EMD Endpoint Effect Reference with Multiple Algorithm Implementations

To provide comprehensive technical context, we expand the original content with implementation insights while preserving core concepts. Below are detailed specifications for EMD endpoint effect reference code with multiple algorithmic approaches:

1. Extreme Value Averaging Algorithm: Determines endpoint effects by calculating the mean of data extremum points. Implementation typically involves identifying local maxima/minima using findpeaks() function and averaging boundary extremes to create symmetric extensions.

2. Boundary Characteristic Scale Extension Algorithm: Eliminates endpoint effects by extending data at boundary characteristic points. Code implementation requires wavelet transform or Hilbert-Huang analysis to identify characteristic scales before applying predictive extrapolation.

3. Extreme Value Extension Algorithm: Corrects endpoint effects through extremum point extensions. The algorithm logic involves projecting the trend of internal extremes beyond boundaries using polynomial fitting or spline interpolation methods.

4. ISBM-based Extension Algorithm: Handles endpoint effects using Improved Boundary Characteristic Scale Extension methodology. This advanced approach combines multi-scale decomposition with adaptive thresholding, often implemented through recursive boundary condition optimization.

5. Parallel Extension Algorithm: Eliminates endpoint effects by extending data along parallel trajectories. Code implementation typically involves calculating tangent directions at endpoints and propagating values along these vectors using linear regression techniques.

6. Mirror Extension Algorithm: Corrects endpoint effects through symmetrical data mirroring. The simplest implementation reflects internal data segments across boundaries, effectively doubling the signal length while maintaining spectral characteristics.

These enhanced descriptions extend the original text's scope while maintaining conceptual integrity, providing developers with practical algorithmic insights for EMD boundary processing.