Disregarding the risk in PS of not registering waves of short periods 
(critical frequencies), the function H (v,T,r) closely resembles the 
"composed transfer function" (see figure 4) as introduced in /12/ with 
the limiting fidelity curve 
à (v,T) = ELI 
p(v) being the amplitude of a sinusoid with frequency v. T/8 is the max- 
imum error that can occur for a parabolic section of the input if the 
second difference is just equal to T. 
For single sinusoids as input to PS, it was found that o = 1/10, a being 
not a constant but very weakly dependent on the magnitude of T. The 
threshold has a much stronger influence on accuracy and time-efficiency 
than the number of sampling runs. The choice of the threshold value 
depends on given accuracy specifications (upper limit) and on the ex- 
pected height measuring error (lower limit). T should at least be larger 
than 2.5 Oy to prevent densification caused by random height measuring 
errors. 
It cannot be expected that H(v,T,r)--reflecting the behaviour of PS if 
applied to single sinusoids--allows estimating the mean square error of 
the reconstructed curve if the input was a linear combination of 
sinusoids. The reliability of PS is likely to be much higher for super- 
imposed sinusoids than for individual sinewaves, especially if the low 
frequency components have large amplitudes (as is the case in most ter- 
rain types). The composed transfer function C(v,T,r) is therefore more 
promising than H(v,T,r). Even the composed transfer function should be 
expected to produce too pessimistic accuracy estimates, since the sam- 
pling density for the low frequency components is higher than defined by 
the segments of the composed transfer function. If very long waves 
(v« 0.01/ A Xin in figure 4) are overlaid by short waves, they will be 
covered not only by the zero-run (Ax) but also by local densifications 
because of the presence of the high frequency components. 
The tests on computer-simulated profiles confirmed these considerations. 
The composed transfer function was computed with a limiting fidelity of 
where p( “i? = 2!F(k)!, !F(k)! being the discrete amplitude spectrum of 
the input as obtained by the Fast Fourier Transform. The m.s.e. of the 
progressively sampled profiles was estimated by: 
n/2 -1 
Q» 
N N 
H 
EL + CE, ,T,r))° F(K) 12 
k=-n/2 
Although the composed transfer function and the estimation formula do 
not express the phase dependency inherent in PS, upper bound estimates 
- 659°