A compact time-frequency representation for gravitational-wave data analysis
Abstract
Time-frequency (wavelet) domain analyses are seeing greater use for gravitational-wave data analysis due to the advantages they have in handling non-stationary noise. A popular choice is the Wilson-Daubechies-Meyer (WDM) wavelet transform, which uses a window function that is very compact in frequency, but more spread out in time. In this work, we consider an alternative window function that is built from a sum of phase-shifted Gaussians. This "Gaussian" window is more symmetric in time-frequency, and consequently more compact. We examine the properties of this window function and the implications it has for gravitational-wave analyses. We calculate the window's time-frequency variance product analytically and verify it numerically. For the symmetric case, where the window has the same form in time and frequency, the construction comes within ∼2.4% of saturating the Heisenberg-Gabor uncertainty limit. We conjecture that this Gaussian window achieves the minimum time-frequency area of any WD wavelet window.
Related
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BibTeX
@misc{pearson2026compact,
title = {{A compact time-frequency representation for gravitational-wave data analysis}},
author = {Noah Pearson and Mesut Çalışkan and Sophie Bini and Neil J. Cornish},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05601},
eprint = {2609.05601},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05601},
}
RIS
TY - UNPB
TI - A compact time-frequency representation for gravitational-wave data analysis
AU - Noah Pearson
AU - Mesut Çalışkan
AU - Sophie Bini
AU - Neil J. Cornish
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05601
UR - https://arxiv.org/abs/2609.05601
AB - Time-frequency (wavelet) domain analyses are seeing greater use for gravitational-wave data analysis due to the advantages they have in handling non-stationary noise. A popular choice is the Wilson-Daubechies-Meyer (WDM) wavelet transform, which uses a window function that is very compact in frequency, but more spread out in time. In this work, we consider an alternative window function that is built from a sum of phase-shifted Gaussians. This "Gaussian" window is more symmetric in time-frequency, and consequently more compact. We examine the properties of this window function and the implications it has for gravitational-wave analyses. We calculate the window's time-frequency variance product analytically and verify it numerically. For the symmetric case, where the window has the same form in time and frequency, the construction comes within ∼2.4% of saturating the Heisenberg-Gabor uncertainty limit. We conjecture that this Gaussian window achieves the minimum time-frequency area of any WD wavelet window.
ER -