Finding n Amplitudes by DFT, what is correct normalization
Do you want to get the peak, or the amplitude, of the time domain signal given the spectrum? Since energy is conserved, the time domain energy amplitude can easily be found by adding the energy from each frequency bin of the spectrum. However, you cannot find the time domain peak simply by looking at the FFT frequency bin magnitudes. Consider an extreme case: the spectrum of an impulse is fairly smooth in spite of the fact that the impulse will have a strong peak.