Analog to Digital Conversion in Physical Measurements

There exist measuring devices where an analog input is converted into a digital output. Such converters can have a nonlinear internal dynamics. We show how measurements with such converting devices can be understood using concepts from symbolic dynamics. Our approach is based on a nonlinear one-to-one mapping between the analog input and the digital output of the device. We analyze the Bernoulli shift and the tent map which are realized in specific analog/digital converters. Furthermore, we discuss the sources of errors that are inevitable in physical realizations of such systems and suggest methods for error reduction.Comment: 9 pages in LATEX, 4 figures in ps.; submitted to 'Chaos, Solitons & Fractals

Ultra-high-frequency piecewise-linear chaos using delayed feedback loops

We report on an ultra-high-frequency (> 1 GHz), piecewise-linear chaotic system designed from low-cost, commercially available electronic components. The system is composed of two electronic time-delayed feedback loops: A primary analog loop with a variable gain that produces multi-mode oscillations centered around 2 GHz and a secondary loop that switches the variable gain between two different values by means of a digital-like signal. We demonstrate experimentally and numerically that such an approach allows for the simultaneous generation of analog and digital chaos, where the digital chaos can be used to partition the system's attractor, forming the foundation for a symbolic dynamics with potential applications in noise-resilient communications and radar

Estimation of Input Variable as Initial Condition of a Chaos Based Analogue to Digital Converter

A realization of an analogue-to-digital converter(ADC) with improved conversion accuracy,using the chaotic behaviour of the tent map,is presented. In this approach, the analogue input signal to be measured, termed as the initial condition is applied to a chaotic map, and the symbolic dynamics resulting from the map evolution, is used to determine the initial condition in digital form. The unimodal piecewise linear tent map (TM) has been used for this purpose, because of its property of generating uniform distribution of points and robust chaos. Through electronic implementation of the TMit is practically impossible to produce an ‘ideal’ TM behaviour with parameter values in the full range [0,1]. Due to component imprecision and various other factors, a non-ideal map with reduced height is observed. For such a map, converting the equivalent symbolic trajectory generated by TM iterations return erroneous results as the partitioning of the phase space embodied in the finite symbolic dynamics no longer has unique correspondence with the initial condition. Two algorithmic solutions have been proposed to minimise the errors associated with a practical system. For one, it has been established that for a reduced-height map the partitioning will not remain of equal size. Considering that the height of the tent map used for this purpose is known from an independent but related research, a technique of partitioning the state space unevenly, depending on the map height has been proposed and has been shown that if the correct partitioning is used, the resulting symbolic dynamics again map uniquely to the initial condition. Alternatively, it has been shown that the degree of deviation of the iterate values can be determined based on the parameter value, which in turn can be adjusted for depending on the symbolic sequence generated by the initial condition to determine the correct decimal equivalent values. The both the approaches proved to be highly effective in obtaining a digital outcome corresponding to the initial condition using 8 symbolic iterations of the map in hardware domain, with the second approach outperforming the first in terms of accuracy, while the first method can easily be pipelined alongside generating the iterates and thus improve the speed. This development is promising because, in contrast to the commercially available ADCs, it places lower demand on the hardware resource and can be effectively implemented to give a real-time operation

Open problems in artificial life

This article lists fourteen open problems in artificial life, each of which is a grand challenge requiring a major advance on a fundamental issue for its solution. Each problem is briefly explained, and, where deemed helpful, some promising paths to its solution are indicated

Periodic input response of a second-order digital filter with two’s complement arithmetic

The dynamic behaviors of a nonlinear second-order digital filter with two’s complement arithmetic under periodic inputs are explored. The conditions for avoiding overflow are derived. Various dynamic periodic responses are analyzed, accompanied by numerous simulation examples

Symbolic analysis for some planar piecewise linear maps

In this paper a class of linear maps on the 2-torus and some planar piecewise isometries are discussed. For these discontinuous maps, by introducing codings underlying the map operations, symbolic descriptions of the dynamics and admissibility conditions for itineraries are given, and explicit expressions in terms of the codings for periodic points are presented.Comment: 4 Figure

Gossip consensus algorithms via quantized communication

This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise ''gossip'' communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature: whether the agents should encode their communication by a deterministic or a randomized quantizer, and whether they should use, and how, exact information regarding their own states in the update.Comment: Accepted for publicatio