page_title: Hexagonal fast Fourier transform
section_title: Array set addressing
hierarchical_section_title: Hexagonal fast Fourier transform / Preliminaries / Array set addressing
caption_attribution_description: English: The figure illustrates representation of a hexagonally sampled data in the form of rectangular arrays using ASA coordinate system.
context_page_description: The hexagonal fast Fourier transform is a variant of the fast Fourier transform that is developed to utilize the advantages of hexagonal sampling.
context_section_description: The array set addressing (ASA) coordinate system has been proposed based on a simple fact that a hexagonal grid can be considered as a combination of two interleaved rectangular arrays. From this, it is easy to address each individual array using familiar integer-valued row and column indices. Now, to select one among these two rectangular arrays, a single binary coordinate is used. From this, a full address for any point in the hexagonal grid can be uniquely represented by three coordinates.
  where the coordinates a, r and c represent the array, row and column respectively. The hexagonal lattice can be separated into rectangular arrays by considering alternate rows as one array and the remaining rows as the other. Figure 1 can be used to illustrate the process of array set addressing, where alternate rows of the hexagonally sampled data are mapped to 0-array and 1-array rectangular arrays.
caption: Representation of hexagonally sampled data in the form of rectangular arrays using ASA coordinate system
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