Boosting confidence in detecting time-dependent ultradian rhythms using wavelet analysis

Abstract

Recently, biologists have shown fractal and oscillatory characteristics in animal behaviortime series. Aspects so different can be explained by a model with added components thatinclude deterministic cycles (ultradian and circadian rhythms), polynomial tendencies, and anunderlying nonlinear process with stationary increments. Such components can be extractedfrom the data using wavelet analysis by selecting the transformation appropriately. In this talk, we will discuss a five-step method that describes the data without making any parametric assumptions about trends in the frequency or amplitude of the components signals and is resilient to noise.1. Visual inspection by Continuous wavelet transform based on real Gaussian motherwavelet in the Cartesian time scale plane2. Visual inspection by Continuous wavelet transform based on complex Morlet motherwavelet in the Polar time scale plane.3. Modal frequency detection by Synchrosqueezed wavelet transform, a linear timescale analysis followed by a synchrosqueezing technique.4. Modal frequency corroboration by Empirical wavelet transform, a wavelet analysis in theFourier domain followed by frequency segmentation to extract the modal components.5- Quantification of coherence and phase difference between different series.