Compactly Supported Orthonormal Complex Wavelets with Dilation 4 and Symmetry

Compactly supported (bi)orthogonal wavelets generated by interpolatory refinable functions

This paper provides several constructions of compactly supported wavelets generated by interpolatory reenable functions. It was shown in D1] that there is no real compactly supported orthonormal symmetric dyadic reenable function, except the trivial case; and also shown in L] and GM] that there is no compactly supported interpolatory orthonormal dyadic reenable function. Hence, for the dyadic d...

Compactly Supported (bi)orthogonal Wavelets Generated by Interpolatory Reenable Functions

This paper provides several constructions of compactly supported wavelets generated by interpolatory reenable functions. It was shown in D1] that there is no real compactly supported orthonormal symmetric dyadic reenable function, except the trivial case; and also shown in L] and GM] that there is no compactly supported interpolatory orthonormal dyadic reenable function. Hence, for the dyadic d...

Matrix Extension with Symmetry and Applications to Symmetric Orthonormal Complex M-wavelets

Matrix extension with symmetry is to find a unitary square matrix P of 2π-periodic trigonometric polynomials with symmetry such that the first row of P is a given row vector p of 2πperiodic trigonometric polynomials with symmetry satisfying pp = 1. Matrix extension plays a fundamental role in many areas such electronic engineering, system sciences, wavelet analysis, and applied mathematics. In ...

Construction of multivariate compactly supported orthonormal wavelets

We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling function φ in the multivariate setting. For simplicity, we start with a standard dilation matrix 2I2×2 in the bivariate setting and show how to construct compactly supported functions ψ1, · · · , ψn with n > 3 such that {2ψj(2x − `, 2ky − m), k, `,m ∈ Z, j = 1, . . . , n} ...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)