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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