The basic idea of providing a noise filter is that you take a signal, with added noise, perform an FFT on the signal, remove all spectral harmonics that have a PSD below some threshold, and then take the IFFT. Selecting the PSD threshold for noise can be tricky. What works well on a synthetic sound might turn a sampled sound into silence.
Journal of Object Technology
Lyon, Douglas A., "The Discrete Fourier Transform, Part 3: The PSD" (2009). Engineering Faculty Publications. 74.
Douglas Lyon, “The Discrete Fourier Transform, Part 3: The PSD”, Journal of Object Technology, Volume 8, no. 6 (September 2009), pp. 17-30