Search Results (3)

In a recently published work, we introduced local Legendre polynomial fitting-based permutation entropy (LPPE) as a new complexity measure for quantifying disorder or randomness in time series. LPPE benefits from the ordinal pattern (OP) concept and incorporates a natural, aliasing-free multiscaling effect by design. The current work extends our previous study by investigating LPPE’s capability to assess fatigue levels using both synthetic and real surface electromyography (sEMG) signals. Real sEMG signals were recorded during biceps brachii fatiguing exercise maintained at 70% of maximal voluntary contraction (MVC) until exhaustion and were divided into four consecutive temporal segments reflecting sequential stages of exhaustion. As fatigue levels rise, LPPE values can increase or decrease significantly depending on the selection of embedding dimensions. Our analysis reveals two key insights. First, using LPPE with limited embedding dimensions shows consistency with the literature. Specifically, fatigue induces a decrease in sEMG complexity measures. This observation is supported by a comparison with the existing multiscale permutation entropy (MPE) variant, that is, the refined composite downsampling (rcDPE). Second, given a fixed OP length, higher embedding dimensions increase LPPE’s sensitivity to low-frequency components, which are notably present under fatigue conditions. Consequently, specific higher embedding dimensions appear to enhance the discrimination of fatigue levels. Thus, LPPE, as the only MPE variant that allows a practical exploration of higher embedding dimensions, offers a new perspective on fatigue’s impact on sEMG complexity, complementing existing MPE approaches. Full article

This study employs the two-dimensional Legendre polynomial fitting (2-D LPF) method to fit M2 tidal harmonic constants from satellite altimetry data within the region of 53°E–131°E, 34°S–6°N, extracting internal tide signals acting on the sea surface. The M2 tidal harmonic constants are derived from the sea surface height (SSH) data of the TOPEX/Poseidon (T/P), Jason-1, Jason-2, and Jason-3 satellites via t-tide analysis. We validate the 2-D LPF method against the 300 km moving average (300 km smooth) method and the one-dimensional Legendre polynomial fitting (1-D LPF) method. Through cross-validation across 42 orbits, the optimal polynomial orders are determined to be seven for 1-D LPF, and eight and seven for the longitudinal and latitudinal directions in 2-D LPF, respectively. The 2-D LPF method demonstrated superior spatial continuity and smoothness of internal tide signals. Further single-orbit correlation analysis confirmed generally higher correlation with topographic and density perturbations (correlation coefficients: 0.502, 0.620, 0.245; 0.420, 0.273, −0.101), underscoring its accuracy. Overall, the 2-D LPF method can use all regional data points, overcoming the limitations of single-orbit approaches and proving its effectiveness in extracting internal tide signals acting on the sea surface. Full article

Exploring the spatial distribution of sea surface height involves two primary methodologies: utilizing gridded reanalysis data post-secondary processing or conducting direct fitting along-track data. While processing gridded reanalysis data may entail information loss, existing direct fitting methods have limitations. Therefore, there is a pressing need for novel direct fitting approaches to enhance efficiency and accuracy in sea surface height fitting. This study demonstrates the viability of Legendre polynomial surface fitting, benchmarked against bicubic quasi-uniform B-spline surface fitting, which has been proven to be a well-established direct fitting method. Despite slightly superior accuracy exhibited by bicubic quasi-uniform B-spline surface fitting under identical order combinations, Legendre polynomial surface fitting offers a simpler structure and enhanced controllability. However, it is pertinent to note that significant expansion of the spatial scope of fitting often results in decreased fitting efficacy. To address this, the current research achieves the precise fitting of sea surface height across expansive spatial ranges through a regional stitching methodology. Full article