Transient analysis with fast Wilson-Daubechies time-frequency transform

The time-frequency transforms are important tools for identification of transient events in the output of the gravitational-wave detectors. Produced by the terrestrial and possibly by astrophysical sources, the transient events can be identified as patterns on the time-frequency plane with the excess power above stationary detector noise. In this paper we consider a particular case of the Wilson-Daubechies time-frequency transform for use in the gravitational-wave burst analysis. The presented Wilson-Daubechies basis shares some properties with the Gabor frames, but circumvents the Balian-Low theorem. It also shares similarity with the Meyer wavelet, which is actively used in the gravitational-wave burst analysis. The main advantages of the Wilson-Daubechies transform are the low computational cost, spectral leakage control, flexible structure of the frequency sub-bands, and the existence of the analytic time-delay filters, which are important for localization of the gravitational-wave sources in the sky. These properties of the Wilson-Daubechies transform may prove useful not only in the transient analysis, but also in other areas of the gravitational wave data analysis and detector characterization.