Institute of Neurophysiology and Cellular Biophysics

Director: Prof. Dr. Dr. D. Schild i.R.

Methods used in the lab

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


Filtering fitting


Signal and noise in time- and Legendre-domain.
Left: Exponential decay x(t), scaled to the interval [-1,1]. Right: The first 17 components of the Legendre spectrum of x(t). The inverse fLT of the first 4 components (red, L0 - L3) gives the red curve in left panel. To fit the data, LMA can be applied in both t- and L-domain. The fit in the L-domain is much faster and usually also more precise.


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).

zipDemonstration routine for Python

The file contains python programs for filtering and fitting. The example code of fitting can be used for single or double exponentials as well as for the deconvolution of exponentials using a system response function. In case you need help, please contact us at the email addresses below.

For more information: Bao G. & Schild D.(2014)

imprint