Local Mean Decomposition Method: Algorithm Explanation and MATLAB Implementation

Local Mean Decomposition (LMD) is an adaptive time-frequency analysis method specifically designed for non-stationary signals. This approach decomposes complex signals into multiple Product Function (PF) components, effectively extracting time-varying characteristics of the signal.

In MATLAB implementation, Local Mean Decomposition typically involves these core algorithmic steps: First, the input signal undergoes extremum point detection using functions like findpeaks() or custom extremum detection algorithms. Then, interpolation methods (such as spline interpolation via spline() function) are employed to construct the local mean function and envelope estimation function. The iterative decomposition process gradually separates PF components from the original signal through multiple iterations, with each iteration extracting one PF component until the residual signal becomes monotonic.

Key considerations for MATLAB implementation include: Accurate extremum identification is crucial for decomposition quality, requiring robust peak detection algorithms; Selection of appropriate interpolation methods (e.g., spline interpolation using interp1() with 'spline' option) for constructing mean curves; Proper setting of iteration termination conditions using while loops with convergence criteria to avoid over-decomposition. Successful debugging in MATLAB 7.0 environment demonstrates excellent compatibility across different MATLAB versions.

Local Mean Decomposition finds extensive applications in mechanical fault diagnosis, biomedical signal processing, and other fields, particularly suitable for analyzing non-stationary signals with significant instantaneous frequency variations. Compared to Empirical Mode Decomposition (EMD), LMD employs different decomposition strategies and can achieve better time-frequency resolution in certain scenarios, especially when handling signals with sharp transient components.