vmd分解的matlab代码

以下是使用Matlab进行VMD分解的示例代码：

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

% Inputs:
% x - the input signal
% K - the number of modes
% alpha - the balancing parameter
% tau - time-step
% dc - boolean variable, whether to add DC component
% init - selection of initialization ('rand' for random, 'fix' for fixed)
% Outputs:
% u - the modes
% omega - the estimated mode center-frequencies
% alpha - the balancing parameter

if nargin < 6
    init = 'rand';
end

if nargin < 5
    dc = 1;
end

if nargin < 4
    tau = 0.5;
end

if nargin < 3
    alpha = 2000;
end

if nargin < 2
    K = 3;
end

x = x(:)';
N = length(x);
t = (0:N-1)*tau;

% FFT parameters
Fs = 1/tau;
freqs = (2*pi/N)*[0:N/2-1 -N/2:-1];
omega = freqs;
omega(N/2+1) = 0;

% Center frequencies
fc = (0:K-1)'*(Fs/K);
fc(K) = Fs/2;

% Initial omega
if strcmp(init, 'rand')
    omega = rand(K,1)*(max(omega)-min(omega)) + min(omega);
elseif strcmp(init, 'fix')
    % User-defined initialization
    omega = [10,20,50]'*(2*pi/N);
else
    error('Unknown initialization choice.')
end

% Sort center frequencies
[~,index] = sort(omega);
fc = fc(index);
omega = omega(index);

% Time-frequency representation
X = x'*exp(-j*t'*omega);

% Main loop
u = zeros(N,K);
h = zeros(N,K);
u_old = u;
iter = 1;

while norm(u-u_old)/norm(u_old) > 1e-7 && iter < 5000
    u_old = u;
    
    % Mode mixing
    for k=1:K
        h(:,k) = hilbert(u(:,k));
        u_hat = fft(u(:,k));
        U_hat = fft(u*h(:,k));
        Omega_hat = fft(omega(k)*h(:,k));
        omega_bar = sum(bsxfun(@times, Omega_hat, abs(U_hat).^2), 1) ./ sum(abs(U_hat).^2, 1);
        X_hat = (X - U_hat) ./ (1 - omega_bar*tau);
        W_hat = bsxfun(@times, Omega_hat, X_hat);
        w = real(ifft(W_hat));
        h(:,k) = hilbert(w);
    end
    
    % Mode filtering
    for k=1:K
        h_k = hilbert(h(:,k));
        u(:,k) = real(h_k);
        omega(k) = atan2(sum(imag(h_k).*diff(u(:,k))), sum(real(h_k).*diff(u(:,k))))/(tau*N);
    end
    
    % Balancing
    if alpha > 0
        u = bsxfun(@times, u, (alpha./(abs(u).^2*ones(K,1))));
    end
    
    % Display
    if mod(iter,100) == 0
        disp(['Iteration: ',num2str(iter)])
    end
    
    iter = iter + 1;
end

% Residual
if dc
    u = [u, ones(N,1)];
end

alpha = alpha./(abs(u).^2*ones(K+dc,1));

end

使用方法：

假设我们要对信号 `x` 进行3个模态的VMD分解，使用默认参数：

[u, omega, alpha] = VMD(x, 3);

其中 `u` 是分解后得到的模态， `omega` 是估计的中心频率， `alpha` 是平衡参数。