Related papers: From filters to wavelets via direct limits
The wavelet group and wavelet representation associated with shifts coming from a two dimensional crystal symmetry group $\Gamma$ and dilations by powers of 3, are defined and studied. The main result is an explicit decomposition of the…
Due to their adaptive nature, empirical wavelets had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case,…
A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the…
It is described how the coefficients of Daubechies wavelet matrices can be approximated by rational numbers in such a way that the perfect reconstruction property of the filter bank be preserved exactly
We define an asymptotically normal wavelet-based strongly consistent estimator for the Hurst parameter of any Hermite processes. This estimator is obtained by considering a modified wavelet variation in which coefficients are wisely chosen…
Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in $L^2(\mathbb{R}^d)$ which only require a single…
We study sigma-ideals and regularity properties related to the "filter-Laver" and "dual-filter-Laver" forcing partial orders. An important innovation which enables this study is a dichotomy theorem proved recently by Miller [1]. [1] Arnold…
We study the boundedness from Hp(Rn) into Lp(Rn) of certain operators generated by wavelets and Borel measures.
We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only…
Pressing questions in cosmology such as the nature of dark matter and dark energy can be addressed using large galaxy surveys, which measure the positions, properties and redshifts of galaxies in order to map the large-scale structure of…
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…
We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…
This work characterizes (dyadic) wavelet frames for $L^2({\mathbb R})$ by means of spectral techniques. These techniques use decomposability properties of the frame operator in spectral representations associated to the dilation operator.…
In this paper, Meyer wavelets with an arbitrary integer scaling factor $N>2$ are defined using wavelets with multiple scaling factors $MN>2$. Expressions for frequency functions of wavelets and corresponding filters are obtained.
The formula for the frequency shift of a plane-polarized light wave reflected from a uniformly moving mirror is derived directly from the constant light speed postulate and the basic principles of wave optics. Unlike the original derivation…
The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet…
We depict and analyze a new effect for wavepackets falling freely under a barrier or well. The effect appears for wavepackets whose initial spread is smaller than the combination $\ds \sqrt{\frac{l_g^3}{|z_0|}}$, between the gravitational…
A novel wavelet-like function is presented that makes it convenient to create filter banks given mainly two parameters that influence the focus area and the filter count. This is accomplished by computing the inverse Fourier transform of…