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Mixed-order sampling of 2-D frequency distributions by using the concept of common superset

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Abstract

It has been found that tiling clusters and pair regions of frequency distributions play an important role in the sampling problems. When a given 2-D frequency distribution is made up of one tiling cluster, first-order sampling can be used, and when it is made up of two tiling clusters with the same periodicity lattice system, second-order sampling can be used by dividing tiling clusters into sets of pair regions. However, what kind of sampling can be used for other complicated 2-D frequency distributions has not been found. The sampling of frequency distributions which are made up of tiling clusters that belong to different periodicity lattice systems is discussed in this paper. We introduce the concept of common superset as the lattice system which is the common superset of all the lattice systems derived from individual tiling clusters. In practice, the sampling of a 2-D frequency distribution made up of one main body components and two debris ones is calculated in this paper. This type of sampling is a mixture of first-order and higher-order samplings. This sampling method can be applied to other 2-D frequency distributions, when there is a common superset for the given frequency distribution.

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  1. National Institute of Technology, Tokyo College, 1220-2 Kunugida-cho, Hachioji, Tokyo, 193-0997, Japan

    Toshihiro Hori

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  1. Toshihiro Hori
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Hori, T. Mixed-order sampling of 2-D frequency distributions by using the concept of common superset. Multidim Syst Sign Process 30, 1237–1262 (2019). https://doi.org/10.1007/s11045-018-0604-2

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  • DOI: https://doi.org/10.1007/s11045-018-0604-2

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