(2) 数字高通滤波器设计 用 MATLAB 直接法设计椭圆型数字高通滤波器,要求:通带ωp=0.3π,Rp=1dB;阻带ωs=0.2π,As=20dB。请描绘滤波器的绝对和相对幅频特性、相频特性、零极点分布图,列出系统传递函数式。
时间: 2024-03-09 20:51:38 浏览: 18
好的,下面是用MATLAB进行椭圆型数字高通滤波器设计的步骤:
1. 计算滤波器的通带角频率ωp和阻带角频率ωs,以及通带最大衰减Rp和阻带最小衰减As。
```matlab
omega_p = 0.3*pi;
omega_s = 0.2*pi;
R_p = 1;
A_s = 20;
```
2. 计算椭圆型数字高通滤波器的阶数n、通带截止频率ωc和椭圆度ε。
```matlab
delta_p = (10^(R_p/20)-1)/(10^(R_p/20)+1);
delta_s = 10^(-A_s/20);
epsilon = sqrt(1/delta_p^2-1);
n = ceil(acosh(sqrt((1/delta_p^2-1)/(1/delta_s^2-1)))/acosh(omega_s/omega_p));
[H, Wn] = ellipord(omega_p, omega_s, R_p, A_s);
[b, a] = ellip(n, R_p, A_s, Wn, 'high');
```
3. 绘制滤波器的绝对和相对幅频特性、相频特性、零极点分布图。
```matlab
% 绝对和相对幅频特性
[H, w] = freqz(b, a);
H_abs = abs(H);
H_rel = H./H_abs;
figure;
subplot(2,1,1);
plot(w/pi, 20*log10(H_abs));
xlabel('Normalized Frequency (\times\pi rad/sample)');
ylabel('Magnitude (dB)');
title('Magnitude Response');
grid on;
subplot(2,1,2);
plot(w/pi, angle(H_rel));
xlabel('Normalized Frequency (\times\pi rad/sample)');
ylabel('Phase (rad)');
title('Phase Response');
grid on;
% 相频特性
figure;
plot(w/pi, unwrap(angle(H)));
xlabel('Normalized Frequency (\times\pi rad/sample)');
ylabel('Unwrapped Phase (rad)');
title('Unwrapped Phase Response');
grid on;
% 零极点分布图
z = roots(b);
p = roots(a);
figure;
zplane(z, p);
title('Pole-Zero Plot');
```
4. 列出滤波器的传递函数式。
```matlab
syms z;
H_z = poly2sym(b, z)/poly2sym(a, z)
```
完整MATLAB代码如下: