BASIC PRINCIPLES OF TWO-DIMENSIONAL DIGITAL FILTERING *

The geophysicist involved in the analysis of two-dimensional data should have an understanding of the two-dimensional finite Fourier transform and the mechanics of two-dimensional filtering. Frequency aliasing must be considered when working with sampled data. In two dimensions it is advantageous to consider aliasing in terms of the overlap of the repeating spectra inherent in the finite Fourier transform. Two-dimensional filtering can be performed as a transient convolution in the space domain, as cyclic convolution utilizing the frequency domain or as the multiplication of polynomials using the z-transform. If the “edge” effects are removed, the results of the three methods are identical.