matlab vmd滤波算法代码

以下是MATLAB VMD滤波算法的示例代码：

function [u, omega] = VMD(x, alpha, tau, K, DC, init)

% x   : signal
% alpha: moderate bandwidth constraint
% tau : time-step of the dual ascent
% K   : number of modes
% DC  : true if the first mode is put and kept at DC (0-freq)
% init: 0 = all omegas start at 0
%       1 = all omegas start equally spaced
%       2 = all omegas initialized randomly

[N, M] = size(x);
if M > N
    x = x';
    N = M;
end

if DC == true
    u = ones(N,1);
else
    u = x;
end

% initialization
v = zeros(N,K);
if init == 0
    omega = zeros(K,1);
elseif init == 1
    omega = (0:K-1)'*pi/K + pi/(2*K)*(1-1/K);
else
    omega = randn(K, 1)*pi;
end

% main loop
err = zeros(K,1);
for k = 1:K
    u = x - sum(v(:,1:k-1),2);
    for iter = 1:1000
        u_hat = fft(u);
        v_hat = zeros(N,1);
        for j = 1:k
            v_hat = v_hat + fft(v(:,j));
        end
        omega_hat = fftshift(omega);
        omega_hat(N/2+1) = 0;
        u_hat = (u_hat - alpha*(v_hat + u_hat.*(abs(omega_hat)<=tau/2)))./(1+alpha*(abs(omega_hat)<=tau/2));
        u = real(ifft(u_hat));
    end
    err(k) = norm(u - sum(v(:,1:k),2));
    if k < K
        [v(:,k), omega(k)] = extract_signal(u, alpha, tau);
    else
        v(:,k) = u;
        omega(k) = 0;
    end
end

end


function [v, omega] = extract_signal(u, alpha, tau)

N = length(u);
u_hat = fft(u);
u_hat(1) = 0;
u_hat(N/2+1) = 0;
omega = quad_min(u_hat, alpha, tau);
v_hat = u_hat.*(abs(omega)<=tau/2);
v = real(ifft(v_hat));

end


function omega = quad_min(u_hat, alpha, tau)

N = length(u_hat);
u = real(ifft(u_hat));
U = toeplitz(u);
d = zeros(N,1);
d(1) = 1;
D = toeplitz(d);
W = diag([0:N/2-1 -N/2:-1]);
W(N/2+1,:) = zeros(1,N);
W = alpha*W*inv(D*U + tau*eye(N))*W;
[Q, L] = eig(W);
[~, ind] = sort(diag(L));
Q = Q(:,ind);
omega = angle(u_hat'* Q(:,1));

end

在这个示例中，输入参数包括信号x、中等带宽约束alpha、双重上升时间步长tau、模式数量K、是否将第一个模式放在DC（0频率）处的标志DC、以及初始值init。函数输出模式v和每个模式的角频率omega。

注意：这个示例代码仅用于了解VMD滤波算法的实现方法。在实际应用中，您需要仔细调整参数并进行必要的预处理和后处理，以便获得最佳的滤波效果。