The signal analyser is now able to produce this graph!

Quick explanation:
The program was give an mp3 file containing a wave of 5 Hz, after running the transform and pasting its output into desmos, it shows us that the wave should have a a sin wave with the x-axis dealation factor of ~31. If we plug this into n/2pi, we get ~4.9338, meaning that we basically got our original wave back!

Obviously there is more that I can do with this graph such as finding phase shift and amplitude. But this was the first main step towards the main purpose of this project, which was to be be able to break down any sound/signal into its component sin waves.

If you are looking for more about how I did this,
here is the math formula I made with inspiration/understanding of how the Fourier transform works: https://www.desmos.com/calculator/il9blockap

and here is a visualization I also made that may also help
https://www.desmos.com/calculator/adde2b4abd

(Yes I know neither of these are FFTs, idk why I called them that)

Anyways the next step will be to write an algorithm to find these peaks!