Characterization of matrix Fourier multipliers for A-dilation Parseval multi-wavelet frames

2015 ◽  
Vol 13 (06) ◽  
pp. 1550051
Author(s):  
Yongdong Huang ◽  
Fengjuan Zhu
Keyword(s):  
Fourier Multipliers ◽  
Frame Theory ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Integral Matrix ◽  
Numerical Examples ◽  
Basic Properties ◽  
New Formula

Let [Formula: see text] be a [Formula: see text] expansive integral matrix with [Formula: see text]. This paper investigates matrix Fourier multipliers for [Formula: see text]-dilation Parseval multi-wavelet frames, which are [Formula: see text] matrices with [Formula: see text] function entries, map [Formula: see text]-dilation Parseval multi-wavelet frames of length [Formula: see text] to [Formula: see text]-dilation Parseval multi-wavelet frames of length [Formula: see text], where [Formula: see text]. We completely characterize all matrix Fourier multipliers for [Formula: see text]-dilation Parseval multi-wavelet frames and construct several numerical examples. As Fourier wavelet frame multiplier, matrix Fourier multipliers can be used to derive new [Formula: see text]-dilation Parseval multi-wavelet frames and can help us better understand the basic properties of frame theory.

scholarly journals Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fengjuan Zhu ◽  
Qiufu Li ◽  
Yongdong Huang
Keyword(s):  
Scaling Function ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Reconstruction Algorithm ◽  
Wavelet Function ◽  
Necessary Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Numerical Examples ◽  
Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed.

The Characterization of a Pair of Canonical Frames Generated by Several Compactly Supported Functions

2010 ◽  
Vol 439-440 ◽  
pp. 1135-1140
Author(s):  
Jun Qiu Wang ◽  
Jian Guo Wang
Keyword(s):  
Scaling Functions ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
The Past ◽  
Single Function ◽  
Dual Wavelet Frames ◽  
Popular Subject ◽  
Compactly Supported Functions ◽  
Dual Wavelet

Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function.

scholarly journals Finite equal norm Parseval wavelet frames over prime fields

2017 ◽  
Vol 15 (04) ◽  
pp. 1750040 ◽  
Author(s):  
Asghar Rahimi ◽  
Niloufar Seddighi
Keyword(s):  
Fourier Transform ◽  
Wave Packet ◽  
Multiplicative Group ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
System Generator ◽  
Prime Fields ◽  
Scaling Matrix ◽  
Multiplicative Subgroups

In the framework of wave packet analysis, finite wavelet systems are particular classes of finite wave packet systems. In this paper, using a scaling matrix on a permuted version of the discrete Fourier transform (DFT) of system generator, we derive a locally-scaled version of the DFT of system generator and obtain a finite equal-norm Parseval wavelet frame over prime fields. We also give a characterization of all multiplicative subgroups of the cyclic multiplicative group, for which the associated wavelet systems form frames. Finally, we present some concrete examples as applications of our results.

On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle

2014 ◽  
Vol 57 (2) ◽  
pp. 254-263 ◽  
Author(s):  
Ole Christensen ◽  
Hong Oh Kim ◽  
Rae Young Kim
Keyword(s):  
Extension Principle ◽  
Sufficient Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Number Of Generators ◽  
Unitary Extension

AbstractThe unitary extension principle (UEP) by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the UEP-type wavelet systems that can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible.

scholarly journals The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates

2006 ◽  
Vol 58 (6) ◽  
pp. 1121-1143 ◽  
Author(s):  
Marcin Bownik ◽  
Darrin Speegle
Keyword(s):  
Regularity Condition ◽  
Finite Union ◽  
Gabor Frame ◽  
Gabor Frames ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Weak Regularity

AbstractThe Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.

scholarly journals Normal Toeplitz Operators on the Bergman Space

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1463
Author(s):  
Sumin Kim ◽  
Jongrak Lee
Keyword(s):  
Toeplitz Operator ◽  
Bergman Space ◽  
Toeplitz Operators ◽  
Basic Properties

In this paper, we give a characterization of normality of Toeplitz operator Tφ on the Bergman space A2(D). First, we state basic properties for Toeplitz operator Tφ on A2(D). Next, we consider the normal Toeplitz operator Tφ on A2(D) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on A2(D).

scholarly journals Nonhomogeneous Wavelet Dual Frames and Extension Principles in Reducing Subspaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jianping Zhang ◽  
Huifang Jia
Keyword(s):  
Wavelet Frames ◽  
Dual Frames ◽  
Reducing Subspaces ◽  
Extension Principles

It can be seen from the literature that nonhomogeneous wavelet frames are much simpler to characterize and construct than homogeneous ones. In this work, we address such problems in reducing subspaces of L2ℝd. A characterization of nonhomogeneous wavelet dual frames is obtained, and by using the characterization, an MOEP and an MEP are derived under general assumptions for such wavelet dual frames.

Infrared spectroscopic characterization of basic properties: Nitromethane as probe molecule

2010 ◽  
Vol 330 (1-2) ◽  
pp. 88-93 ◽  
Author(s):  
Ruth L. Martins ◽  
Claudia de O. Veloso ◽  
Claudio A. Mota ◽  
Martin Schmal
Keyword(s):  
Spectroscopic Characterization ◽  
Probe Molecule ◽  
Basic Properties ◽  
Infrared Spectroscopic

Microstructure and Basic Properties of Domestic Butyl Rubber 1751

2014 ◽  
Vol 912-914 ◽  
pp. 235-242
Author(s):  
Nai Xiu Ding ◽  
Pei Yan Zuo ◽  
Yi Jia ◽  
Li Li Wang ◽  
Hai Tao Wang
Keyword(s):  
Molecular Mass ◽  
Gel Permeation Chromatography ◽  
Mechanical Analysis ◽  
Volatile Matter ◽  
Matter Content ◽  
Butyl Rubber ◽  
Gravimetric Analysis ◽  
Average Molecular Mass ◽  
Basic Properties

The characterization of microstructure and basic properties of domestic butyl rubber 1751 ( IIR 1751) was performed with different testing , such as 1H-NMR spectrum, gel permeation chromatography, dynamic mechanical analysis, thermal gravimetric analysis and differential scanning calorimeter. And the comparison with Butyl 268 and Butyl 301 was made. The results showed that IIR1751 had a narrower molecular mass distribution, lower number-average molecular mass and lower weight-average molecular mass. The unsaturation degree of IIR1751 was close to Butyl 268 and Butyl 301. Its thermal stability was higher than the other and its ash content and volatile matter content was lower. Its glass transition temperature was same to Butyl 268’s, which was slightly higher than the Butyl 301. Dispersion of carbon black in IIR1751 vulcanizates was poor, but IIR1751 vulcanizates had good processing property, had a longer scorch safety period and fast curing rate. Its fatigue performance was good and its mechanical properties can achieve a better balance.

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