An explicit method for the construction of a tight wavelet frame generated by the Walsh polynomials with the help of extension principles was presented by Shah (Shah, 2013). In this article, we extend the notion of wavelet frames to periodic wavelet frames generated by the Walsh polynomials on R by using extension principles. We first show that under some mild conditions, the periodization of a...

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...

We study the Laplacian pyramid (LP) as a frame operator, and this reveals that the usual reconstruction is suboptimal. With orthogonal filters, the LP is shown to be a tight frame, thus the optimal linear reconstruction using the dual frame operator has a simple structure as symmetrical with the forward transform. For more general cases, we propose an efficient filter bank for reconstruction in...

This paper proves a sharp lower bound for Newton polygons of L-functions of exponential sums of one-variable rational functions. Let p be a prime and let Fp be the algebraic closure of the finite field of p elements. Let f(x) be any one-variable rational function over Fp with l poles of orders d1, . . . , dl. Suppose p is coprime to d1 · · · dl. We prove that there exists a tight lower bound wh...

Abstract. A Weyl-Heisenberg frame for L(R) is a frame consisting of translates and modulates of a fixed function in L(R), i.e. (EmbTnag)m,n∈Z , with a, b > 0, and g ∈ L(R). In this paper we will give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g so that (EmbTnag) is an orthonormal basis for L (R). These resu...

A Wilson orthonormal basis was constructed in 1991 by I. Daubechies, S. Jaffard and J.L. Journé from Gabor tight frame elements, when the redundancy of the Gabor system is 2. In 1994 P. Auscher gave a characterization of the atoms for which the Wilson system is an orthonormal basis. Afterwards, K. Gröchenig posed a question whether the construction of an orthonormal Wilson basis is possible for...

Let G be a p-adic connected reductive group with Lie algebra g. For a parabolic subgroup P ⊂ G and a finite-dimensional locally analytic representation V of a Levi subgroup of P, we study the induced locally analytic G-representation W = IndP (V ). Our result is the following criterion concerning the topological irreducibility of W : If the Verma module U(g) U(p) V ′ associated to the dual repr...

This paper studies the construction of hexagonal tight wavelet frame filter banks which contain three “idealized” high-pass filters. These three high-pass filters are suitable spatial shifts and frequency modulations of the associated low-pass filter, and they are used by Simoncelli and Adelson in [37] for the design of hexagonal filter banks and by Riemenschneider and Shen in [30, 31] for the ...