kunkelalexander / when-fourier-fails-python

A collection of notebooks on strategies to accurately interpolate discontinuous and non-periodic data on a uniform grid.

when-fourier-fails-python

Explore strategies to overcome Gibb's and Runge's phenomenon when handling discontinuous and non-periodic data on uniform grids. The different notebooks implement:

• Arbitrary-order finite difference stencils
• Filters
• Mollifiers (Boyd's imbricate bell Fourier extension of the second kind or the Local Fourier Basis (LFB) method)
• Subtraction methods (Polynomial and trigonometric subtraction)
• Inverse Polynomial Reconstruction (IPR)
• SVD extensions (Boyd's Fourier extension of the third kind)
• Gram-Fourier extension (Gram-FE) (see the 'tables' folder for some pre-computed extensions and the corresponding notebook for their computation and usage)

Please look at the linked blog post for a more structure introduction.