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

ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)

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.

Authors 5

1. A. Vajpeyi

   University of Auckland

   Affiliation as printed

   Department of Statistics , University of Auckland , 38 Princes St , Auckland , New Zealand

2. Giorgio Mentasti

   Centre National de la Recherche Scientifique · Université Toulouse III - Paul Sabatier · Université Paris Cité · Laboratoire AstroParticule et Cosmologie · Institut National de Physique Nucléaire et de Physique des Particules · Laboratoire des 2 Infinis Toulouse · Université de Toulouse

   Affiliation as printed

   Infinis -Toulouse (L2IT-IN2P3) , Université de Toulouse , CNRS , UPS , F-31062 Toulouse Cedex 9 , France

   Université Paris Cité , CNRS , Astroparticule et Cosmologie , F-75013 Paris , France

3. Quentin Baghi

   Centre National de la Recherche Scientifique · Université Toulouse III - Paul Sabatier · Université Paris Cité · Laboratoire AstroParticule et Cosmologie · Institut National de Physique Nucléaire et de Physique des Particules · Laboratoire des 2 Infinis Toulouse · Université de Toulouse

   Affiliation as printed

   Infinis -Toulouse (L2IT-IN2P3) , Université de Toulouse , CNRS , UPS , F-31062 Toulouse Cedex 9 , France

   Université Paris Cité , CNRS , Astroparticule et Cosmologie , F-75013 Paris , France

4. Ollie Burke

   University of Glasgow

   Affiliation as printed

   Laboratoire des

   School of Physics and Astronomy , University of Glasgow , University Avenue , Glasgow , G12 8QQ , UK

5. Lorenzo Speri Aachen Leiden Observatory

   Leiden University · European Space Agency · Leiden Observatory · European Space Research and Technology Centre

   Affiliation as printed

   European Space Agency (ESA) , European Space Research and Technology Centre (ESTEC) , Keplerlaan 1 , 2201 AZ Noordwijk , the Netherlands

   Leiden Observatory , Leiden University , P.O. Box 9513 , 2300 RA Leiden , the Netherlands