Explain and implement in C++ the FFT algorithm "Cooley-Tukey". Also, implement the naive DFT and compare the naive DFT with the FFT using: a sample of the signal x(t) = t and then x(t)=t^5. Use your own C++ classes and create a GUI with QtCreator.

Requirements

1.- Application compiling and running, application robustness (try many cases!),
2.- Quality of programming: coding style, comments, use of memory, functions variables used, ...
3.- GUI efficiency and visual aspect,
4.- Project management: choice of classes (UML), links between algorithm classes and GUI classes, ...
5- Proof of correctness,
6.- Comparison of the theoretical time efficiency vs observed one.