MATLAB Source Code for Empirical Mode Decomposition (EMD)

This is a MATLAB source code that performs Empirical Mode De decomposition.

function [IMF,Residual]=emd(x)

%emd: Perform empirical mode decomposition to decompose a signal into Intrinsic Mode Functions (IMFs)

% [IMF,Residual]=emd(x)

%Input:

% x: the input signal (must be a row vector)

%Output:

% IMF: matrix containing intrinsic mode functions as columns

% Residual: the final residual signal after extracting all IMFs

%Author: Deng Bin, Zhang Zhilin

%Date: 4-10-2010

%Reference:

%Norden E. Huang et al, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. A(1998)454:903-995.

%DOI:10.1098/rspa.1998.0193

% Note: This program was written and tested in MATLAB R2016a. Using other MATLAB versions might generate errors or warnings.

% Check if input signal is a vector using size validation

if size(x,1)~=1

error('Input signal must be a row vector');

end

% Initialize IMF matrix with maximum 10 components and working signal

IMF=zeros(length(x),10);

h=x;

n=1;

% Main decomposition loop - iterates up to 10 IMF components

while n<=10

% Stop decomposition when signal length becomes too short (<=3 points)

if length(h)<=3

Residual=h;

break;

end

% Extract envelope using cubic smoothing spline interpolation

% csaps function creates smoothing spline with specified smoothing parameter

p=csaps(1:length(h),h,1-1e-5*(length(h)-1));

m=h-ppval(p,1:length(h))';

% Check if the extracted component meets IMF criteria

if isimf(m)

IMF(:,n)=m';

n=n+1;

h=h-m;

else

h=m;

end

end

% Remove unused IMF columns from the pre-allocated matrix

IMF(:,n:end)=[];

% IMF validation function - checks component properties

function flag=isimf(x)

%isimf: Determine whether x qualifies as an intrinsic mode function

% flag=isimf(x)

%Input:

% x: the candidate signal component

%Output:

% flag: boolean result indicating IMF status (true/false)

%Author: Deng Bin, Zhang Zhilin

%Date: 4-10-2010

%Reference:

%Norden E. Huang et al, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. A(1998)454:903-995.

%DOI:10.1098/rspa.1998.0193

% Initialize flag to true (assume valid IMF initially)

flag=true;

% Check if signal is too short for meaningful IMF analysis

if length(x)<=2

flag=false;

return;

end

% Monotonicity check: verify if signal is strictly increasing or decreasing

if x(1)

for i=3:length(x)

if x(i-1)>=x(i)

flag=false;

break;

end

end

else

for i=3:length(x)

if x(i-1)<=x(i)

flag=false;

break;

end

end

end

% Extremum point balance check: verify equal number of local maxima and minima

if sum(x(1:end-2)x(2:end-1) & x(3:end)>x(2:end-1))

flag=false;

end

% Zero signal check: reject components with negligible amplitude

if sum(abs(x))

flag=false;

end

end