Comparison of spectral decompositions in locomotion time series

Abstract

This work focuses on comparing three methods for detecting and extracting rhythms through additive decomposition in non-stationary signals with noise and characteristics similar to those of long-range correlation. Two of these methods are based on time-frequency decomposition using the Continuous Wavelet Transform (CWT) and the Synchrosqueezing Transform (SST), which are optimal for non-stationary cases. The third method is Singular Spectrum Analysis (SSA), an algebraic method for analysing weakly stationary signals, which decomposes the trajectory matrix into singular values. The comparative analysis revealed a robust circadian rhythm detected by all three methods across the three tested smoothing windows. However, the detection of ultradian cycles was less consistent, showing differences between the methods, mainly related to the challenge of defining the associated noise model.