A theorem on higher-order absolute differences taken from successive terms of bounded sequences is proved. This theorem establishes the property of bistability of such difference series and suggests a method for converting periodic discrete-time signals into the binary digital form based only on the computation of absolute differences. MSC: 37E05; 37M10; 94A12
A method for analyzing discrete processes based on consideration of their higher difference structure is presented. Two kinds of processes, deterministic systems (discrete dynamical systems) and the sequences of random binary independent variables, are considered. Two main statements, computation of higher absolute differences and restoring the original by a given higher order difference image, are studied. Some applications to dynamical systems are given.
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