Wavescan: Multiresolution Time-Frequency Transform of Gravitational-Wave Data

Sergey Klimenko

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arXiv · 2201.01096

Wavescan: Multiresolution Time-Frequency Transform of Gravitational-Wave Data

Sergey Klimenko

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Abstract

Identifying transient signals embedded in non-stationary noise requires analyzing the time-dependent spectral components of the observed time series. The time-frequency distribution of the signal power can be estimated with Gabor atoms, or wavelets, localized in time and frequency by a window function. Such analysis is constrained by the Heisenberg-Gabor uncertainty principle, which limits the simultaneous time and frequency localization achievable with individual wavelets. Moreover, the resulting time-frequency distribution is subject to temporal and spectral leakage, limiting the identification of sharp or rapidly varying features in the power spectrum. This paper introduces a time-frequency transform that uses a stack of wavelets to scan local power across multiple scales. At each time-frequency location, a wavelet least affected by the leakage is selected from the stack to obtain high-resolution localization of power. The resulting wavelet scan ("wavescan") extends conventional multiresolution analysis by enhancing time-frequency localization and mitigating local power distortions caused by temporal and spectral leakage. The paper describes the principal components of the wavescan framework, including the estimation of the time-varying spectrum, identification of transient signals in the time-frequency data, and reconstruction of the corresponding time-domain waveforms. To demonstrate the performance of the method, the wavescan transform is applied to gravitational-wave data from the LIGO detectors.

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BibTeX RIS

Sergey Klimenko. 2026-09-08. Wavescan: Multiresolution Time-Frequency Transform of Gravitational-Wave Data. https://arxiv.org/abs/2201.01096

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