Tight frame oversampling and its equivalence to shift-invariance of affine frame operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Tight frame oversampling and its equivalence to shift-invariance of affine frame operators

Authors:	Charles K. Chui Qiyu Sun

Affiliation:	Department of Mathematics and Computer Science, University of Missouri--St. Louis, St. Louis, Missouri 63121-4499 -- and -- Department of Statistics, Stanford University, Stanford, California 94305 ; Department of Mathematics, National University of Singapore, Singapore 119260, Republic of Singapore

Abstract:	Let $Psi={psi_1, ldots, psi_L}subset L^2:=L^2(-infty, infty)$ generate a tight affine frame with dilation factor , where , and sampling constant (for the zeroth scale level). Then for , oversampling (or oversampling by ) means replacing the sampling constant by . The Second Oversampling Theorem asserts that oversampling of the given tight affine frame generated by preserves a tight affine frame, provided that is relatively prime to (i.e., ). In this paper, we discuss the preservation of tightness in oversampling, where (i.e., and ). We also show that tight affine frame preservation in oversampling is equivalent to the property of shift-invariance with respect to $frac{1}{mN_0}mathbf{Z}$ of the affine frame operator $Q_{0,N_0}$ defined on the zeroth scale level.

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