The bistability of higher-order differences of discrete periodic signals

Abstract

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 theorem on higher-order differences of two-state Markov chains

“…The difference analysis is a method for studying irregular and random time series, based on consideration of higher-order absolute differences taken from the series' progressive terms. This method allowed us to reveal some new aspects in dynamical systems: e.g., the higher-order-difference version for Lyapunov exponent [3] and bistability of higher-order differences, taken from periodic time series [6], have been established.…”