The hexagonal fast fourier transform
| Autor: | James B. Birdsong, Nicholas I. Rummelt |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Theoretical computer science
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| Zdroj: | ICIP |
| DOI: | 10.1109/icip.2016.7532670 |
| Popis: | The discrete Fourier transform is an important tool for processing digital images. Efficient algorithms for computing the Fourier transform are known as fast Fourier transforms (FFTs). One of the most common of these is the Cooley-Tukey radix-2 decimation algorithm that efficiently transforms one-dimensional data into its frequency domain representation. The orthogonality of rectangular sampling allows the separability of the Fourier kernel which enables the use of the Cooley-Tukey algorithm on two-dimensional digital images that have been sampled rectangularly. Hexagonal sampling provides many benefits over rectangular sampling, but it does not result in the orthogonal rows and columns that can be transformed independently as is done with rectangular samples. Use of the Array Set Addressing (ASA) coordinate system for hexagonally sampled images has been shown to provide a separable Fourier kernel, leading to an efficient FFT, however its implementation is composed of nonstandard transforms that require custom routines to evaluate. This work develops a hexagonal FFT in ASA coordinates that uses only the standard Fourier transform, allowing the user to implement the hexagonal FFT using standard FFT routines. |
| Databáze: | OpenAIRE |
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