Abstract
Second-order sampling has been discussed in the contexts of 2-D frequency distributions made up of two tiling clusters with lattice systems having the same periodicity, while mixed-order sampling has been discussed for those made up of tiling clusters with lattice systems having different periodicities. However, there has been no discussion when the 2-D frequency distribution is made up of a large number of tiling clusters with lattice systems having the same periodicity. This paper describes a method of finding higher-order samplings for the frequency distributions made up of one main body of frequency components and deleted components in these situations. Smith normal forms and Vandermonde determinants play an important role in this method by guaranteeing the existence of higher-order samplings and finding, in practice, the sampling positions and sampling functions. The positions and functions of fifth-order sampling of a 2-D checkerboard-shaped frequency distribution are explicitly presented as an application of the proposed method.
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Toshihiro Hori: Retired.
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Hori, T. Higher-order sampling of 2-D frequency distributions by using Smith normal forms and Vandermonde determinants. Multidim Syst Sign Process 31, 385–410 (2020). https://doi.org/10.1007/s11045-019-00665-4
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DOI: https://doi.org/10.1007/s11045-019-00665-4