{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-new-acceleration-paradigm-for-discrete","title":"A New Acceleration Paradigm for Discrete CosineTransform and Other Fourier-Related Transforms","arxiv_id":"2110.01172","date":"2021-10-04","proceeding":null,"authors":["Zixuan Jiang","Jiaqi Gu","David Z. Pan"],"abstract":"Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel computing systems. Public MD DCT implementations leverage a straightforward method that decomposes the computation into multiple 1D DCTs along every single dimension, which inevitably has non-optimal performance due to low computational efficiency, parallelism, and locality. In this paper, we propose a new acceleration paradigm for MD DCT. A three-stage procedure is proposed to factorize MD DCT into MD FFT and highly-optimized preprocessing/postprocessing with efficient computation and high arithmetic intensity. Our paradigm can be easily extended to other Fourier-related transforms and other parallel computing systems. Experimental results show that our 2D DCT/IDCT CUDA implementation has a stable, FFT-comparable execution time, which is $2\\times$ faster than the previous row-column method. Several case studies demonstrate that a promising efficiency improvement can be achieved with our paradigm. The implementations are available at https://github.com/JeremieMelo/dct_cuda/tree/reconstruct.","url_abs":"https://arxiv.org/abs/2110.01172v1","url_pdf":"https://arxiv.org/pdf/2110.01172v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-new-acceleration-paradigm-for-discrete","repo_url":"https://github.com/jeremiemelo/dct_cuda","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}