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  寶嘎就 2011-05-16 00:00:00

  function imf = emd(x，n);%%Z好把函數(shù)名改為emd1之類的，以免和Grilling的emd沖突 %%n為你想得到的IMF的個(gè)數(shù) 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) %%篩選停止準(zhǔn)則 % find local max/min points d = diff(h); % approximate derivative %%求各點(diǎn)導(dǎo)數(shù) 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 %%導(dǎo)數(shù)為0的點(diǎn)，即”駐點(diǎn)“，但駐點(diǎn)不一定都是極值點(diǎn)，如y=x^3的x=0處 if sign(d(i-1))~=sign(d(i+1)) % it is a maximum %%如果駐點(diǎn)兩側(cè)的導(dǎo)數(shù)異號(hào)（如一邊正，一邊負(fù)），那么該點(diǎn)為極值點(diǎn) maxmin = [maxmin， i]; %%找到極值點(diǎn)在信號(hào)中的坐標(biāo)（不分極大值和極小值點(diǎn)） end elseif sign(d(i))~=sign(d(i+1)) % we are straddling a zero so%%如y=|x|在x=0處是極值點(diǎn)，但該點(diǎn)倒數(shù)不存在，所以不能用上面的判 斷方法 maxmin = [maxmin， i+1]; % define zero as at i+1 (not i) %%這里提供了另一類極值點(diǎn)的判斷方法 end end if size(maxmin，2) < 2 % then it is the residue %%判斷信號(hào)是不是已經(jīng)符合殘余分量定義 break end % divide maxmin into maxes and mins %% 分離極大值點(diǎn)和極小值點(diǎn) 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 envelopes; form imf maxenv = spline(maxes，h(maxes)，1:N); %%用樣條函數(shù)插值擬合所有的極大值點(diǎn) minenv = spline(mins， h(mins)，1:N); %%用樣條函數(shù)插值擬合所有的極小值點(diǎn) m = (maxenv + minenv)/2; % mean of max and min enveloppes %%求上下包絡(luò)的均值 prevh = h; % copy of the previous value of h before modifying it %%h為分解前的信號(hào) h = h - m; % substract mean to h %% 減去包絡(luò)均值 % calculate standard deviation eps = 0.0000001; % to avoid zero values SD = sum ( ((prevh - h).^2) ./ (prevh.^2 + eps) ); %% 計(jì)算停止準(zhǔn)則 end imf = [imf; h]; % 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

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