🧮〰️ Implement Robust Weighted Least Squares Regression-based Fourier transform

[MothNik]

Now, with the Hermite-functions and a CI properly set up, the core functionality of the package can be implemented:

The Robust Weighted Least Squares approach to Fourier Transform as described in

Mihály Dobróka, Hajnalka Szegedi and Péter Vass: Inversion-Based Fourier Transform as a New Tool for Noise Rejection, 2017, DOI

[MothNik]

✔️ Checklist of things to do

• [x] (1) implement auxiliary functions that help converting between Discrete and Continuous Fourier Transform
• [x] (2) test auxiliary Fourier functions
• [x] (3) add center to the Hermite functions in order to shift them
• [x] (4) test center functionality
• [x] (5) update function documentation, examples, and README to mention the new center functionality
• [x] (6) implement fast approximations of important Hermite function points, namley the
  • [x] (6.1) the position of the outermost root,
  • [x] (6.2) the position and value of the outermost extreme point, and
  • [x] (6.3) the point of numerical vanishing in the outermost tails
• [] (7) implement functions to compute the Discrete/Continuous Fourier Transform and or its Inverse for a Hermite function
• [] (8) test Hermite function Fourier transforms
• [x] (9) implement object-oriented interface to Hermite functions and their Fourier transforms
• [ ] (10) implement Least Squares fit for the Fourier transform with robust weighting scheme (currently static order and alpha)

[MothNik]

A PR to develop will be made now that the first 6 points on the checklist are done. It's a good place to make a PR to keep it "small" and also self-consistent in terms of topic covered.

[MothNik]

Point (7) was partially merged into point (9) because a completely separate function interface made no sense. The class interface now offers the static method eval as a function interface with the class HermiteFunctionBasis just wrapped around it to handle all the input validation and magic methods like __len__. HermiteFunctionBasis.__call__ now just specifies an internal call to eval.

[MothNik]

I will put this temporarily on ice after noticing that Hermite functions are not necessarily the best basis functions to tackle this problem. I will still work on this, but I think the package needs a bit of a generalization first.