The continuous wavelet transform and window functions. (English) Zbl 1338.46052
A new idea for pseudo-orthants is constructed. Using the technique of pseudo-orthants, an inversion formula for wavelets in higher dimensions is derived which is valid over \({\mathbb R^{n}} \times {\mathbb R^{n}}\), whereas the formula derived by Daubechies and Meyer works only on \({\mathbb R} \times {\mathbb R^{n}}\). Thus, the formula provided by the authors is more general than that of Daubechies and Meyer. Further, examples of non-separable wavelets using a new scheme of window functions for higher dimensions is proposed that enhances the domain of wavelets and its applications.
Reviewer: Manish Kumar (Hyderabad)
MSC:
| 46F12 | Integral transforms in distribution spaces |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
References:
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