# What is the error propagation in an FFT (Fast Fourier Transform)?

I use an insert FFT graph feature on a program called logger pro. If I have the uncertainty of my input data, can I know what the uncertainty of the FFT computation will be?

• The FFT computation, per se, does not have error (does not introduce error). Are you asking how the possible errors in your real space data get transformed into errors in your frequency space? – Jon Custer Nov 29 '18 at 3:13
• @JonCuster yes, how do errors from my data transfer to the frequency data that is obtained? Does it assume the same percentage error value? – Kidus Amare Nov 29 '18 at 3:55

FFT is just an algorithm that computes the discrete fourier transform(DFT) of a signal. DFT is linear, meaning $$F(aX+bY)=aF(X) + bF(Y)$$ Thus, if you can split your signal into the "real" part and the "error" part, you can do a FFT of the error part to get the uncertainty in frequency-space.