10. FOURIER FILTER

The Fourier filter is a type of filtering function that is based on manipulation of specific frequency components of a signal. It works by taking the Fourier transform of the signal, then attenuating or amplifying specific frequencies, and finally inverse transforming the result. The example shown here is a simple low-pass, sharp cut-off filter, which simply cuts off all frequencies above a user-specified limit. The assumption is made here that the frequency components of the signal fall predominantly at low frequencies and those of the noise fall predominantly at high frequencies. The user tries to find a cut-off frequency that will allow most of the noise to be eliminated while not distorting the signal significantly. An example of the application of the Fourier filter is given in Figure 14.

Figure 14. The signal at the top left seems to be only random noise, but its power spectrum (top right) shows that high-frequency components dominate the signal. The power spectrum is expanded in the X and Y directions ( bottom left) to show more clearly the low-frequency region. Working on the hypothesis that the components above the 20th harmonic are noise, the Fourier filter function can be used to delete the higher harmonics and to reconstruct the signal from the first 20 harmonics. The result (bottom right) shows the signal contains two bands at about x=200 and x=300 that are totally obscured by noise in the original signal.

Figure 15. Peak area measurement for overlapping peaks, using the perpendicular drop method.