When I sample a certain digital signal with increasing sampling frequency, the fast Fourier transform of the sampled signal becomes finer and finer. (the image follows) Previously I thought higher sampling frequency makes the sampled signal more similar to the original one, so the Fourier transform of a signal sampled at very high frequency would be the same as the FT of the original signal. But in fact the FT of the sampled signal is much narrower. How to explain this phenomenon? As the FT is different in different sampling conditions, why the original signal can still be correctly reconstructed?