Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2303.17510 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929211510358016 |
|---|---|
| author | Murasko, Noel Bowman, John C. |
| author_facet | Murasko, Noel Bowman, John C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17510 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hybrid Dealiasing of Complex Convolutions Murasko, Noel Bowman, John C. Numerical Analysis 65R99, 65T50 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. |
| title | Hybrid Dealiasing of Complex Convolutions |
| topic | Numerical Analysis 65R99, 65T50 |
| url | https://arxiv.org/abs/2303.17510 |