Investigate different implementations of the PSS Complex Fourier Transform (CXFT) component

The current Cheetah implementations and availability of FFT algorithms were checked (e.g., version of used FFTW library). A decision was made that we do not proceed with FPGA algorithms for now, but only explore CPU and GPU-based codes. There is currently no CPU-based FFT in Cheetah, but such an algorithm seems worthwhile exploring. There was the idea to look for a streaming FFT algorithm for the new CPU implementation. This and continued development of FFT algorithms required an evaluation of recent  literature to identify a potentially more efficient algorithm.   General bechmarking results documenting pro and cons of various CPU and GPU algorithms (including new versions of the Cheetah GPU implemention and considered CPU code) were found and documented (see attachment). A promising new code was identified that may help with a performance improvement of ~factor 2.   Before we can create the features for further development of the CXFT, we have to benchmark the chosen codes in the framework of Cheetah with PSS-tailored parameters. This will be the next step.