Two Critical Parameters in Phase Space Reconstruction

In phase space reconstruction, delay time and correlation dimension are recognized as two crucial parameters. These parameters can be efficiently adjusted in MATLAB implementations using functions like dtw() for delay calculation and correlationSum() for dimension estimation. Beyond these core parameters, reconstruction results can be optimized by tuning additional factors such as the cutoff frequency of noise filters through butter() or cheby1() functions, and the time window size using moving window techniques. Following reconstruction, further data analysis can be performed using MATLAB's signal processing toolbox (e.g., pspectrum() for spectral analysis) and statistical functions (e.g., corrcoef() for correlation analysis) to gain deeper insights into data characteristics and patterns. Therefore, research and practice in phase space reconstruction require not only theoretical knowledge but also proficiency in MATLAB programming, including understanding of key algorithms like Taken's embedding theorem and Grassberger-Procaccia algorithm, along with advanced data processing capabilities.