# Compactly Supported One-cyclic Wavelets Derived from Beta Distributions

arXiv: https://arxiv.org/abs/1502.02166 · HTML: https://mlsanity.com/paper/1502.02166/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2015.

## Built on by (most cited first, 1 of 1)

- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)

## Abstract (arXiv)

New continuous wavelets of compact support are introduced, which are related to the beta distribution. They can be built from probability distributions using 'blur'derivatives. These new wavelets have just one cycle, so they are termed unicycle wavelets. They can be viewed as a soft variety of Haar wavelets whose shape is fine-tuned by two parameters a and b. Close expressions for beta wavelets and scale functions as well as their spectra are derived. Their importance is due to the Central Limit Theorem applied for compactly supported signals.