Notice that the amplitude of the feature is not affected, provided a 

 full wave form is sampled. 



The effect of directional sampling in the spatial frequency domain 



can be calculated using the previous relationship in combination with 



the similarity theorem of Fourier transforms (see Bracewell, 1978, 



p. 101). The similarity theorem states that given the transform pair 



£(x) S PCs), then 



f(ax)l5 |a|-l F(s/a) 



Applying the geometry for directional sampling of linear features, i.e., 

 a - I cos 9 I 



f(|cos 9| . x) :d |co8 e|-^ . F (s/cos 9) 



Because |co8 9| must always be less than one, the effect of oblique 

 sampling in the frequency domain is to shift the amplitude peak to lower 

 frequencies, narrow its width, and increase its amplitude. This is a 

 result of the fact that a signal of equal height but lower frequency has 

 greater power than its higher frequency counterpart. It is Important to 

 note that these theorems assume an infinite continuous signal. In ana- 

 lyzing finite length signals, it is necessary to normalize the spectrum 

 by the sample length, that Is, divide each amplitude estimate by the 

 number of values in the time series. This normalization preserves the 

 true amplitude of the individual waveforms, and allows comparisons 

 between samples of different length. The effect of anlsotropy on sam- 

 pling a surface with continuous spectra is developed in a later section. 



34 



