nspab.m

主要是希尔伯特——黄HHT中的EMD分解过程的工具箱

function h1= nspab(data,nyy,minw,maxw,dt)

% The function NSPAB generates a smoothed HHT spectrum of data(n,k)  
% in time-frequency space, where  
% n specifies the length of time series, and 
% k is the number of IMF components.
% The frequency-axis range is prefixed.
% Negative frequency sign is reversed.
%
% MATLAB Library function HILBERT is used to calculate the Hilbert transform.
%
% Example, [h,xs,w] = nspab(lod78_p',200,0,0.12,1,3224).
%
% Functions CONTOUR or IMG can be used to view the spectrum,
%    for example contour(xs,w,h) or img(xs,w,h).
%
% Calling sequence-
% [h,xs,w] = nspab(data,nyy,minw,maxw,t0,t1)
%
% Input-
%        data        - 2-D matrix data(n,k) of IMF components
%        nyy        - the frequency resolution
%        minw        - the minimum frequency
%        maxw        - the maximum frequency
%        t0        - the start time
%        t1        - the end time
% Output-
%        h        - 2-D matrix of the HHT spectrum, where
%                  the 1st dimension specifies the number of frequencies,
%                  the 2nd dimension specifies the number of time values
%        xs        - vector that specifies the time-axis values
%        w        - vector that specifies the frequency-axis values

% Z. Shen (JHU)                July 2, 1995 Initial

%----- Get dimensions (number of time points and components)
[npt,knb] = size(data);

%----- Get time interval


%----- Apply Hilbert Transform
data=hilbert(data);
a=abs(data);
omg=abs(diff(unwrap(angle(data))))/(2*pi*dt);

%----- Smooth amplitude and frequency   
filtr=fir1(8,.1); 
for i=1:knb  
    a(:,i)=filtfilt(filtr,1,a(:,i));
   omg(:,i)=filtfilt(filtr,1,omg(:,i));
end


%----- Limit frequency and amplitude
for i=1:knb
   for i1=1:npt-1
      if omg(i1,i) >=maxw,
         omg(i1,i)=maxw;
         a(i1,i)=0;
      elseif omg(i1,i)<=minw,
         omg(i1,i)=minw;
         a(i1,i)=0;
      else
      end
   end
end
clear filtr data

%va=var(omg(200:1200))

%----- Get local frequency
dw=maxw - minw;
wmx=maxw;
wmn=minw;

%----- Construct the ploting matrix
clear p;
h1=zeros(npt-1,nyy+1);
p=round(nyy*(omg-wmn)/dw)+1;
for j1=1:npt-1
   for i1=1:knb
      ii1=p(j1,i1);        
      h1(j1,ii1)=h1(j1,ii1)+a(j1,i1);
   end
end

%----- Do 3-point to 1-point averaging
[nx,ny]=size(h1);
%n1=fix(nx/3);
%h=zeros(n1,ny);
%for i1=1:n1
   %h(i1,:)=(h1(3*i1,:)+h1(3*i1-1,:)+h1(3*i1-2,:));
%end
%clear h1;

%----- Do 3-points smoothing in x-direction
fltr=1./3*ones(3,1);
for j1=1:ny
  h1(:,j1)=filtfilt(fltr,1,h1(:,j1));
end
clear fltr;


%----- Define the results
%w=linspace(wmn,wmx,ny-1)';
%xs=linspace(t0,t1,nx)';
h1=flipud(rot90(h1));
h1=h1(1:ny-1,:);