{
  "abstract": "Frequency-comb spectra can arise from distinct time-domain waveforms. We develop a Fourier-based framework that relates waveform symmetry, regularity, and modulation to the structure of overtone- and sideband frequency combs. Analytical derivations show that symmetry determines the allowed harmonic orders, while waveform regularity governs spectral decay: discontinuities produce $n^{-1}$ scaling, derivative discontinuities yield $n^{-2}$ scaling, and smooth nonlinear mappings can produce rapidly decaying harmonics. For modulated carriers, we distinguish consecutive sidebands, symmetry-induced missing orders, and nonuniformly spaced frequency components. In particular, spectral sparsity does not necessarily imply a nonuniform frequency lattice. Comparisons of analytical coefficients with calculated time-domain signals and Fourier spectra establish the correspondence between waveform properties and spectral signatures. The results provide a mathematical basis for interpreting frequency-comb structures while identifying the limitations of magnitude-only spectra in determining their underlying physical mechanisms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01085",
  "author_total": 2,
  "authors": [
    {
      "name": "Madhurendra Mishra"
    },
    {
      "name": "Adarsh Ganesan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/43chqb7mpyvdh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01085",
  "fulltext_url": null,
  "id": "43chqb7mpyvdh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01085",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nlin.PS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01085",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/43chqb7mpyvdh.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.01085",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01085"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "On the Time-Domain Waveforms Leading to Frequency Comb Spectra",
  "title_text": "On the Time-Domain Waveforms Leading to Frequency Comb Spectra",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/43chqb7mpyvdh",
  "venue": "arXiv",
  "versions": []
}