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It has been a while since I study DSP, so I'm not sure if FFT can mathematically recover all the original sine waves (FT can). But I don't think it is possible practically, at least.



Yes, if you use the FFT or any discrete FT, you can perfectly recreate the signal up to the Nyquist frequency. To perfectly recreate the whole signal, you'd need infinite Fourier coefficients.


Thanks




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