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Title: Correlation and spectral properties of higher-dimensional paperfolding and Rudin-Shapiro sequences
Authors: BarbĂ©, AndrĂ© ×
von Haeseler, F #
Issue Date: Mar-2005
Publisher: Iop publishing ltd
Series Title: Journal of Physics A. Mathematical and General vol:38 issue:12 pages:2599-2622
Abstract: We consider higher-dimensional generalizations of the classical one-dimensional 2-automatic paperfolding and Rudin-Shapiro, sequences on N. This is done by considering the same automaton-structure as in the one-dimensional case, but using binary number systems in Z(m) instead of in N. The correlation function and the diffraction spectrum for the resulting m-dimensional paperfolding and Rudin-Shapiro point sets are calculated through the corresponding sequences with values +/- 1. They are shown to be quasi-independent of the dimension m and of the particular binary number system under consideration. It is shown that any paperfolding sequence thus obtained has a discrete spectrum. The Rudin-Shapiro sequences have an absolutely continuous Lebesgue spectral measure.
URI: 
ISSN: 0305-4470
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
× corresponding author
# (joint) last author

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