Hybrid Dealiasing of Complex Convolutions
| Autor: | Murasko, Noel, Bowman, John C. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Efficient algorithms for computing linear convolutions based on the fast Fourier transform are developed. A hybrid approach is described that combines the conventional practice of explicit dealiasing (explicitly padding the input data with zeros) and implicit dealiasing (mathematically accounting for these zero values). The new approach generalizes implicit dealiasing to arbitrary padding ratios and includes explicit dealiasing as a special case. Unlike existing implementations of implicit dealiasing, hybrid dealiasing tailors its subtransform sizes to the convolution geometry. Multidimensional convolutions are implemented with hybrid dealiasing by decomposing them into lower-dimensional convolutions. Convolutions of complex-valued and Hermitian inputs of equal length are illustrated with pseudocode and implemented in the open-source FFTW++ library. Hybrid dealiasing is shown to outperform explicit dealiasing in one, two, and three dimensions. Comment: 19 pages, 17 figures, to appear in the SIAM Journal on Scientific Computing. Code can be found at https://github.com/dealias/fftwpp |
| Databáze: | arXiv |
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