经验模态分解算法matlab代码

以下是一份简单的经验模态分解（Empirical Mode Decomposition，EMD）的MATLAB代码：

function [IMF,residual] = emd(x)
% EMD - Empirical Mode Decomposition
% USAGE: [IMF,residual] = emd(x)
%
% INPUT:
%   x - input signal (must be a column vector)
%
% OUTPUT:
%   IMF - matrix of intrinsic mode functions (each as a row)
%   residual - residual signal
%
% Reference: Huang et al., "The empirical mode decomposition and the
% Hilbert spectrum for nonlinear and non-stationary time series analysis,"
% Proc. R. Soc. Lond. A, Vol. 454, pp. 903-995, 1998.

% Set stopping criterion
epsilon = 0.1;

% Initialize variables
t = 0;
IMF = [];
h = x;

% Loop until stopping criterion is satisfied
while (sum(abs(h)) > epsilon)
    t = t + 1;
    % Find local extrema
    maxs = find((h(2:end-1) > h(1:end-2)) & (h(2:end-1) > h(3:end))) + 1;
    mins = find((h(2:end-1) < h(1:end-2)) & (h(2:end-1) < h(3:end))) + 1;
    % If there are no extrema, just set the residual to be the input
    if isempty(maxs) || isempty(mins)
        residual = h;
        break;
    end
    % Make sure maxs and mins start with a max and min respectively
    if maxs(1) < mins(1)
        maxs = [1; maxs];
    end
    if mins(1) < maxs(1)
        mins = [1; mins];
    end
    % Make sure maxs and mins end with a max and min respectively
    if maxs(end) < mins(end)
        mins = [mins; length(h)];
    end
    if mins(end) < maxs(end)
        maxs = [maxs; length(h)];
    end
    % Make the envelopes
    upper = spline(maxs,h(maxs),1:length(h));
    lower = spline(mins,h(mins),1:length(h));
    % Find the average envelope
    mean_env = (upper + lower) / 2;
    % Extract the IMF
    IMF(t,:) = h - mean_env;
    % Update the signal for the next iteration
    h = mean_env;
end

% Set the residual
residual = x - sum(IMF);

end

这个代码实现了EMD的基本过程，将输入信号分解成一组基本模态函数（IMF），并返回剩余信号（residual）。需要注意的是，EMD是一种迭代算法，停止准则（上述代码中为epsilon）的选择会影响分解结果的质量。