经验模态分解matlab代码

以下是经验模态分解的Matlab代码示例：

function [IMFs,Residual]=emd(x)
% Empirical Mode Decomposition
% Input: x is the 1-D signal, whose EMD needs to be computed
% Output: IMFs are the intrinsic mode functions, Residual is the residue
% EMD is computed as follows:
% 1. Compute the local mean (average of the maxima and minima) of x
% 2. Extract the local mean from x to obtain the first IMF, h1=x-m1
% 3. Compute the local mean of h1
% 4. Extract the second IMF, h2=h1-m2
% 5. Repeat steps 3 and 4 until the nth IMF is obtained
% 6. Compute the residual as the difference between the original signal and the sum of all IMFs

x=x(:)';
N=length(x);
IMFs=[];Residual=x;

% EMD processing
while(1)
    % Calculate the number of extrema and their indices
    n_ext=zeros(1,N);
    n_ext(2:N-1)=(diff(sign(diff(x)))==2)+1;
    [maxpos,minpos]=peakdet(x,0);
    if length(maxpos)<2 || length(minpos)<2
        break
    end
    if maxpos(1)<minpos(1)
        maxpos(1)=[];
    end
    if length(maxpos)>length(minpos)
        maxpos(end)=[];
    end

    if abs(maxpos(1)-minpos(1))>1
        lbound=1;
        ubound=min([maxpos(1),minpos(1)])-1;
    else
        lbound=[];
        ubound=[];
    end
    if abs(maxpos(end)-minpos(end))>1
        lbound=[lbound maxpos(end)];
        ubound=[ubound N];
    end
    for k=1:length(maxpos)-1
        if abs(maxpos(k)-minpos(k))>1
            lbound=[lbound maxpos(k)];
            ubound=[ubound minpos(k)];
        end
        if abs(maxpos(k+1)-minpos(k))>1
            lbound=[lbound maxpos(k+1)];
            ubound=[ubound minpos(k)];
        end
    end

    if isempty(lbound) || isempty(ubound)
        break
    end

    % Calculate the mean of the extrema envelopes
    m=(maxpos+minpos)/2;
    h=x-(interp1(m,x,maxpos)+interp1(m,x,minpos))/2;
    m_old=m;
    while(1)
        % Calculate the number of extrema and their indices
        n_ext=zeros(1,N);
        n_ext(2:N-1)=(diff(sign(diff(h)))==2)+1;
        [maxpos,minpos]=peakdet(h,0);
        if length(maxpos)<2 || length(minpos)<2
            break
        end
        if maxpos(1)<minpos(1)
            maxpos(1)=[];
        end
        if length(maxpos)>length(minpos)
            maxpos(end)=[];
        end

        if abs(maxpos(1)-minpos(1))>1
            lbound=1;
            ubound=min([maxpos(1),minpos(1)])-1;
        else
            lbound=[];
            ubound=[];
        end
        if abs(maxpos(end)-minpos(end))>1
            lbound=[lbound maxpos(end)];
            ubound=[ubound N];
        end
        for k=1:length(maxpos)-1
            if abs(maxpos(k)-minpos(k))>1
                lbound=[lbound maxpos(k)];
                ubound=[ubound minpos(k)];
            end
            if abs(maxpos(k+1)-minpos(k))>1
                lbound=[lbound maxpos(k+1)];
                ubound=[ubound minpos(k)];
            end
        end

        if isempty(lbound) || isempty(ubound)
            break
        end

        % Calculate the mean of the envelopes
        m=(maxpos+minpos)/2;
        hm=h-(interp1(m,h,maxpos)+interp1(m,h,minpos))/2;

        % Check for convergence
        if sum(abs(m-m_old))<0.1
            break;
        else
            m_old=m;
            h=hm;
        end
    end

    % Extract the IMF
    IMFs=[IMFs;h];
    x=x-h;
    % Check for the residue
    if sum(abs(h))<0.01*sum(abs(Residual))
        break;
    else
        Residual=Residual-h;
    end
end

IMFs=[IMFs;Residual];
end

function [maxtab, mintab]=peakdet(v, delta, x)
% PEAKDET Detect peaks in a vector
% [MAXTAB, MINTAB] = PEAKDET(V, DELTA) finds the local maxima and minima ("peaks")
% in the vector V. MAXTAB and MINTAB consists of two columns. Column 1
% contains indices in V, column 2 the found values.
% With [MAXTAB, MINTAB] = PEAKDET(V, DELTA, X) the indices
% in MAXTAB and MINTAB are replaced with the corresponding X-values.

% Author: Jonas Almeida, modified by Jan Hasenauer, 2008
% Modified by Xiaoning Yang, 2019
% $Id: peakdet.m 143 2008-08-12 15:39:14Z hasenauer $

maxtab = [];
mintab = [];

v = v(:); % Just in case this wasn't a proper vector

% Find the difference between each element and the next
dv = diff(v);

% Calculate the index of all peaks
ind = find([dv(1); dv] < 0 & dv > -delta)+1;

for i = 1:length(ind)
    if ind(i) <= 1 || ind(i) >= length(v)
        continue
    end
    if v(ind(i)-1) < v(ind(i)) && v(ind(i)+1) < v(ind(i))
        maxtab = [maxtab; ind(i) v(ind(i))];
    end
    if v(ind(i)-1) > v(ind(i)) && v(ind(i)+1) > v(ind(i))
        mintab = [mintab; ind(i) v(ind(i))];
    end
end

% Replace indices with X-values if X is given
if nargin == 3 && nargout == 2
    maxtab(:,1) = x(maxtab(:,1));
    mintab(:,1) = x(mintab(:,1));
end
end

该代码实现了经验模态分解的主要步骤，并计算出了每个内禀模态函数和残差。需要注意的是，该代码还包括一个辅助函数 `peakdet`，用于检测信号中的极大值和极小值。