Generalized Multiresolution Structure Research Articles

The Study of Tight Periodic Wavelet Frames and Wavelet Frame Packets and Applications

Information science focuses on understanding problems from the perspective of the stake holders involved and then applying information and other technologies as needed. A necessary and sufficient condition is identified in term of refinement masks for applying the unitary extension principle for periodic functions to construct tight wavelet frames. Then a theory on the approxi-mation order of truncated tight frame series is established, which facilitates construction of tight periodic wavelet frames with desirable approximation order. The pyramid decomposition scheme is derived based on the generalized multiresolution structure.

The Research of Dual Quarternary Pseudoframes for Hardy Space and Applications in Engineering Materials

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering.. In this work, the notion of the quarternary generalized multiresol- ution structure (TGMS) of subspace is proposed. The characteristics of quarternary affine pseudoframes for subspaces is investigated. Construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a TGMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a TGMS is established.

Parameterization of Masks for Tight Wavelet Frames and Multiple Pseudoframes and Applications in Mechanical Engineering

Mechanical engineering is a discipline of engineering that applies the principles of engine ering, physics and materials science for analysis, design, manufacturing, and maintenance of mecha nical systems. In this work, the construction of 4-band tight wavelet frames with symmetric proper-ties using symmetric extension and parameterization of the paraunitary matrix. The notion of an 4-band generalized multiresolution structure of subspace is proposed. The characteristics of affine pseudoframes for subspaces is investigated. The construction of a generalized multiresolution structure of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obta-ined based on such a generalized multiresolution structure and a sufficient condition for its exist-ence is presented. A constructive method for affine frames of based on a generalized multi-resolution structure is presented.

The Characteristics of Trivariate Vector-Valued Super-Wave Wraps and Applications in Materials Engineering

The rise of wavelet analysis in applied mathematics is due to its applications and the flex- ibility. We introduce vector-valued wave wraps with multi-scale dilation factor for space , which is the generalization of univariate wavelet packets. A method for constructing a sort of orthogo-nal vector-valued wavelet wraps in three-dimensional space is presented and their orthogonality traits are characterized by virtue of iteration method and time-frequency analysis method. The orthog-onality formulas concerning these wave packets are established. Moreover, it is shown how to obtain new Riesz bases of space from these wave wraps. The notion of multiple pseudo fames for subspaces with integer translation is proposed. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

The Characters of Dual Harmonic Frames of Subspaces and Applications in Signal Processing Theory

Digital signal processing is the processing of digitized discrete-time samp-led signals. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors. Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure (GMS) of is also introduced. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

Study of Matrix Transfer Multipliers for Normalized Pseudoframe Wavelets and Applications in Material Engineering

Materials engineers design, produce and evaluate materials and their use. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace L^2(R^2) is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of L^2(R^2) is studied. The pyramid decom position scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of L^2(R^2) based on a BGMS is established.

Study of Matrix Multipliers for Normalized Frame Multi-Wavelets and Applications in Engineering Material Technology

Frame theory has been the focus of active research for twenty years, both in theory and applications. Matrix Fourier multipliers send every orthonoamal wavelet to an orthonoamal wavelet. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

The Stability and Perturbation of Bivariate Gabor Frames and Applications in Material Engineering

Material science broadly encompasses the fundamental study of solid matter with the goal of engineering new materials with superior properties, and ultimately enabling altogether new types of devices The window functions and bivariate Gabor frames are introduced. The existence of bivariate Gabor frames with compact support is discussed. Sufficient conditions for irregular bivariate Gabor system to be frames are presented by means of frame multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a sort of orthogonal bivariate vector-valued wavelets with compact support is proposed, and their properties are investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

The Research of Trivariate Normalized Tight Frames and Pseudoframes of Subspace Based on a Pyramid Decomposition Scheme

The notion of trivariate normalized tight frames and a generalized multiresolution struc-ture and the concept of subspace trivariate affine pseudoframes are introduced. The pyramid decom-position scheme of a generalized multiresolution structure (GMRS) is established, which is generaliz-ation of Mallat's pyramid algorithm. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space is presented. Moreover, affine trivariate pseudo frame expansions of are constructed by virtue of the pyramid decomposition scheme.

Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science

Manufacturing science focuses on understanding problems from the perspective of the stakeholders involved and then applying manufacturing science as needed. We investigate semi-orthogonal frame wavelets and Parseval frame wavelets in with a dilation factor. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace.The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multireso-lution structure of Paley-Wiener subspaces of is investigated.

