Constructing pairs of dual bandlimited frame wavelets in L^2(R^n)

Constructing Pairs of Dual Bandlimited Frame Wavelets in L(r)

Given a real, expansive dilation matrix we prove that any bandlimited function ψ ∈ L(R), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple constr...

Constructing pairs of dual bandlimited framelets with desired time localization

G-dual function-valued frames in L2(0,∞)

In this paper, g-dual function-valued frames in L2(0;1) are in- troduced. We can achieve more reconstruction formulas to ob- tain signals in L2(0;1) by applying g-dual function-valued frames in L2(0;1).

A CHARACTERIZATION OF AFFINE DUAL FRAMES IN L2(Rn )

We give a characterization of all (quasi) aane frames in L 2 (R n) which have a (quasi) aane dual in terms of the two simple equations in the Fourier transform domain. In particular, if the dual frame is the same as the original system, i.e. it is a tight frame, we obtain the well known characterization of wavelets. Although these equations have already been proven under some special conditions...

Orthogonal Non{Bandlimited Wavelets on the Sphere

This paper introduces orthogonal non{bandlimited wavelets on the sphere with respect to a certain Sobolev space topology. The construction of those kernels is based on a clustering of the index set N = f(n; k) 2 N0 Zj n k ng associated to the system of spherical harmonics fYn;kg(n;k)2N . The wavelets presented here form reproducing kernels of the spans of the clustered harmonics. More explicitl...