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We propose to apply to the detection of Gravitational Waves a new methoddeveloped for the spectral analysis of noisy time-series of damped oscillators.  From the Pad\'e Approximations of the time-series Z-transform, a JacobiMatrix (J-Matrix) is constructed. We show that the J-Matrix has bound stateswith eigenvalues strictly inside the unit circle. Each bound state can beidentified with one precise damped oscillator. Beside these bound states, thereis an essential spectrum sitting on the unit circle which represents the noise.In this picture, signal and noise are clearly separated and identified in thecomplex plane. Furthermore, we show that the J-transform enjoys the exceptionalfeature of lossless undersampling. We take advantage of the above properties ofthe J-transform to develop a procedure for the search of Gravitational Wavebursts in interferometric data series such as those of LIGO and VIRGO projects.Successful application of our procedure to simulated data having a poor signalto noise ratio, highlights the power of our method.

J-transform applied to the detection of Gravitational Waves: preliminary results