Filtering in the Frequency Domain

Abstract

We introduce the idea that a surface profile is comprised of sinusoids of various wavelengths and therefore a profile (or topography) may be transformed into the frequency domain where it can be viewed in terms of its wavelength content. Filtering therefore involves suppression of certain wavelength bands, followed by reconstruction (inverse transform). We describe this frequency domain approach to filtering using a simulated surface profile containing two sinusoids of different wavelength. We describe how the Fourier transform is performed, how a filter is defined so that one of the constituent sinusoids is suppressed, how it is applied on the profile, and finally how the reconstructed profile is generated. The entire process of frequency domain filtering for this two-sinusoid profile is worked out in MATLAB. Exercises at the end of the chapter (with answers at the end) further elaborate on the methods described in this chapter.