T co 
= | VA + S a (27 n -w) coswk dw 
o t AX C AX 
From which : 
oo Go 
2T n 27 n 
20) = 7 Nem RU Po(-w+2 2) (6) 
From this relationship it can be noticed that if the con- 
tinuous profile contains no variations at frequencies 
above the Nyquist frequency, such that PF cC? = 0 for 
w>T/ ax , then : 
Fa) = F_(w) . 
In this case no information is lost by sampling . But more 
generally , the effect of sampling will be that variations 
at frequencies above the Nyquist frequency will be folded 
back and produce an effect at a frequency lower than the 
Nyquist frequency in the spectrum of the discrete data. 
The frequencies w,-w+2MW/ax , w+ 2WAx, ..... are 
called aliases of one another (Chatfield,1975) 
3. ESTIMATING THE SAMPLING DENSITY OF DEM PROFILES 
From the previous discussion it was shown that aliasing 
will cause no troubles if Ax is chosen small enough to 
ensure that F(w) =0 for w> T/ox. 
In the case of DEM data processing it is not possible to 
determine the continuous spectrum E (c) , therefore , 
it is only possible to assume a value for the sampling 
interval Ax and compute the discrete spectrum of the 
sampled data . If the resulting estimate of the discrete 
spectrum approaches zero near the Nyquist frequency T/Ax , 
then our choice of Ax was sufficiently small and can be 
used for the given profile . However , if the values of the 
discrete spectrum does not reach zero near the Nyquist 
frequency , then the chosen value of the sampling interval 
was larger than that required for the given terrain and 
should be reduced accordingly. 
The criterion presented by the discrete spectrum approach 
can be used in a progressive sampling process to determine 
the most suitable sampling interval for a given terrain. 
-. 209; +