function imf = emd(x)
% Empiricial Mode Decomposition (Hilbert-Huang Transform)
x
= transpose(x(:));
imf = [];
while ~ismonotonic(x)
x1 = x;
sd = Inf;
kk = 1;
while ((sd<0.2)&(sd > 0.3)) | ~isimf(x1)
kk = kk + 1;
s1 = getspline(x1);
s2 = -getspline(-x1);
x2 = x1-(s1+s2)/2;
sd = sum((x1-x2).^2)/sum(x1.^2);
x1 = x2;
end
imf{end+1} = x1;
x
= x-x1;
end
imf{end+1} = x;
% FUNCTIONS
% extra equationss
function u = ismonotonic(x)
u1 = length(findpeaks(x))*length(findpeaks(-x));
if u1 > 0
u = 0;
else
u = 1;
end
function u = isimf(x)
N = length(x);
u1 = sum(x(1:N-1).*x(2:N) < 0);
u2 = length(findpeaks(x))+length(findpeaks(-x));
if abs(u1-u2) > 1
u = 0;
else
u = 1;
end
function s = getspline(x)
N = length(x);
p = findpeaks(x);
s = spline([0 p N+1],[0 x(p) 0],1:N);
function HHT(datafile,monthName);
data = load(datafile);
data = cell2mat(struct2cell(data));
% load datafile for one month
% CHANGE NUMBER AND NAME RESPECTIVELY
k = 1;
noData = [];
for i = 1 : 96 : size(data,1)-95
if isempty(find(isnan(data(i:i+95))))
imf{k} = emd(data(i:i+95));
else
noData = [noData k];
imf{k} = [];
end
k = k + 1;
end
isData = 1:size(data,1)/96;
isData(isData(noData)) = [];
k = 1;
for i = 1 : size(imf,2)
if ~isempty(imf{i})
ii{k} = imf{i};
k = k+1;
end
end
imf = ii;
% if isempty(find(isnan(d(end-95:end))))
%
imf{k} = emd(d(end-95,end));
% else
%
noData = [noData size(d,1)/96];
% end
clear k i ;
imfHilb = cell(size(imf));
for i = 1 : size(imf,2)
for j = 1 : size(imf{i},2)
imfHilb{i}{j} = hilbert(imf{i}{j});
end
end
clear i j;
% amplitude spectrum
k = 1;
for i = 1 : size(imfHilb,2)
figure;
x = 0:95;
day = zeros(1,96);
for j = 1 : size(imfHilb{i},2)
subplot(size(imfHilb{i},2),1,j);
plot(x,abs(imfHilb{i}{j}));
ylabel('amplitude');
xlabel('time');
%
title(['day ',int2str(i),' IMF ',int2str(j)]);
title([monthName,' day ',int2str(isData(k)),' IMF
',int2str(j)]);
day = day + abs(imfHilb{i}{j});
end
figure;
plot(x,day);ylabel('amplitude'); xlabel('time');
title([monthName,' day ',int2str(isData(k))]);
k = k+1;
end
clear i j k;
% CHANGE NUMBER AND NAME RESPECTIVELY
SaveAllFigures([monthName]);
% don't forget to delete figures after processing
% for k = 1 : size(data,2)
%
for i = 1 : 96 : size(data{k},2)
%
imf{k} = emd(data{k});
%
for m = 1 : size(imf{k),2}
%
hilberImf{k}{m} = hilbert(imf{k}{m});
%
end
%
end
% end
clear isData noData ii k isData
function n = findpeaks(x)
% Find peaks.
% n = findpeaks(x)
n
= find(diff(diff(x) > 0) < 0);
u
= find(x(n+1) > x(n));
n(u) = n(u)+1;
function SaveAllFigures(opt,filetype)
% filetype by default .fig
% opt is string array ; the name of the figures
if nargin == 0
opt='Unknown';
end
if nargin < 2
filetype = 'fig';
end
ChildList = sort(get(0,'Children'));
for cnum = 1:length(ChildList)
if strncmp(get(ChildList(cnum),'Type'),'figure',6)
saveas(ChildList(cnum), [opt, '_', num2str(ChildList(cnum)), '.'
filetype]);
end
end