fLTlib 1.0

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The finite Legendre transform for filtering and fitting of exponentials and other smooth functions

A method is introduced for effectively filtering or fitting noisy exponentials or other smooth experimental data.

The method consists of two steps: (1) The transform of the noisy signal from the time-domain (t-domain) into the Legendre-domain (L-domain) and (2a) reconstruction and effective noise removal using the lower Legendre components (filtering), or (2b) fitting of the lower Legendre components using a nonlinear least squares method to find the amplitudes and the decay times of noisy exponentials (fitting).