Multiresolution analysis on local fields and characterization of scaling functions

2012 ◽  
Vol 3 (2) ◽  
Author(s):  
Biswaranjan Behera ◽  
Qaiser Jahan
Keyword(s):  
Multiresolution Analysis ◽  
Local Fields ◽  
Scaling Functions

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.

scholarly journals Frame Multiresolution Analysis on Local Fields of Positive Characteristic

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Firdous A. Shah
Keyword(s):  
Multiresolution Analysis ◽  
Positive Characteristic ◽  
Scaling Function ◽  
Local Fields ◽  
Wavelet Frames ◽  
Shift Invariant Spaces ◽  
Frame Multiresolution Analysis ◽  
Invariant Spaces ◽  
The Scaling Function

We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces. In contrast to the standard setting, the associated subspace V0 of L2(K) has a frame, a collection of translates of the scaling function φ of the form φ(·-u(k)):k∈N0, where N0 is the set of nonnegative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of frame multiresolution analysis (FMRA) on local fields of positive characteristic. Finally, we provide a characterization of wavelet frames associated with FMRA on local field K of positive characteristic using the shift-invariant space theory.

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.

scholarly journals Vector valued nonuniform nonstationary wavelets and associated MRA on local fields

2021 ◽  
Vol 17 (2) ◽  
pp. 19-46
Author(s):  
O. Ahmad ◽  
A. H. Wani ◽  
N. A. Sheikh ◽  
M. Ahmad
Keyword(s):  
Multiresolution Analysis ◽  
Complete Characterization ◽  
Local Fields ◽  
Dimension Function ◽  
Vector Valued

Abstract In this paper we study nonstationary wavelets associated with vector valued nonuniform multiresolution analysis on local fields. By virtue of dimension function a complete characterization of vector valued nonuniform nonstationary wavelets is 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.

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