A SPECTRAL ANALYSIS METHOD FOR ESTIMATING THE SAMPLING 
DENSITY OF DIGITAL ELEVATION MODELS . 
Dr. Mohsen Mostafa Hassan 
M.S.D. 
Cairo , Egypt. 
ABSTRACT 
Terrain surfaces represent continuous space signals which 
are sampled at pre-determined intervals to form Digital 
Elevation Models . The main problem in sampling terrain 
relief is how to choose an appropriate value for the 
sampling density . The approach used in this research is 
based on the sampling theory and the analysis of terrain 
data in the frequency domain. It is known that sampling 
density must be chosen so that variations in the continu- 
ous terrain surface are negligible at frequencies higher 
than the Nyquist frequency . If the discrete spectrum of 
the DEM data does not approach zero near the Nyquist 
frequency , & smaller value of the sampling interval should 
be tried. The method is illustrated and tested in the uni- 
variate mode , furthermore , the mathematical dereviation 
for the bi-variate mode is also presented . 
1. INTRODUCTION 
The interval at which the observations are taken is usually 
one of the most important factors in DEM data acquisition. 
In the digital Pfoceasine of DEM data , the spacing between 
points is normally assumed to be unity . This assumption 
is employed to simplify the notations , however , in practi- 
cal data collection , the spacing to be used depends on the 
type of the terrain surface . The observations must be 
chosen close enough to ensure the accurate reconstruction 
of the original signals from the sampled values. 
It is clear that sampling leads to some loss of information 
and that loss gets worse as the sanpling interval increases. 
However, it is uneconomic to use very small sampling in- 
tervals , and s0 a compromise value must be sought . The 
objective of this investigation is to fined a theoretically 
sound method to determine this compromise value . The method 
is performed in the frequency domain where the spectral 
density function is determined and analysed . An estimate 
of the spectrum of a given set of data can be determined 
by the transformation of these data from the spatial 
domain to the frequency domain using the Fourier transform. 
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