Wavelet Function Properties Based on Shannon Function
Zuo-Xian Fu, Qing Lin, Caixia Deng · 2024
It is proved that the wavelet function constructed by Shannon function is an orthogonal wavelet and satisfies admissiblility condition. It has properties such as frequency spectrum limitation, symmetry and almost everywhere smoothness. The wavelet transform is combined with the theory of reproducing kernel Hilbert space(RKHS) to describe the image space of the wavelet transform. Using the reproducing kernel function of Paley Wiener space, we provide easier analytical expression of the reproducing kernel function of the image space of this wavelet transform. In addition, the inversion formula, Parseval equation and sampling theorem of the wavelet transform have been established. This research enriches on the theory of RKHS, but also provides a theoretical basis for effective application of this wavelet in practical problems.