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 dat
a set as real numbers and the second one as purely imaginary and we add them together. This complex set of data is analyzed using Pade 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.
