{
  "abstract": "This work introduces low-complexity, multiplierless approximations for the 32-point discrete Fourier transform. The proposed methods are obtained by minimizing the Frobenius error compared against the DFT matrix over a set of trivial multipliers. A row-wise, symmetry-constrained parameterization is employed to reduce the search space size, rendering the task computationally tractable. The resulting approximations could outperform the reference method in the literature according to energy-based error measurements. A sparse matrix factorization is provided for efficient computation; the arithmetic costs are 152 real additions and 34 bit-shifts only.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01115",
  "author_total": 3,
  "authors": [
    {
      "name": "L. Andrade-Silva"
    },
    {
      "name": "W. A. S. Aleixo"
    },
    {
      "name": "R. J. Cintra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgzs8rvsjjxnw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01115",
  "fulltext_url": null,
  "id": "bgzs8rvsjjxnw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01115",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "1711|Digital Filter Design and Implementation"
    ]
  ],
  "openalex": "W7206162077",
  "pdf_url": "https://arxiv.org/pdf/2609.01115",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgzs8rvsjjxnw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01115",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01115"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "32-point DFT Approximations Based on Minimal Frobenius Error and DFT Symmetries",
  "title_text": "32-point DFT Approximations Based on Minimal Frobenius Error and DFT Symmetries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/bgzs8rvsjjxnw",
  "venue": "arXiv",
  "versions": []
}