METHOD FOR EVALUATING, SELECTING AND OPTIMZING BILINEAR TIME-FREQUENCY TRANSFORMS FOR THE STUDY OF ULTRAFAST OPTICAL RESPONSES

摘要

The invention relates to a method for analysing an oscillating signal obtained from spectroscopy of a material. The method provides to generate a synthetic signal comprising a plurality of frequency components mimicking real signals. The parameters of a plurality of stored time-frequency transforms are optimized by maximizing a goodness parameter defined as the combination of two similarity parameters: a first similarity parameter indicating the similarity of the time integral of the time-frequency transform of the synthetic signal to a Fourier transform of the same synthetic signal (similarity in frequency) and a second similarity parameter indicating the similarity in time between at least one frequency component of the synthetic signal and a corresponding frequency component of the time-frequency transform of the synthetic signal (similarity in time). The transform that is able to provide the greatest fidelity to the starting signal (the one exhibiting the highest goodness parameter) is identified from the comparison. Finally the acquired signal is analysed by means of the optimized time-frequency transform having the greater goodness parameter or by means of a combination of a plurality of time-frequency transforms having the greater goodness parameters.