A new kind of wavelet based on super-Gaussian spectrum functions

Some popular wavelets such as the Morlet, the Gabor and Mexican hat wavelet, etc., are originated from the Gaussian spectrum function (GSF). To build a unified frame for a variety of existing wavelets, in this paper the GSF is generalized to the super-Gaussian spectrum function (SGSF), upon which by using multiresolution analysis a novel class of wavelets called the U-wavelet is constructed. By changing a few of its parameters, a large number of scaling functions and corresponding wavelets can easily be generated. It is shown that not only a variety of existing wavelets either become member of U-wavelet of be approximated at the desired accuracy by its special members but also a new way of generating exotic wavelets is paved for designers and researchers