Identification of GW bursts in high noise using Pad\'e filtering

TL;DR

This paper introduces a method using Padé Approximations of the Z-transform to detect gravitational wave bursts in highly noisy data from two antennas, effectively distinguishing signals from noise.

Contribution

The paper presents a novel application of Padé filtering to identify signals in high noise environments by analyzing complex conjugate poles in the Z-transform.

Findings

Successfully detects simulated gravitational wave bursts in noisy data

Differentiates signal poles from noise poles using residue analysis

Effective in both white and colored noise conditions

Abstract

We consider the case of highly noisy data coming from two different antennas, each data set containing a damped signal with the same frequency and decay factor but different amplitude, phase, starting point and noise. Formally, we treat the first data set as real numbers and the second one as purely imaginary and we add them together. This complex set of data is analyzed using Pad\'e Approximations applied to its Z-transform. Complex conjugate poles are representative of the signal; other poles represent the noise and this property allows to identify the signal even in strong noise. The product of the residues of the complex conjugate poles is related to the relative phase of the signal in the two channels and is purely imaginary when the signal amplitudes are equal. Examples are presented on the detection of a fabricated gravitational wave burst received by two antennas in the presence of either white or highly colored noise.