用MATLAB实现bemd

由于没有具体的数据和代码实现需求，我们这里给出一个基本的MATLAB代码实现bemd的示例：

% Bivariate Empirical Mode Decomposition (BEMD) Algorithm
% Reference: "Bivariate Empirical Mode Decomposition" by Bai et al. (2009)

function [imf1,imf2,residue] = bemd(signal1,signal2,level,radius)

% signal1 - the first signal to be decomposed
% signal2 - the second signal to be decomposed
% level - the number of decomposition levels
% radius - radius of the sifting window

% initializations
imf1 = zeros(length(signal1),level);
imf2 = zeros(length(signal2),level);

% calculate residue
residue1 = signal1;
residue2 = signal2;

% loop for each level
for i = 1:level
    
    % calculate the Intrinsic Mode Functionset1
    [imf1(:,i)] = sift_bimd(residue1,radius);
    [imf2(:,i)] = sift_bimd(residue2,radius);
    
    % calculate the residue
    residue1 = residue1 - imf1(:,i);
    residue2 = residue2 - imf2(:,i);
    
end

% save the residue
residue = [residue1,residue2];

end


function [imf] = sift_bimd(signal,radius)

% initializations
N = length(signal);
iter = 0;
h = 0.5;

while min(abs(signal-hilbert(signal)))>0.1*std(signal)
    
    % check for iterations
    if iter>200
        break;
    end
    
    % calculate local extrema
    [tmax,maxInd] = findpeaks(signal);
    [tmin,minInd] = findpeaks(-1*signal);
    
    % check for empty extrema
    if isempty(maxInd)||isempty(minInd)
        break;
    end
    
    % ensure that the first and last extrema are type "max"
    if maxInd(1)<minInd(1)
        maxInd(1) = [];
    end
    if minInd(end)<maxInd(end)
        minInd(end) = [];
    end
    
    % check for empty extrema
    if isempty(maxInd)||isempty(minInd)
        break;
    end
    
    % calculate spline envelopes
    maxEnv = spline(maxInd,signal(maxInd),1:N)';
    minEnv = spline(minInd,signal(minInd),1:N)';
    
    % calculate mean envelope
    meanEnv = (maxEnv+minEnv)/2;
    
    % calculate mean-corrected signal
    meanSig = signal-meanEnv;
    
    % shift towards zero
    if meanSig(1)>0
        meanSig = meanSig-meanSig(1);
    end
    if meanSig(1)<=0
        meanSig = meanSig+meanSig(1);
    end
    
    % calculate new signal as shifted mean-corrected signal
    newSignal = meanSig;
    for j=1:length(maxInd)
        newSignal(maxInd(j)-radius:maxInd(j)+radius) = ...
          newSignal(maxInd(j)-radius:maxInd(j)+radius) - ...
          meanSig(maxInd(j))/(2*(radius+1));
    end
    for j=1:length(minInd)
        newSignal(minInd(j)-radius:minInd(j)+radius) = ...
          newSignal(minInd(j)-radius:minInd(j)+radius) + ...
          meanSig(minInd(j))/(2*(radius+1));
    end
    
    % update iteration
    iter = iter+1;
    signal = newSignal;
    
end

% save the IMF
imf = signal;

end