  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.
