EMD-SVD-FRFTmatlab代码

以下是EMD-SVD-FRFT的Matlab代码实现：

function [IMF, residue] = EMD_SVD_FRFT(x, N, alpha, tol)
% Input arguments:
% x - the signal to be decomposed
% N - maximum number of IMFs
% alpha - FRFT parameter
% tol - stopping criterion
% Output arguments:
% IMF - matrix containing the IMFs
% residue - the residue signal

IMF = [];
residue = x;

for n = 1:N
    % Compute the SVD of the residue signal
    [U, S, V] = svd(residue);
    % Get the first singular value
    s = S(1);
    % Compute the FRFT of the first left singular vector
    f = frft(U(:, 1), alpha);
    % Check if the stopping criterion is satisfied
    if s < tol
        break;
    end
    % Add the first left singular vector to the IMF matrix
    IMF = [IMF, f];
    % Compute the residue signal
    residue = residue - s*U(:, 1)*V(:, 1)';
end

% Add the residue signal to the IMF matrix
IMF = [IMF, residue];

end

function f = frft(x, alpha)
% Compute the FRFT of the signal x with parameter alpha

N = length(x);
f = zeros(N, 1);

for k = 1:N
    for n = 1:N
        f(k) = f(k) + x(n)*exp(-1i*pi*alpha*(n-1/2)*(k-1/2)/N);
    end
end

end

使用方法：

x = ...; % 输入信号
N = ...; % 最大IMF数量
alpha = ...; % FRFT参数
tol = ...; % 停止准则
[IMF, residue] = EMD_SVD_FRFT(x, N, alpha, tol); % 进行EMD-SVD-FRFT分解

其中，IMF为包含所有IMF的矩阵，residue为分解后的残差信号。