High flexible orthonormal basis of wavelets and its Hilbert transform pair

摘要

We have already proposed the orthonormal wavelet basis with an arbitrary real dilation factor and the orthonormal basis of wavelets having customizable frequency bands. In this paper, based on them, we propose a new types of orthonormal basis of wavelets, having not only customizable frequency bands, but also variable wavelet shapes in the time domain. This basis has flexible scaling functions, which can be translated in the time domain under the control of an arbitrary real constant, and according to its constant number, its wavelets have variable shapes in the time domain. Additionally, based on this basis, we construct a Hilbert transform pair of orthonormal bases of wavelets having shift invariance.