I'm really intrigued with Fourier Transforms, and was wondering if someone could clarify a few points for me:
1) Is there only one possible decomposition of any given transform into sine waves?
2) Knowing what a Fourier Transform does, I've concocted the following algorithm (which I'm aware would be useless in real life) and I'm curious if it would work:
- Input Data Points
- Execute sinusoidal regression
- calculate output of resultant sinusoidal function for the x values of given data points
- Subtract, yeilding new data points
- Jump back to step 2 using new data points unless data points are more or less linear at this point
(If question number two didn't make any sense to you, the basic idea is to do sinusoidal regression on the data points, "subtract" the resultant function, and repeat, yeilding a bunch of sinusoidal functions comprising the output of the Fourier transform)
3) Can you explain to someone (whose highest level of math education is roughly Calculus AB) how a FFT or DFT works?