MATLAB Implementation of LMD Decomposition Method with B-spline Envelope Processing

LMD decomposition is an adaptive signal processing method primarily used for time-frequency analysis of non-stationary signals. The core concept involves decomposing complex signals into several Product Function (PF) components, where each PF component is obtained by multiplying an envelope signal with a pure frequency-modulated signal. In LMD implementation, B-spline interpolation is commonly used to construct the signal's upper and lower envelopes. Compared to traditional methods, B-spline envelopes offer better smoothness and local adaptability, enabling more accurate characterization of signal features. The main implementation steps include: Extrema Identification: First detect local extrema points of the signal as the foundation for envelope construction. MATLAB implementation typically uses findpeaks() function with appropriate threshold settings to ensure reliable extrema detection. B-spline Envelope Fitting: Apply B-spline curve interpolation to the extrema points to obtain upper and lower envelopes. The code utilizes spline() or spapi() functions with controllable knot sequences and spline order parameters. Component Separation: Iteratively remove envelope modulation to gradually separate PF components. This involves repeated envelope estimation and demodulation operations until convergence criteria are met. Termination Conditions: Stop decomposition when the residual signal becomes monotonic or meets predetermined criteria. The implementation should include checks for residual signal properties and maximum iteration limits. Key MATLAB implementation considerations include proper boundary handling for extrema points and setting appropriate iteration convergence conditions. By adjusting the order of B-splines, developers can balance envelope smoothness with computational efficiency. Typical implementation uses while-loops with convergence monitoring and includes safeguards against infinite iterations through maximum cycle counters.