Separating a mixture of chaotic signals

TL;DR

This paper introduces a method to separate mixed signals, including chaotic and arbitrary signals, by exploiting properties of logistic family maps that preserve symbolic sequences, enabling effective signal separation.

Contribution

It presents a novel approach to separating mixed signals using properties of logistic family maps that maintain symbolic sequences, allowing for the separation of chaotic and arbitrary signals.

Findings

Successful separation of mixed chaotic and arbitrary signals

Applicability to signals generated by various maps within the logistic family

Potential for use in secure communications and signal processing

Abstract

Chaos is popularly associated with its property of sensitivity to initial conditions. In this paper we will show that there can be a flip side to this property which is quite fascinating and highly useful in many applications. As a result, we can mix a large number of chaotic signals and one completely arbitrary signal and later a recipient of this transformed and weighted mixture can separate each of the signals, one by one. The chaotic signals, could be generated by various maps which belong to the logistic family. The arbitrary signal, could be a message, some random noise, some periodic signal or a chaotic signal generated by a source, either belonging or not belonging to the family. The key behind this procedure is a family of maps which can dovetail into each other without altering each of their predecessor's symbolic sequence.