On the Time-Domain Waveforms Leading to Frequency Comb Spectra
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.
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BibTeX
@misc{mishra2026timedomain,
title = {{On the Time-Domain Waveforms Leading to Frequency Comb Spectra}},
author = {Madhurendra Mishra and Adarsh Ganesan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01085},
eprint = {2611.01085},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01085},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Time-Domain Waveforms Leading to Frequency Comb Spectra
AU - Madhurendra Mishra
AU - Adarsh Ganesan
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01085
UR - https://arxiv.org/abs/2611.01085
AB - 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.
ER -