2010/09/10 by B. A. Bailey, Bailey, Benjamin Aaron
Computer Science · Mathematics · #Digital Filter Design and Implementation #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1009.2043
openalex publication_date 2010/09/10 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
In this paper, we investigate frames for L2[-\π,\π]d consisting of\nexponential functions in connection to oversampling and nonuniform sampling of\nbandlimited functions. We derive a multidimensional nonuniform oversampling\nformula for bandlimited functions with a fairly general frequency domain. The\nstability of said formula under various perturbations in the sampled data is\ninvestigated, and a computationally managable simplification of the main\noversampling theorem is given. Also, a generalization of Kadec's 1/4 Theorem\nto higher dimensions is considered. Finally, the developed techniques are used\nto approximate biorthogonal functions of particular exponential Riesz bases for\nL2[-\π,\π], and a well known theorem of Levinson is recovered as a\ncorollary.\n