Compare scipy/numpy regular FFT with `hfft` and `ihfft` routines to compute impedances and wake functions

[elenafuengar]

[KeonHKim]

I compared the existing wake-impedance conversion functions with a new approach based on an ihfft formulation.
Through this comparison, I found a normalization issue in the current implementation.
I have therefore fixed this normalization issue and uploaded the new method accordingly.
Based on this updated approach, I am planning to revise the existing scripts.

Current method:
https://github.com/ImpedanCEI/wakis/blob/main/tests/test_004_wakes_and_impedances.py

New method:
test_004_wakes_and_impedances_bug_fixed_example.ipynb

[elenafuengar]

Hi Keon,

Thank you very much for your contribution and all the discussion over email, I've really learned a lot !

Would you like me to make the modifications myself based on your notebook or would you like to contribute with a pull request?

Let me know, and thanks again !! 🫶

[KeonHKim]

Hello Elena,

Thank you very much and sorry for the delay.
I think it would be fine if you go ahead and make the modifications yourself based on the notebook.
Once that’s done, I can follow up by adding some additional features on my side, for example the conversion between transverse planes (since Wakis currently only supports the longitudinal conversion), as well as support for the non-ultrarelativistic case.

[KeonHKim]

In the previous version, the analytic impedance function for the cosine or sine wake was accidentally omitted.
In this version, benchmark cases for the resonator and resistive-wall models are also included.

004_Wakefield_simulation_enhanced.ipynb