Generalized interpolating refinable function vectors
نویسندگان
چکیده
Interpolating scalar refinable functions with compact support are of interest in several applications such as sampling theory, signal processing, computer graphics, and numerical algorithms. In this paper, we shall generalize the notion of interpolating scalar refinable functions to compactly supported interpolating d-refinable function vectors with any multiplicity r and dilation factor d. More precisely, we are interested in a d-refinable function vector φ = [φ1, . . . ,φr] such that φ is an r × 1 column vector of compactly supported continuous functions with the following interpolation property φ` ( m r + k ) = δkδ`−1−m, ∀ k ∈ Z,m = 0, . . . , r − 1, ` = 1, . . . , r, where δ0 = 1 and δk = 0 for k 6= 0. Now for any function f : R 7→ C, the function f can be interpolated and approximated by
منابع مشابه
Analysis and Construction of Multivariate Interpolating Refinable Function Vectors
In this paper, we shall introduce and study a family of multivariate interpolating refinable function vectors with some prescribed interpolation property. Such interpolating refinable function vectors are of interest in approximation theory, sampling theorems, and wavelet analysis. In this paper, we characterize a multivariate interpolating refinable function vector in terms of its mask and ana...
متن کاملInterpolating Filters with Prescribed Zeros and Their Refinable Functions
In this paper, we study the minimally supported interpolating filters with prescribed zeros and their corresponding refinable functions.
متن کاملOrthogonality Criteria for Compactly Supported Refinable Functions and Refinable Function Vectors
A refinable function φ(x) : Rn → R or, more generally, a refinable function vector 8(x) = [φ1(x), . . . , φr (x)]T is an L1 solution of a system of (vector-valued) refinement equations involving expansion by a dilation matrix A, which is an expanding integer matrix. A refinable function vector is called orthogonal if {φj (x − α) : α ∈ Zn, 1 ≤ j ≤ r} form an orthogonal set of functions in L2(Rn)...
متن کاملAnalysis of Optimal Bivariate Symmetric Refinable Hermite Interpolants
Multivariate refinable Hermite interpolants with high smoothness and small support are of interest in CAGD and numerical algorithms. In this article, we are particularly interested in analyzing some univariate and bivariate symmetric refinable Hermite interpolants, which have some desirable properties such as short support, optimal smoothness and spline property. We shall study the projection m...
متن کامل