x E 
- 
* 
; A 
SN 
1- 
0 . — - 
  
AX, 
  
  
  
  
  
  
LE 
Figure 3: Zero-sample for r = 2, A = 4 
If T is larger than zero, the risk of insufficient densification is not 
restricted to isolated frequencies but extended to a range of fre- 
quencies, also around v = 1/2 (see figure 2). The "risk ranges" become 
wider the larger the T. 
The larger the number of densification runs, the larger the number of 
critical frequencies. If r = 4, then VF (1/32: i171, ..., 10).'Im 
general: y = j/27"1 A ie Obviously the larger r for a 
* Xmin’ 
given Ax min’ the lower the fidelity of PS, although the effect is by far 
not as severe for actual terrain profiles as it is for single sinusoids, 
as will be outlined later. The maximum number of runs is a free process 
parameter, whereas minimum grid spacing depends on the required resolu- 
tion of the DEM. The negative effect on accuracy of choosing a very 
coarse initial grid spacing (i.e., larger r) has to be traded off 
against its positive effect on time-efficiency of sampling. 
The influence of the threshold on long waves (i.e., v < 0.065 in figure 
2) can be formulated as: 
H(v, T,r) > ® (v,T) = 1 - aT; for frequencies v lower than the ones cap- 
tured by Ax.. 
min 
  
  
  
  
  
  
  
© 
. 
J 
À 
  
  
e 
. 
v 
  
  
o 
+ 
N 
  
9.1 
  
  
  
  
9 vm T an oy T y 
0 0.1 0.2 0.3 0.4 0.5 
Figure 4: Composed transfer function C(y,T,r) for p(v) = 1, 
$(v)21-T/10; rz4, T-2 
- 658 +