Probably there's a similar question, but I could't find it through all questions about FT
As the title says, how many Fourier coefficients are enough, to be able to "resume" the original function, using inverse discrete Fourier transform?
For example, in the definition from Wikipedia, it looks like we need N coefficients, where N is the number of given points from the original discrete function. I also noticed, that for FFT (fast Fourier transform), the number of calculated coefficients is the same as the number of given points.
Is this always like this? Or we may have fewer coefficients? Or more? And is there a way to estimate this number of necessary coefficients?
I ran some test with randomly generated "control points" of a discrete function and applied DFT and IDFT (in this order) and all control points were recreated.