matlab实现ceemd

CEEMD（Complete Ensemble Empirical Mode Decomposition）是一种基于局部特征的信号分解方法，可以将非平稳信号分解为若干个本征模态函数（IMF）。以下是MATLAB实现CEEMD的示例代码：

function [imf] = ceemd(x, MAX_ITER, ens)
% x: input signal
% MAX_ITER: maximum number of sifting iterations
% ens: ensemble size
% imf: intrinsic mode functions

N = length(x);
imf = zeros(ens, N);

for ii = 1:ens
    % add white noise to signal
    x1 = x + randn(1,N);
    % initialize the residue as the original signal
    h = x1;
    % set the sifting stopping criterion threshold
    std_h = std(h);
    if std_h == 0
        imf(ii,:) = h;
        continue;
    end
    eps = 0.01 * std_h;
    for jj = 1:MAX_ITER
        % calculate the upper and lower envelopes
        u = h;
        l = h;
        for kk = 1:5
            u = u + hilbert(l-u);
            l = l + hilbert(u-l);
        end
        % calculate the average envelope
        m = (u+l)/2;
        % extract the residue
        r = h - m;
        % check if the residue is an IMF
        if is_imf(r, eps, 5)
            imf(ii,:) = r;
            break;
        end
        % update the residue
        h = r;
    end
end
end

function [is_imf] = is_imf(x, eps, max_iter)
% x: input signal
% eps: threshold for sifting stopping criterion
% max_iter: maximum number of sifting iterations
% is_imf: true if x is an IMF, false otherwise

% initialize the sifting stopping criterion threshold
std_x = std(x);
if std_x == 0
    is_imf = false;
    return;
end
e = eps * std_x;

% initialize the maximum number of sifting iterations
iter = 0;
while iter < max_iter
    % calculate the upper and lower envelopes
    u = x;
    l = x;
    for kk = 1:5
        u = u + hilbert(l-u);
        l = l + hilbert(u-l);
    end
    % calculate the average envelope
    m = (u+l)/2;
    % extract the residue
    r = x - m;
    % check if the residue satisfies the sifting stopping criterion
    if sum(abs(r)) < e
        is_imf = true;
        return;
    end
    % update the signal
    x = r;
    % increment the number of sifting iterations
    iter = iter + 1;
end

is_imf = false;
end

其中，`ceemd`函数是主函数，它接受三个输入参数：输入信号 `x`、最大迭代次数 `MAX_ITER` 和集合大小 `ens`，并返回若干个IMF组成的矩阵 `imf`。`is_imf`函数是一个辅助函数，用于判断一个信号是否是IMF。