用双线性变换法设计原型低通为巴特沃兹型的数字IIR低通滤波器

由天下分享时间：2024/12/25 0:07:32 加入收藏我要投稿点赞

clc; clear all

Rp = 1; % 通带衰减/dB Rs = 40; %阻带衰减/dB OmegaP1_1=400; % 通带边界频率 OmegaS1_1=500; % 阻带边界频率 Fp=2000; % 抽样频率

Wp1=2*pi*OmegaP1_1/Fp; % 通带频率模数转换 Ws1=2*pi*OmegaS1_1/Fp; % 阻带频率模数转换 OmegaP1=2*Fp*tan(Wp1/2); % 通带频率非线性变换 OmegaS1=2*Fp*tan(Ws1/2); % 阻带频率非线性变换 Eta_P=OmegaP1/OmegaP1; %归一化 Eta_S=OmegaS1/OmegaP1;%归一化 Lemta_P_EquivalentLowPass=Eta_P;

Lemta_S_EquivalentLowPass=Eta_S; % 估计滤波器阶数

[N,Wn]=buttord(Lemta_P_EquivalentLowPass, Lemta_S_EquivalentLowPass, Rp, Rs,'s'); %设计滤波器

[num1,den1]=butter(N,Wn,'s'); [num2,den2]=lp2lp(num1,den1,OmegaP1); [num,den]=bilinear(num2,den2,Fp); [z,p,k]=tf2zp(num,den) %显示传输函数 w = 0:pi/255:pi; h = freqz(num,den,w);

g = 20*log10(abs(h)); % 绘制增益响应 figure;

plot(w/pi,g);grid %绘制巴特沃兹低通滤波器幅频特性 axis([0 1 -60 5]); xlabel('\\omega /\\pi'); ylabel('增益/ dB'); title('巴特沃兹低通滤波器'); figure;

zplane(z,p);%绘制传输函数零极点 title('传输函数的零极点'); M=100; n=0:M;

x1=sin(2*pi*0.15*n); x2=sin(2*pi*0.3*n); x=x1+x2; figure;

subplot(2,2,1)%绘制x1的波形 plot(x1);

grid on;

axis([0,100,-2,2]); xlabel('t'); ylabel('x1(t)'); title('x1的波形'); subplot(2,2,2)%绘制x1的波形 plot(x2); grid on;

axis([0,100,-2,2]); xlabel('t'); ylabel('x2(t)'); title('x2的波形');

subplot(2,2,3)%绘制输入x的波形 plot(x); grid on;

axis([0,100,-2,2]); xlabel('t'); ylabel('x(t)');

title('输入信号x的波形') hanshu=impz(num,den,600); y=juanji(x,hanshu);

subplot(2,2,4);%绘制输出y的波形 plot(y); grid on;