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arXiv · 2606.20269

An explicit and differentiable Wilson-Daubechies-Meyer transform for gravitational-wave data analysis

Avi Vajpeyi·Giorgio Mentasti·Quentin Baghi·Ollie Burke·Lorenzo Speri
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Abstract

The Wilson-Daubechies-Meyer (WDM) time-frequency transform has been widely used in gravitational-wave astronomy, yet a self-contained, mathematically explicit reference for practitioners remains lacking. This is especially true for those wishing to adopt the transform in modern Python and JAX inference workflows. We present wdm_transform, an open-source Python package implementing the WDM wavelet-packet time-frequency transform, and document its mathematical foundations, statistical properties, and practical implementation for gravitational-wave data analysis. The package supplies NumPy and JAX backends, both transforms (forward and inverse) validated to floating-point precision, with the JAX backend enabling GPU-accelerated transforms of million-point data streams in tens of milliseconds. As a worked example, we verify that the WDM-domain likelihood reproduces frequency-domain posteriors for a resolved LISA galactic binary under a shared stationary noise model, confirming numerical equivalence of the two representations in that controlled setting. This work paves the way for systematic optimisation of WDM tilings, a particularly promising direction for the non-stationary noise, stochastic backgrounds, and data gaps anticipated in future detectors, and for direct comparisons with alternative time-frequency representations needed to meet the challenges of future gravitational-wave data analysis.

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Avi Vajpeyi, Giorgio Mentasti, Quentin Baghi, Ollie Burke, Lorenzo Speri. 2026-06-18. An explicit and differentiable Wilson-Daubechies-Meyer transform for gravitational-wave data analysis. https://arxiv.org/abs/2606.20269

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