The Characterization of Multiple Harmanic Riesz Bases of Affine Subspaces and Applications

An information system is any combination of information technology and people's act- ivities that support operations, management and decision making. Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. The definition of multiple harmonic frames for subs -paces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multiresolution structure of Paley -Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

The Description of the Semi-Local Hardy Space by Gabor Frames

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, the notion of the binary generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of binary multiscale pseudo- -frames for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of L^2(R^2) is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of L^2(R^2) based on a BGMS is established.

Generalized multiresolution structures in reducing subspaces of L 2(ℝ d )

In this paper, we introduce the notion of generalized multiresolution structure (GMS) in the setting of reducing subspaces of L2(ℝd). For a general expansive matrix, we obtain a necessary and sufficient condition for GMS, and prove the existence of GMS in a reducing subspace. Using GMS, we obtain a pyramid decomposition and a frame-like expansion for signals in reducing subspaces.

Subspace Affine Dual Multiple Frames with Multi-filter Functions and a General Multiresolution Structure

Abstract Frames have become the focus of active research, both in theory and in applications. The notion of a generalized multiresolution structure of L2(R) is formulated. The definition of dual multiple frames for subspaces of L2(R) is proposed. The construction of a generalralized multiresolution structure (GMS) of Paley-Wiener subspaces of L2(R) is investigated. The sufficient condition for the existence of multiple pseudoframes for subspaces of L2(R) is obtained based on such a GMS. A sufficient condition on the existence of dual multiple pseodoframes is presented by means of paraunitary vector filter bank theory.

The Research of Bivariate Minimum-Energy Frames and Frames of Subspace and Application in Particle Physics

Materials science is an applied science concerned with the relationship between the struc- ture and properties of materials. Frames have become the focus of active research field, both in the- ory and in applications. In the article, the binary minimum-energy wavelet frames and frame multi- resolution are introduced. A precise exist-ence criterion for minimum-energy frames in terms of an ineqity condition on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient con-dition for the existence of affine pseudoframes is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresolution structure.

The Research of Bivariate Minimum-Energy Frames and Frames of Subspace and Application in Particle Physics

Materials science is an applied science concerned with the relationship between the struc- ture and properties of materials. Frames have become the focus of active research field, both in the- ory and in applications. In the article, the binary minimum-energy wavelet frames and frame multi- resolution are introduced. A precise exist-ence criterion for minimum-energy frames in terms of an ineqity condition on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient con-dition for the existence of affine pseudoframes is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresolution structure.

The Features of Multiscale Pseudoframes and Gabor Frames According to Bivariate Filter Functions

The advantages of wavelet analysis and their promising featu-res in various application have attracted a lot of interest and effort in re-cent years. Frame analysis has become popular much later in sampling theory, time-frequency analysis and wavelet theory. In this work, the notion of the binary generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of binary multiscale pseudof-rames for subspaces is investigated. The construction of a BGMS of Paley-Wiener subspace ofis studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established. A method for designing a class of affine bivariate dual frames in bi-dimensional space is presented. The results we obtain gains much improvement.

A Study of Binary Minimum-Energy Shortly Supported Wavelet Frames Associated with a Scaling Function

Frames have become the focus of active research field, both in theory and in applications. In the article, the binary minimum-energy wavelet frames and frame multiresolution resolution are introduced. A precise existence criterion for minimum-energy frames in terms of an ineqity conditi- -on on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient condition for the existence of affine pseudoframes is obtained by virtue of a generalized multiresolution analysis. The pyramid de -composition scheme is established based on such a generalized multiresolution structure.

The Excellent Traits of a Class of Orthogonal Quarternary Wavelet Wraps with Short Support

The frame theory has been one of powerful tools for researching into wavelets. In this article, the notion of orthogonal nonseparable quarternary wavelet wraps, which is the generalizati- -on of orthogonal univariate wavelet wraps, is presented. A novel approach for constructing them is presented by iteration method and functional analysis method. A liable approach for constructing two-directional orthogonal wavelet wraps is developed. The orthogonality property of quarternary wavelet wraps is discussed. Three orthogonality formulas concerning these wavelet wraps are estabished. A constructive method for affine frames of L2(R4) is proposed. The sufficient condition for the existence of a class of affine pseudoframes with filter banks is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresolution structure.

The Information Fusion Method Based on a Sort of Multiple Pseudoframes with Arbitrary Real Translation Constant

Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. The definition of multiple pseudofames for subspaces with real number translation is proposed. The notion of a generalized multiresolution structure (GMS) of is also introduced. The pyramid decomposition scheme is derived based on a GMS. As a major new constribution the sufficient condition for the existence of multiple pseudoframes for subspaces is derived based on such a GMS.