Understanding fft signal decomposition

Question

I've read a lot about FFT on both Stackoverflow and other websites but there are few questions i still don't understand based on this topic.

1. Upon showing frequency domain graph, does FFT consider all possible sine waves that constructed input signal in the first place or it just does for some 'reasonable' amount of sine waves that have biggest amplitude?
2. When looking some examples of frequency domain, by some logical understanding, there should be infinite amount of sine waves that constructed some signal in first place, so why is there no infinite amount of possible frequencies peaks?
3. If frequency domain would be represented in 1D, would every line represent some particular sine wave that constructed input signal in first place?

Answer 1

1) An FFT or DFT "breaks down" a strictly real waveform into a finite number of sine waves, basis vectors for those N/2 frequencies that are exactly integer periodic within the FFT's length N. Any other frequencies are represent by a mix of all the other basis frequencies. (The mix will be shaped like the sum of 2 periodic Sinc or Dirichlet functions).

If you want more frequency resolution, you need to sample the input waveform for a longer length of time, and then use a longer FFT.

2) Whatever the sum of an infinite number of frequencies was in the original signal, they will be aliased and broken down into a mix of only N/2 basis frequencies by the sampling process, the FFT window length, and the FFT itself.

Because the FFT result vector can contain N/2 result bins, and any peak (that looks like a peak on a graph) requires a "dip" on either side (usually specified as 3 dB lower), there can only be a maximum N/4 peaks visible in a graph of the FFT result. Any other "peaks" will be hidden or blended into those.

An FFT magnitude spectrum graphing or plotting program can plot a lot more points, but those higher resolution plot points are just interpolations of the N/2 FFT result points.

3) Every FFT result bin (is that what you mean by line?) represents either an exact frequency of sinusoid (the frequency of one of the N/2 basis vectors), or a portion of a decomposition of some other non-periodic-in-aperture frequency of waveform into basis vectors. See Fourier decomposition.