Question

matlab的数字滤波器的仿真怎么实现

Answer 1

fp = 30;
fs = 35;
Fs = 100;
wp = 2*pi*fp/Fs;
ws = 2*pi*fs/Fs;
wp = tan(wp/2);
ws = tan(ws/2); % 通带最大衰减为0.5dB，阻带最小衰减为40dB
[N, wn] = buttord(wp, ws, 0.5, 40, 's'); % 模拟低通滤波器极零点
[z, p, k] = buttap(N); % 由极零点获得转移函数参数
[b, a] = zp2tf(z, p, k); % 由原型滤波器获得实际低通滤波器
[B, A] = lp2lp(b, a, wp);
[bz, az] = bilinear(B, A, .5);
[h, w] = freqz(bz, az, 256, Fs);
figure
plot(w, abs(h))
grid on

图1 巴特沃斯数字低通滤波器
1-2基于Butterworth模拟滤波器原型，使用双线性状换设计数字滤波器：各参数值为：通带截止频率Omega=0.2*pi,阻带截止频率Omega=0.3*pi,通带波动值Rp=1dB,阻带波动值Rs=15dB,设Fs=4000Hz。
代码：
wp=0.2*pi;ws=0.3*pi;
Fs=4000;T=1/Fs;
OmegaP=(2/T)*tan(wp/2);
OmegaS=(2/T)*tan(ws/2);
rp=1;rs=15;as=15;
ripple=10^(-rp/20);attn=10^(-rs/20);
[n,wn]=buttord(OmegaP,OmegaS,rp,rs,'s');
[z,p,k]=Buttap(n);
[b,a]=zp2tf(z,p,k);
[bt,at]=lp2lp(b,a,wn);
[b,a]=bilinear(bt,at,Fs);
[db,mag,pha,grd,w]=freqz_m(b,a);
%
%下面绘出各条曲线
subplot(2,2,1);plot(w/pi,mag);title('Magnitude Frequency幅频特性');
xlabel('w(/pi)');ylabel('|H(jw)|');
axis([0,1,0,1.1]);
set(gca,'XTickMode','manual','XTick',[0 0.2 0.3 1]);
set(gca,'YTickMode','manual','YTick',[0 attn ripple 1]);grid

subplot(2,2,2);plot(w/pi,db);title('Magnitude Frequency幅频特性(db)');
xlabel('w(/pi)');ylabel('dB');
axis([0,1,-30,5]);
set(gca,'XTickMode','manual','XTick',[0 0.2 0.3 1]);
set(gca,'YTickMode','manual','YTick',[-60 -as -rp 0]);grid

subplot(2,2,3);plot(w/pi,pha/pi);title('Phase Frequency相频特性');
xlabel('w(/pi)');ylabel('pha(/pi)');
axis([0,1,-1,1]);

subplot(2,2,4);plot(w/pi,grd);title('Group Delay群延时');
xlabel('w(/pi)');ylabel('Sample');
axis([0,1,0,15]);
set(gca,'XTickMode','manual','XTick',[0 0.2 0.3 1]);grid
运行结果：

图2巴特沃思数字低通滤波器幅频-相频特性

1-3设计一巴特沃斯高通数字滤波器，要求通带截止频率0.6*pi，通带衰减不大于1dB，阻带衰减15DB，抽样T=1。
Wp=0.6*pi;
Ws=0.4*pi;
Ap=1;
As=15;
[N,wn]=buttord(Wp/pi,Ws/pi,Ap,As); %计算巴特沃斯滤波器阶次和截止频率
%频率变换法设计巴特沃斯高通滤波器
[db,mag,pha,grd,w]=freqz_m(b,a); %数字滤波器响应
plot(w,mag);
title('数字滤波器幅频响应|H(ej\Omega)|')

图3巴特沃斯数字高通滤波器

2-1用窗函数法设计一个线性相位FIR低通滤波器，并满足性能指标:通带边界频率
Wp=0.5*pi,阻带边界频率Ws=0.66*pi,阻带衰减不小于40dB,通带波纹不大于3dB。选择汉宁窗。
代码：
wp =0.5*pi;
ws=0.66*pi;
wdelta =ws-wp;
N= ceil(8*pi/wdelta)
if rem(N,2)==0
N=N+1;
end

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