Sampling and recovery of multidimensional bandlimited functions via frames

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:367

Article

Bailey, Benjamin

关键词: Frames;    Sampling;    Kadec;    Levinson;    Riesz basis;    Oversampling;   

DOI  :  10.1016/j.jmaa.2009.12.051

来源: Elsevier

【 摘 要 】

In this paper, we investigate frames for L(2)inverted right perpendicular-pi, pi inverted left perpendicular(d) consisting of exponential functions in connection to oversampling and nonuniform sampling of bandlimited functions. We derive a multidimensional nonuniform oversampling formula for bandlimited functions with a fairly general frequency domain. The stability of said formula under various perturbations in the sampled data is investigated, and a computationally manageable simplification of the main oversampling theorem is given. Also, a generalization of Kadec's 1/4 theorem to higher dimensions is considered. Finally, the developed techniques are used to approximate biorthogonal functions of particular exponential Riesz bases for L(2)inverted right perpendicular-pi, pi inverted left perpendicular, and a well-known theorem of Levinson is recovered as a corollary. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free