scholarly journals Characterization of scaling functions in a multiresolution analysis

2004 ◽  
Vol 133 (4) ◽  
pp. 1013-1023 ◽  
Author(s):  
P. Cifuentes ◽  
K. S. Kazarian ◽  
A. San Antolín
Keyword(s):  
Multiresolution Analysis ◽  
Scaling Functions

On scaling functions of non-uniform multiresolution analysis in L2(ℝ)

2019 ◽  
Vol 18 (02) ◽  
pp. 1950055
Author(s):  
Hari Krishan Malhotra ◽  
Lalit Kumar Vashisht
Keyword(s):  
Frequency Domain ◽  
Multiresolution Analysis ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Scaling Functions ◽  
Necessary And Sufficient

The main purpose of this paper is to provide a characterization of scaling functions for non-uniform multiresolution analysis (NUMRA, in short). Some necessary and sufficient conditions for scaling functions of wavelet NUMRA in the frequency domain are also obtained.

CONSTRUCTING MULTIPLE WAVELET PACKETS WITH FIFS

Fractals ◽  
2001 ◽  
Vol 09 (02) ◽  
pp. 165-169
Author(s):  
GANG CHEN ◽  
ZHIGANG FENG
Keyword(s):  
Multiresolution Analysis ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Scaling Functions ◽  
Wavelet Packet Decomposition ◽  
Fractal Interpolation ◽  
Fractal Interpolation Functions ◽  
Interpolation Functions

By using fractal interpolation functions (FIF), a family of multiple wavelet packets is constructed in this paper. The first part of the paper deals with the equidistant fractal interpolation on interval [0, 1]; next, the proof that scaling functions ϕ1, ϕ2,…,ϕr constructed with FIF can generate a multiresolution analysis of L2(R) is shown; finally, the direct wavelet and wavelet packet decomposition in L2(R) are given.

ORTHONORMAL MRA WAVELETS: SPECTRAL FORMULAS AND ALGORITHMS

2012 ◽  
Vol 10 (01) ◽  
pp. 1250008 ◽  
Author(s):  
F. GÓMEZ-CUBILLO ◽  
Z. SUCHANECKI ◽  
S. VILLULLAS
Keyword(s):  
Multiresolution Analysis ◽  
Matrix Representation ◽  
Infinite Product ◽  
Scaling Functions ◽  
Compactly Supported ◽  
Orthonormal Bases ◽  
Spectral Decompositions ◽  
Product Matrix ◽  
Orthonormal Wavelets

Spectral decompositions of translation and dilation operators are built in terms of suitable orthonormal bases of L2(ℝ), leading to spectral formulas for scaling functions and orthonormal wavelets associated with multiresolution analysis (MRA). The spectral formulas are useful to compute compactly supported scaling functions and wavelets. It is illustrated with a particular choice of the orthonormal bases, the so-called Haar bases, which yield a new algorithm related to the infinite product matrix representation of Daubechies and Lagarias.

A Feasible Algorithm for Designing Biorthogonal Binary Finitely Supported Multiwavelet Functions

2011 ◽  
Vol 225-226 ◽  
pp. 1092-1095
Author(s):  
Bao Min Yu
Keyword(s):  
Wavelet Analysis ◽  
Multiresolution Analysis ◽  
Natural Science ◽  
Matrix Theory ◽  
Scaling Functions ◽  
Science And Engineering ◽  
Engineering Computation ◽  
Feasible Algorithm ◽  
Definition Of ◽  
Vector Valued

Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this paper, the notion of vector-valued multiresolution analysis is introduced and the definition of the biorthogonal vector-valued bivariate wavelet functions is given. The existence of biorthogonal vector-valued binary wavelet functions associated with a pair of biorthogonal vector-valued finitely supported binary scaling functions is investigated. An algorithm for constructing a class of biorthogonal vector-valued finitely supported binary wavelet functions is presented by virtue of multiresolution analysis and matrix theory.

scholarly journals ON THE CHARACTERIZATION OF SCALING FUNCTIONS ON NON-ARCHEMEDEAN FIELDS

2021 ◽  
Vol 7 (1) ◽  
pp. 3
Author(s):  
Ishtaq Ahmed ◽  
Owias Ahmad ◽  
Neyaz Ahmad Sheikh
Keyword(s):  
Multiresolution Analysis ◽  
Scaling Function ◽  
Real Life ◽  
Discrete Subgroup ◽  
Local Fields ◽  
Mathematical Tool ◽  
Spectral Pair ◽  
Spectral Pairs ◽  
The Given

In real life application all signals are not obtained from uniform shifts; so there is a natural question regarding analysis and decompositions of these types of signals by a stable mathematical tool.  This gap was filled by Gabardo and Nashed [11]   by establishing a constructive algorithm based on the theory of spectral pairs for constructing non-uniform wavelet basis in \(L^2(\mathbb R)\). In this setting, the associated translation set \(\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z\) is no longer a discrete subgroup of \(\mathbb R\) but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we characterize the scaling function for non-uniform multiresolution analysis on local fields of positive characteristic (LFPC). Some properties of wavelet scaling function associated with non-uniform multiresolution analysis (NUMRA) on LFPC are also established.

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