Beta Wavelet - Beta Wavelets

Beta Wavelets

Since is unimodal, the wavelet generated by

has only one-cycle (a negative half-cycle and a positive half-cycle).

The main features of beta wavelets of parameters and are:

The parameter is referred to as “cyclic balance”, and is defined as the ratio between the lengths of the causal and non-causal piece of the wavelet. The instant of transition from the first to the second half cycle is given by

The (unimodal) scale function associated with the wavelets is given by

.

A closed-form expression for first-order beta wavelets can easily be derived. Within their support,