Python - prolate spheroidal wave functions expanded on Legendre polynomials
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computation of prolate spheroidal wave functions by expansion on Legendre polynomials in Python language
- significant improvement in speed compared to DPSS with only slightly compiled code. Code optimization is likely possible.
- DPSS computed with tridiagonal matrices are not the best confinment windows
- calculation of 1-\lamda with concentration integration more precise when n < Integer(NW/2) compared to DPSS (Percival Walden) and Wang methods
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Calculation of Legendre polynomials on max N+1 polynomials at once in dPSWF/PolyLegendre_Roots.py returns an object where roots, calibration factors, evaluation functions
Calculation of all PSWF up to order OrderN at once on a given vector on [-1,1] in dPSWF/PSWF_Legendre returns an object with psi functions, lambda values, and functions for example to compute the values on other intervals
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/dPSWF : the two main functions of the package
/test : test of the software
/perf : performance evaluation /perf/utils : functions to compute Fourier transforms, confinement values, noise equivalent bandwidth of a window
/comparisons : comparison with dpss, with other windows in Welch spectrum evaluation
/dev : used for the software development
/examples : use cases
############# INSTALLATION ############
with pip
F. Bondu, Institut FOTON, CNRS/Université de Rennes, 2025