Different Wavelets, Their Properties and Advantages

Abstract

In this article we discuss the concept of wavelets, different forms of wavelets and their properties, graphs of different wavelets and their Fourier transforms are shown. We have also discussed the comparative advantages of wavelet transforms over Fourier transforms- in analyzing signals.

Capturing temporal heterogeneity of communities: a temporal β-diversity based on Hill numbers and time series analysis

“…Here, we propose a temporal γ, α and β-diversity measures based on time series analysis and Hill numbers diversity theory that provides an interpretable, efficient and comparable tool to characterize temporal community heterogeneity. The use of wavelet analysis for developing a temporal diversity framework enhanced the robustness of the results and circumvents sampling effort-related problems (42,47). To perform this analysis, we approximate the abundance time series data to simulate a continuous abundance curve as in other studies (37,49,52,54).…”

“…Wavelet analysis through the τ parameter partially takes into account this variation. Mathematically, the τ parameter controls the slope of the modeled curve, but this parameter is not modified in conventional wavelet analysis (47,49,53). Biologically, the τ parameter reflects the rate of change in the occurrence and abundance of species; this prompted us to assign an objective τ-value for each species in the studied community.…”

“…We developed our temporal α, γ and β-diversity measures based on the wavelet transform analysis (45)(46)(47) and the Hill numbers diversity approach (26,27,48) diversity measures were developed specifically for the decomposition approach. By considering the fully stationary behavior of abundance species data and the gaps associated with variation in sampling effort, wavelet time series analysis was used to standardize and fill gaps in abundance information through an estimated continual abundance curve, and this permits the distance-based Hill numbers diversity measure to be used (26), with the area under the curve as the basis of the pairwise distance measure.…”

“…The copyright holder for this preprint this version posted September 27, 2023. ; https://doi.org/10.1101/2023.09.25.559413 doi: bioRxiv preprint potentially exhibit their own rate of change in abundance through time (51). Thus, a fixed parameter value (usually 2 in most analyses) is not an appropriate assumption, and a more objective value is needed for each species (47,52,53). In this way, a correct fixed 𝝉 must consider the resolution (sampling time interval), the total sampling effort (T), and the steepness of the abundance changes in the raw data.…”