A spectral theory for stationary random closed sets is developed
and provided with a sound mathematical basis. The definition and a
proof of the existence of the Bartlett spectrum of a stationary
random closed set as well as the proof of a Wiener-Khinchin
theorem for the power spectrum are used to two ends. First,
well-known second-order characteristics like the covariance can be
estimated faster than usual via frequency space. Second, the
Bartlett spectrum and the power spectrum can be used as
second-order characteristics in frequency space. Examples show
that in some cases information about the random closed set is
easier to obtain from these characteristics in frequency space
than from their real-world counterparts.
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