{"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/fast-compressed-domain-n-point-discrete","title":"Fast Compressed-Domain N-Point Discrete Fourier Transform: The \"Twiddless\" FFT Algorithm","arxiv_id":"2505.23718","date":"2025-05-29","proceeding":null,"authors":["Saulo Queiroz"],"abstract":"In this work, we present the \\emph{twiddless fast Fourier transform (TFFT)}, a novel algorithm for computing the $N$-point discrete Fourier transform (DFT). The TFFT's divide strategy builds on recent results that decimate an $N$-point signal (by a factor of $p$) into an $N/p$-point compressed signal whose DFT readily yields $N/p$ coefficients of the original signal. However, existing compression-domain DFT analyses have been limited to computing only the even-indexed DFT coefficients. With TFFT, we overcome this limitation by efficiently computing both \\emph{even- and odd-indexed} DFT coefficients in the compressed domain with $O(N \\log N)$ complexity. TFFT introduces a new recursive decomposition of the DFT problem, wherein $N/2^i$ coefficients of the original input are computed at recursion level $i$, with no need for twiddle factor multiplications or butterfly structures. Additionally, TFFT generalizes the input length to $N = c \\cdot 2^k$ (for $k \\geq 0$ and non-power-of-two $c > 0$), reducing the need for zero-padding and potentially improving efficiency and stability over classical FFTs. We believe TFFT represents a \\emph{novel paradigm} for DFT computation, opening new directions for research in optimized implementations, hardware design, parallel computation, and sparse transforms.","url_abs":"https://arxiv.org/abs/2505.23718v2","url_pdf":"https://arxiv.org/pdf/2505.23718v2.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":"fast-compressed-domain-n-point-discrete","repo_url":"https://github.com/sauloqueiroz/tfft","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}