用matlab 写一个 N+2型滤波器耦合矩阵综合的程序

以下是一个示例程序，用于实现N+2型滤波器耦合矩阵综合。

% 定义滤波器阶数和频率范围
N = 4; 
Wp = [0.2 0.3]; 
Ws = [0.1 0.4];

% 计算归一化通带截止频率和阻带截止频率
wp = 2*pi*Wp; 
ws = 2*pi*Ws; 
Wn = 1; 
B = wp(2)-wp(1); 
D = ws(2)-ws(1);

% 计算归一化通带和阻带频率
W1 = (wp(1)+wp(2))/2/Wn;
W2 = (ws(1)+ws(2))/2/Wn;

% 计算归一化通带和阻带宽度
BW1 = B/Wn;
BW2 = D/Wn;

% 定义滤波器类型和参数
ftype = 'ellip'; 
Rp = 1; 
Rs = 30;

% 计算滤波器参数
[n, Wn] = ellipord(W1, W2, Rp, Rs); 
[b, a] = ellip(n, Rp, Rs, Wn, ftype);

% 计算耦合矩阵
C = zeros(N+2, N+2); 
for i = 1:N+2 
    for j = 1:N+2 
        if i == j 
            C(i,j) = 1; 
        elseif i < j 
            C(i,j) = 0.5^(j-i); 
        else 
            C(i,j) = 0.5^(i-j); 
        end 
    end 
end 

% 计算综合滤波器系数
b1 = b*C(1,:)'; 
b2 = b*C(2,:)'; 
for i = 3:N+2 
    bi = b*C(i,:)'; 
    b1 = conv(b1, bi); 
end 
a1 = a*C(1,:)'; 
a2 = a*C(2,:)'; 
for i = 3:N+2 
    ai = a*C(i,:)'; 
    a1 = conv(a1, ai); 
end 

% 绘制幅频响应图
[H, W] = freqz(b1, a1); 
mag = 20*log10(abs(H)); 
plot(W/pi, mag); 
xlabel('Normalized Frequency (\times\pi rad/sample)'); 
ylabel('Magnitude (dB)'); 
title('N+2 Type Filter Bank using Elliptic Filters');

这个程序使用了 MATLAB 的 Signal Processing Toolbox 中的 `ellipord` 和 `ellip` 函数来计算滤波器参数，使用了 `freqz` 函数来绘制幅频响应图。同时，该程序还计算了耦合矩阵并使用卷积操作计算了综合滤波器系数。