How is Fourier transform used in noise reduction?
Using information of the Fourier transform of trigonometric functions, dominant components can be distinguished from the noisy data. After filtering out weaker components we can compute IDFT of the remaining coefficients resulting in a filtered signal in the time domain.
What is spectral subtraction?
The spectral subtraction is historically one of the first algorithms proposed for the enhancement of single channel speech. In this method, the noise spectrum is estimated during speech pauses, and is subtracted from the noisy speech spectrum to estimate the clean speech.