MATLAB Implementation of Empirical Mode Decomposition (EMD) Algorithm

Below is the MATLAB code implementation example for the Empirical Mode Decomposition (EMD) algorithm. function [IMFs, R] = EMD(x) % Initialize IMFs (Intrinsic Mode Functions) and residual component R IMFs = []; R = x; % Iterative IMF extraction until residual R becomes monotonic while ~ismonotonic(R) % Extract extrema points from current residual signal extrema = find_extrema(R); % Interpolate to obtain upper and lower envelopes upper = envelope(extrema, 'upper'); lower = envelope(extrema, 'lower'); % Calculate current IMF component as mean of envelopes IMF = (upper + lower) / 2; % Update residual by subtracting current IMF R = R - IMF; % Append current IMF to IMFs collection IMFs = [IMFs, IMF]; end % Return all IMFs and final residual component IMFs = [IMFs, R]; end % Check if a signal is monotonic using differential analysis function result = ismonotonic(x) % Monotonic if all differences are non-negative or all are non-positive result = all(diff(x) >= 0) || all(diff(x) <= 0); end % Detect all local extrema (maxima and minima) in the signal function extrema = find_extrema(x) % Find local maxima where second difference changes sign from positive to negative maxima = find(diff(sign(diff(x))) < 0) + 1; % Find local minima where second difference changes sign from negative to positive minima = find(diff(sign(diff(x))) > 0) + 1; % Combine and sort all extrema positions extrema = sort([maxima, minima]); end % Generate envelope lines through cubic Hermite interpolation (PCHIP) function envelope_line = envelope(extrema, type) % Select appropriate extrema based on envelope type if strcmp(type, 'upper') envelope_extrema = extrema(extrema(:, 2) > 0); else envelope_extrema = extrema(extrema(:, 2) < 0); end % Interpolate envelope using piecewise cubic Hermite interpolation envelope_line = interp1(envelope_extrema(:, 1), envelope_extrema(:, 2), 1:length(extrema), 'pchip'); end This implementation demonstrates the core EMD algorithm workflow: iterative envelope extraction using cubic interpolation, IMF calculation through envelope averaging, and monotonicity-based stopping criteria. The code provides essential functions for extrema detection, envelope generation, and signal decomposition suitable for non-stationary signal analysis. We hope this MATLAB implementation helps you understand and apply the Empirical Mode Decomposition algorithm effectively. Please feel free to consult if you have any technical questions or need further clarification.