Add Exponential of Semicircle Window
- Dominant language
- Julia
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Description
We want to integrate the "exponential of semicircle" window proposed in this paper: https://arxiv.org/abs/1808.06736
I am not completely sure but my FINUFFT wrapper indicates that it is slightly more accurate than Kaiser-Bessel.
Remarks:
* The window is completely simple
* Its Fourier transform seem to have no analytical form and therefore it is approximated using Gauss-Legendre-Quadrature (equation 3.10 from the paper)
* The implementation in FINUFFT is here: https://github.com/flatironinstitute/finufft/blob/master/src/finufft.cpp#L227. But if I get it right they applied some caching tricks that result in this https://github.com/flatironinstitute/finufft/blob/master/src/finufft.cpp#L167 But these implementations should only be used for debugging purpose, the mathematics is straight forward and permits a cleanroom implementation.
* Both functions require the Gauss-Legendre nodes, which are calculated here: https://github.com/flatironinstitute/finufft/tree/master/contrib Of course we would not use that but instead go for a Julia package. A quick search pointed me at https://github.com/JuliaApproximation/FastGaussQuadrature.jl
This would be a nice "good first time contributor" project if somebody want to have look at it. Otherwise I will five it a go when time permits.
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