IIR滤波器设计总结1培训讲学

1、Good is good, but better carries it.精益求精，善益求善。IIR滤波器设计总结1-IIR模拟滤波器设计1.低通Butterworth滤波器设计(1)技术指标通带截止频率：SKIPIF10阻带截止频率：SKIPIF10通带最大衰减：SKIPIF10阻带最小衰减：SKIPIF103dB截止频率：SKIPIF10(2)归一化SKIPIF10，SKIPIF10，SKIPIF10(3)滤波器阶数SKIPIF10，SKIPIF10，SKIPIF10（向上取整）(4)滤波器3dB截止频率SKIPIF10，阻带有余量，SKIPIF10，通带有余量(5)极点极点：SKIPIF1

2、0归一化极点：SKIPIF10(6)系统函数：SKIPIF10，归一化系统函数：SKIPIF102.低通ChebyshevI型滤波器设计(1)技术指标通带截止频率：SKIPIF10阻带截止频率：SKIPIF10通带最大衰减：SKIPIF10阻带最小衰减：SKIPIF103dB截止频率：SKIPIF10(2)归一化SKIPIF10，SKIPIF10(3)滤波器阶数SKIPIF10，SKIPIF10，SKIPIF10（向上取整）(4)极点极点实部：SKIPIF10，极点虚部：SKIPIF10SKIPIF10，SKIPIF10归一化极点：SKIPIF10(5)系统函数系统函数：SKIPIF10，归一

3、化系统函数：SKIPIF102.频率变换模拟低通滤波器的频率变换：归一化原型低通滤波器截止频率为1，则有类型映射新截止频率低通SKIPIF10SKIPIF10高通SKIPIF10SKIPIF10带通SKIPIF10SKIPIF10：上限截止频率SKIPIF10：下限截止频率带阻SKIPIF10SKIPIF10：上限截止频率SKIPIF10：下限截止频率3.IIR数字滤波器设计(1)脉冲响应不变法(a)DF指标SKIPIF10AF指标SKIPIF10(b)将得到的模拟域指标映射为对应的归一化低通指标类型指标归一化映射归一化低通滤波器参数高通SKIPIF10，SKIPIF10，SKIPIF10，S

4、KIPIF10SKIPIF10SKIPIF10SKIPIF10，SKIPIF10，SKIPIF10带通SKIPIF10，SKIPIF10，SKIPIF10，SKIPIF10，SKIPIF10，SKIPIF10SKIPIF10，SKIPIF10SKIPIF10，SKIPIF10，SKIPIF10，SKIPIF10SKIPIF10SKIPIF10，SKIPIF10，SKIPIF10SKIPIF10带阻SKIPIF10，SKIPIF10，SKIPIF10，SKIPIF10，SKIPIF10，SKIPIF10SKIPIF10，SKIPIF10SKIPIF10，SKIPIF10，SKIPIF10，SKI

5、PIF10SKIPIF10SKIPIF10，SKIPIF10，SKIPIF10SKIPIF10(c)设计归一化低通butterworth模拟滤波器(chebyshev滤波器)(d)映射为所需类型的归一化AF(d)去归一化，得到要设计的AF(e)将AF传递函数分解为一阶部分分式之和：SKIPIF10(f)将上式中每个部分分式映射为Z域表示：SKIPIF10。(2)双线性变换法(a)DF指标SKIPIF10AF指标SKIPIF10(b)将得到的模拟域指标映射为对应的归一化低通指标（见上页表格）(c)设计归一化低通butterworth模拟滤波器(chebyshev滤波器)(d)映射为所需类型的归一

6、化AF(d)去归一化，得到要设计的AF(e)将AF传递函数映射为待设计的DF：SKIPIF10*对chebyshev滤波器，高通和低通归一化时不用3dB截止频率SKIPIF10而用通带截止频率SKIPIF10。4.低通数字滤波器的Z域直接频率变换原型数字滤波器3dB截止频率为SKIPIF10，则有类型映射设计参数低通SKIPIF10SKIPIF10SKIPIF10：目的滤波器截止频率高通SKIPIF10SKIPIF10SKIPIF10：目的滤波器截止频率带通SKIPIF10SKIPIF10SKIPIF10SKIPIF10：带通DF通带下限截止频率SKIPIF10：带通DF通带上限截止频率带阻S

7、KIPIF10SKIPIF10SKIPIF10SKIPIF10：带通DF通带下限截止频率SKIPIF10：带通DF通带上限截止频率滤波器结构变换HYPERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/residuez.htmlresiduezz-transformpartial-fractionexpansionHYPERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/sos

8、2tf.htmlsos2tfConvertdigitalfiltersecond-ordersectiondatatotransferfunctionformHYPERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/sos2zp.htmlsos2zpConvertdigitalfiltersecond-ordersectionparameterstozero-pole-gainformHYPERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b

9、/help/toolbox/signal/help.jar%21/tf2sos.htmltf2sosConvertdigitalfiltertransferfunctiondatatosecond-ordersectionsformHYPERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/tf2zp.htmltf2zpConverttransferfunctionfilterparameterstozero-pole-gainformHYPERLINKjar:file:/D:/Prog

10、ram%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/tf2zpk.htmltf2zpkConverttransferfunctionfilterparameterstozero-pole-gainformHYPERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/zp2sos.htmlzp2sosConvertzero-pole-gainfilterparameterstosecond-ordersectionsformHY

11、PERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/zp2tf.htmlzp2tfConvertzero-pole-gainfilterparameterstotransferfunctionform模拟滤波器设计Butterworth低通滤波器z,p,k=butter(n,Wn,s)z,p,k=butter(n,Wn,ftype,s)b,a=butter(n,Wn,s)b,a=butter(n,Wn,ftype,s)直接设计数字滤波器z,p,k=butter(n,Wn)z,p,k=

12、butter(n,Wn,ftype)b,a=butter(n,Wn)b,a=butter(n,Wn,ftype)ChebyshevI型低通滤波器设计z,p,k=cheby1(n,R,Wp,s)z,p,k=cheby1(n,R,Wp,ftype,s)b,a=cheby1(n,R,Wp,s)b,a=cheby1(n,R,Wp,ftype,s)z,p,k=cheby1(n,R,Wp)z,p,k=cheby1(n,R,Wp,ftype)b,a=cheby1(n,R,Wp)b,a=cheby1(n,R,Wp,ftype)滤波器频带变换FrequencyTransformationTransformati

13、onFunctionLowpasstolowpassnumt,dent=HYPERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/lp2lp.htmllp2lp(num,den,Wo)At,Bt,Ct,Dt=lp2lp(A,B,C,D,Wo)Lowpasstohighpassnumt,dent=HYPERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/lp2hp.htmllp2hp(num,den,Wo)At,Bt,Ct,Dt=lp2hp(A,B,C,D,Wo)Lowpasstobandpassnumt,dent=HYPERLINKjar:file:/D:/Program%20Files/MATLAB/R2009b/help/toolbox/signal/help.jar%21/lp2bp.htmllp2bp(num,d