MothNik / robust_fourier

Noise- and Outlier-Robust Fourier Transform with Hermite Functions with NumPy and Numba
MIT License
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🤕🔨 Change definition of the `alpha`-parameter to be more Fourier-friendly #14

Closed MothNik closed 4 months ago

MothNik commented 4 months ago

The previous definition of the scaling with the coefficient $\alpha$ lead to the Hermite polynomials

DilatedHermitePolynomials

and Hermite functions

DilatedHermiteFunctions

So, when $\alpha$ is less than 1, the function is shrinking towards the y-axis which made perfect sense (smaller alpha, smaller function).

This was okay until I realised that this was their definition in the frequency and not the time domain. Now, this is where the weird effects happen. When $\alpha$ is small in the frequency domain, the Hermite functions in the time domain are getting stretched. With this unintuitive behaviour, it's getting super confusing to select $\alpha$ properly given only the time domain. Therefore - now that there is if at all a handful of people using this repository - I need to change the definition to $\alpha{new}=\frac{1}{\alpha{old}}$ which leads to

Dilated_Hermite_Polynomials_Of_Generic_X

and

Dilated_Hermite_Functions_Of_Generic_X

MothNik commented 4 months ago

✔️ Checklist of things to do

MothNik commented 4 months ago

Ready to be closed 👍