EMD算法分解信号后，怎么将这些信号重构呢？求高手指点

有个碰逗叫BOUDRAA的人发明了一种算法，叫连贯均方误差法，就是分别求每个IMF分量的平方，取完后求和再取平均，求和的点数是N，即采样点的点数。假如你分解得到了M个IMF分量，那么就应该有M个这样的数，把得到的返丛这些数圆整，求出最小的整数，记为K。那么K之前的包括K的这些分量相加应该是噪声的信号，笑世卖K之后的加上剩余信号即为重构信号。不过目前该方法被证实不适合信噪比低得信号，不过一般的处理效果还可以。

function imf = emd(x,n)%%最好把函数名改为emd1之类的，以免和Grilling的emd冲突

%%n为你想得到做局的IMF的个数

c = x('% copy of the input signal (as a row vector)

N = length(x)-

% loop to decompose the input signal into n successive IMFs

imf = []% Matrix which will contain the successive IMF, and the residuefor t=1:n

% loop on successive IMFs

%-------------------------------------------------------------------------

% inner loop to find each imf

h = c% at the beginning of the sifting process, h is the signal

SD = 1% Standard deviation which will be used to stop the sifting process

while SD >0.3 % while the standard deviation is higher than 0.3 (typical value) %%筛选停止准则

% find local max/min points

d = diff(h)% approximate derivative %%求各点导数

maxmin = []% to store the optima (min and max without distinction so far)

for i=1:N-2

if d(i)==0% we are on a zero %%导数为0的点，即”此明驻点“，但驻点不一定都是极值点，如y=x^3的x=0处

if sign(d(i-1))~=sign(d(i+1)) % it is a maximum %%如果驻点两侧的导数异号（如一边正，一边负），那么该点为极值点

maxmin = [maxmin, i]%%找到极值点在信号中的坐标（不分极大值和极小值点）

end

elseif sign(d(i))~=sign(d(i+1)) % we are straddling a zero so%%如y=|x|在x=0处是极值点，但该点倒数不存在，所以不能用上面的判

断方法

maxmin = [maxmin, i+1] % define zero as at i+1 (not i) %%这里提供了另一类极值点的判断方法

end

end

if size(maxmin,2) <2 % then it is the residue %%判断信号是不是已经符合残余分量定义

break

end

% divide maxmin into maxes and mins %% 分离极大值纯扒让点和极小值点

if maxmin(1)>maxmin(2) % first one is a max not a min

maxes = maxmin(1:2:length(maxmin))

mins = maxmin(2:2:length(maxmin))

else% is the other way around

maxes = maxmin(2:2:length(maxmin))

mins = maxmin(1:2:length(maxmin))

end% make endpoints both maxes and mins

maxes = [1 maxes N]

mins = [1 mins N]

%------------------------------------------------------------------------- % spline interpolate to get max and min envelopesform imf

maxenv = spline(maxes,h(maxes),1:N) %%用样条函数插值拟合所有的极大值点

minenv = spline(mins, h(mins),1:N)%%用样条函数插值拟合所有的极小值点

m = (maxenv + minenv)/2% mean of max and min enveloppes %%求上下包络的均值

prevh = h% copy of the previous value of h before modifying it %%h为分解前的信号

h = h - m% substract mean to h %% 减去包络均值

% calculate standard deviation

eps = 0.0000001% to avoid zero values

SD = sum ( ((prevh - h).^2) ./ (prevh.^2 + eps) )%% 计算停止准则

end

imf = [imfh]% store the extracted IMF in the matrix imf

% if size(maxmin,2)<2, then h is the residue

% stop criterion of the algo. if we reach the end before n

if size(maxmin,2) <2

break

end

c = c - h% substract the extracted IMF from the signal

end

return

参考资料

http://zhidao.baidu.com/link?url=Dv2ef87TOGx8zcbCT1UJsZ2kutWrm4FuT5kbMZY5mAAn5yv7APibQ1y8fSag5JvbF2fKlI5jhgpTXu95SDRgi_

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