = = - ( ) ( ) A H a W s 如何由 2 确定 ？ P178
ButterworthFilter：巴特沃思滤波器低通巴特沃思滤波器是全极点系统[H(j2)2·N阶幅度平方频率响应为1A(2) = H,(j2) P=12N321 +j.其中N为滤波器阶数0.52为3dB截止频率；，为通带截止频率；2为阻带截止频率22pe3dB带宽
|Ha(jW)|2 1 Wp Wc W 0.5 Ws • •低通巴特沃思滤波器是全极点系统 • N 阶幅度平方频率响应为 其中N为滤波器阶数， c为3dB截止频率； p为通带截止频率； Ws为阻带截止频率 ( ) 2 2 2 1 ( ) | ( )| 1 c a N j j A H j W = = + 3dB带宽
Magnitude-squared frequency response of lowpass Butterworth filtersH(2)P2N-1阶导数为零，响应最平，又称为最平幅度逼近1.11.00.9N10.80.70.60.50.40.3N=10.2N=2N=30.1NN=49Q22019-5-9-15-
2019-5-9 -15- Wp
巴特沃思滤波器ButterworthFilter:H,(s)H.(-s) = A"(2)a=-js =[ H.(j2) [2ln=-jsti21D2N+7其极点为：元/N,2p-1j元2N28,=(-1)2e2p-1=N.cos(+)1元)+2.sin元22Np = 1, 2, ..., 2N滤波器之阶数：N3dB截止频率：2KH.(s)=i2N-II(s - 8%)（因果稳定）k=02k-1元22N2eS9ack = 1, 2, ..., N
( ) ( ) ( ) ( ) = - cos sin , , . , p j N N p c c p p c N c N s j e j p N p p p p p W W - + - - = = + + + = 1 2 1 1 2 2 2 2 1 2 1 2 2 2 2 1 1 2 2 /N 2 2 2 ( ) ( ) ( ) | ( )| 1 1 ( ) a a js a js N c H s H s A H j s j =- =- - = = = + 其极点为： W s j s j ( ) 2 1 2 2 1 2 ; , , . , k N j k c s e k N p p + - = = ( ) 1 0 ( ) a N k k K H s s s - = = Õ - k = 1 p = 1