In digital filtering, a Fourier transform is performed on a noisy spectrum to convert it to the frequency domain.  The resulting power spectrum is then multiplied by a filter function to remove all undesired frequency components.  (The filter function is equal to 0 at all frequencies to be removed, and equal to 1 at all other frequencies.)  An inverse Fourier transform then converts the data back to the original domain.

In this simulation, a noisy spectrum is simulated by adding together two sine waves with user-defined frequencies, amplitudes, and phase difference, along with Gaussian white noise.  The power spectrum is calculated and displayed.  The cutoff frequencies of a band-pass filter are entered, and the original data is displayed with all frequencies outside of the filter removed.

(Reference: Skoog, Holler, and Crouch Principles of Instrumental Analysis, 6th Ed Thomson Brooks/Cole 2007)