Detection of gravitational wave transients using Malvar-Wilson wavelets

 

Jerzy Usowicz

ju@astro.uni.torun.pl

Torun Radio Astronomy Observatory

 

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The Detection Algorithm  
(Ravier-Amblard algorithm)

 

The data are organized as a binary tree:

 

—         the root  – the coarsest segmentation level      (the whole signal)

—         the leafs – the finest segmentation level   (the shortest segments)

 

The algorithm works as follows:

 

1.    partition of the time series x(t) in equal segments x_j^l(t), at a resolution level l

2.    compute the Malvar-Wilson wavelet coefficients C^l_jk on these segments  (DCTiv)

3.    estimate the 4^th order cumulant  Cum4_j^l  or kurtosis K4_j^l at level l    (CUM4  or K4) to differentiate between Gaussian and non-Gaussian segments

4.    repeat the above three steps from the finest to the coarsest segmentation level

5.    apply the segmentation test on Cum4_j^l  or K4_j^l  at each resolution level l   

a.    merge segments of the same nature

b.    split segments of the different nature

c.    the desired partition R only retains merged segments    (gaussian) and finest segments that have not been associated (non-gaussian)  

6.    compute the detection statistics (Cum4 or K4  of each element of the retained partition R)