in this paper, we characterize multiresolution analysis(mra) parseval frame multiwavelets in l^2(r^d) with matrix dilations of the form (d f )(x) = sqrt{2}f (ax), where a is an arbitrary expanding dtimes d matrix with integer coefficients, such that |deta| =2. we study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of mra tight frame multiwav...

In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f )(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwa...

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...

Multiwavelets are generated from refinable function vectors by using multiresolution analysis. In this paper we investigate the approximation properties of a multivariate refinable function vector associated with a general dilation matrix in terms of both the subdivision operator and the order of sum rules satisfied by the matrix refinement mask. Based on a fact about the sum rules of biorthogo...

This paper deals with multiwavelets which are a recent generalization of wavelets in the context of multirate lter banks and their applications to signal processing and especially compression. By their inherent structure, multiwavelets are t for processing multi-channel signals. First, we will recall some general results on multiwavelets and the convergence of the iterated matrix product. Then,...

This paper deals with multiwavelets which are a recent generalization of wavelets in the context of multirate lter banks and with their applications to signal processing and especially compression. By their inherent structure, multiwavelets are t for processing multi-channel signals. First, we will recall some general results on multi lters by looking at them as time-varying lters. Then, we wil...

This paper deals with multiwavelets which are a recent generalization of wavelets in the context of multirate lter banks and with their applications to signal processing and especially compression. By their inherent structure, multiwavelets are t for processing multi-channel signals. First, we will recall some general results on multiilters by looking at them as time-varying lters. Then, we wil...

‎a numerical technique based on the collocation method using legendre multiwavelets are‎‎presented for the solution of forced duffing equation‎. ‎the operational matrix of integration for‎‎legendre multiwavelets is presented and is utilized to reduce the solution of duffing equation‎‎to the solution of linear algebraic equations‎. ‎illustrative examples are included to demonstrate‎‎the validity...

Yang Shouzhi, Lou Zengjian Department of Mathematics, Shantou University, Shantou 515063, P.R.China Abstract A algorithm is presented for constructing orthogonal multiscaling functions and multiwavelets with multiplicity r+s(s ≥ 1, s ∈ Z) in terms of any given orthogonal multiscaling functions with multiplicity r. That is, let Φ(x) = [φ1(x), φ2(x), · · · , φr(x)] be an orthogonal multiscaling f...

The lifting scheme has been found to be a exible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix lters with a nite number of lifting steps. Based on the proposed lifting scheme, multiwavelet transforms that m...