The finite Legendre transform (fLT) 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).
In this version (v1.2), we also release a pure-python solution to give a real platform independent support, in case the c/c++ library is not work.
Source code for fLTlib can be found at our web page.