SPATIAL FILTERING IN THE WAVE-VECTOR DOMAIN

Spatial data can be represented in the two‐ dimensional frequency (wave‐vector) domain. This much simplifies the achievement of any desired transfer response in a linear digital filter. Similar results have been obtained approximately by convolution (also termed correlation) in space with a weighted coefficient set. The equivalence of wave‐vector filtering and a special form of convolution filtering is demonstrated. Given the availability of a fast Fourier transform, computational advantage lies with the former. The regional trend is removed from data prior to wave‐vector filtering, and this combined procedure gives one solution to problems arising at the edge of the data. In the appendix, a computationally convenient form of the two‐dimensional fast Fourier transform is given for arrays with side lengths not restricted to powers of two. Considerable savings in computing time and storage allocation are shown when real data are used.