Continuous wavelets of compact support alpha can be built,[1] which are related to the beta distribution. The process is derived from probability distributions using blur derivative. 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 and . Closed-form expressions for beta wavelets and scale functions as well as their spectra are derived. Their importance is due to the Central Limit Theorem by Gnedenko and Kolmogorov applied for compactly supported signals.[2]
- ^ de Oliveira, Hélio Magalhães; Schmidt, Giovanna Angelis (2005). "Compactly Supported One-cyclic Wavelets Derived from Beta Distributions". Journal of Communication and Information Systems. 20 (3): 27–33. arXiv:1502.02166. doi:10.14209/jcis.2005.17.
- ^ Gnedenko, Boris Vladimirovich; Kolmogorov, Andrey (1954). Limit Distributions for Sums of Independent Random Variables. Reading, Ma: Addison-Wesley.