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Here is one way to do things:

  1. Analog signal goes in…
  2. And is converted to digital…
  3. Fourier transform converts time-based samples to frequency domain…
  4. Some changes are made to frequencies…
  5. Inverse Fourier transform converts back to time domain…
  6. Digital is converted to analog output…

Some things can be done in the time domain without having to do the Fourier transforms…