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Say I have a noisy signal in which I want to denoise.

There's two methods I'm considering

  1. FFT denoising, where I take the FFT of the signal and then threshold somewhere, attenuate all the frequencies below this threshold, and then take the IFFT.
  2. Low pass filtering, which in the Fourier domain is just attenuating all the frequencies above a particular frequency anyway.

My question is, what's the difference? Aren't we effectively selecting the frequencies we want at the end of the day? When would I prefer one over the other? I can only think using FFT denoising if we know the noise spans ALL of the spectrum including the lower frequencies.

Nobody Special
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