信号处理6.4双线性变换法.ppt

利用MATLAB实现IIR数字滤波器 椭圆(C)型数字滤波器 确定数字滤波器的阶数及参数Wc [N, Wc] = ellipord(Wp, Ws, Ap, As) DF系统函数分子、分母多项式的确定 低通 [num,den] = ellip(N,Ap,As,Wc) 高通 [num,den] = ellip(N,Ap,As,Wc,high) 带通 [num,den] = ellip(N,Ap,As,Wc) 带阻 [num,den] = ellip(N,Ap,As,Wc,stop) * 带通、带阻中W=[W1, W2] * 模拟低通原型 (prototype) buttap cheb1ap besselap ellipap cheb2ap 频率变换 lp2lp lp2hp lp2bp lp2bs 综合设计 butter cheby1 cheby2 ellip besself MATLAB中IIR设计的主要函数 IIR 滤波器最小阶数的计算 buttord cheb1ord cheb2ord ellipord 离散化 bilinear impinvar * 例：利用MATLAB实现数字带阻滤波器 Wp1=2.8113rad/s, Wp2=2.9880rad/s, Ap?1dB ,  Ws1=2.9203rad/s, Ws2=2.9603rad/s, As ?10dB Wp=[2.813,2.9880];Ws=[2.9203,2.9603]; Ap=1;As=10; [N,Wc]=buttord(Wp/pi,Ws/pi,Ap,As) [numd,dend]=butter(N,Wc,stop) 运行结果 N =2 numd =[0.9522, 3. 7327, 5.5624, 3.7327, 0.9522] dend =[1.0000, 3.8242 , 5.5601, 3.6412, 0.9067] * 例：利用AF-BW filter及双线性变换法设计一DF，满足 ?p=0.2p, ?s=0.6p, ?p?2dB, ?s?15dB %Design DF BW low-pass filter using impulse invariance %DF BW LP specfication Wp=0.2*pi; Ws=0.6*pi; Ap=2; As=15; T=2;Fs=1/T; %Sampling frequency(Hz) %Analog Butterworth specfication wp=2*tan(Wp/2)/T;ws=2*tan(Ws/2)/T; %determine the order of AF filter and the 3-dB cutoff frequency [N,wc]=buttord(wp,ws,Ap,As,s) %determine the AF-BW filter [numa,dena]=butter(N,wc,s) * 例：利用AF-BW filter及双线性变换法设计一DF，满足 ?p=0.2p, ?s=0.6p, ?p?2dB, ?s?15dB %determine the DF filter [numd,dend]=bilinear(numa,dena,Fs) %plot the frequency response w=linspace(0,pi,1024); h=freqz(numd,dend,w); plot(w/pi,20*log10(abs(h))); axis([0 1 -50 0]);grid; xlabel(Normalized frequency); ylabel(Gain,dB); %computer Ap As of the designed filter w=[Wp Ws];h=freqz(numd,dend,w); fprintf(Ap= %.4f\n,-20*log10( abs(h(1)))); fprintf(As= %.4f\n,-20*log10( abs(h(2)))); * 例：利用AF-BW filter及双线性变换法设计一DF，满足 ?p=0.2p, ?s=0.6p, ?p?2dB, ?s?15dB ?