Finite Precision

This paper proposes a new Least Mean Square (LMS) based algorithm aimed for acoustic echo cancellation. The algorithm is an elaboration of an existing algorithm developed for the Konftel 200 conference phone. The purpose of the algorithm is to reduce the effects of quantization with only a small increase in computational load as compared to the LMS algorithm. The algorithm makes use of the specific transfer characteristic of certain systems, e.g. hands-free phones, in combination with finite wordlength precision arithmetic. It is shown, both analytically and with simulations that the new algorithm outperforms the LMS algorithm when implemented in a two's-complement arithmetic system identification scheme.

This paper presents an analysis of the effects of noise and precision on a simplified model of the clarinet driven by a variable control parameter. When the control parameter is varied the clarinet model undergoes a dynamic bifurcation. A consequence of this is the phenomenon of bifurcation delay: the bifurcation point is shifted from the static oscillation threshold to an higher value called dynamic oscillation threshold. In a previous work [8], the dynamic oscillation threshold is obtained analytically. In the present article, the sensitivity of the dynamic threshold on precision is analyzed as a stochastic variable introduced in the model. A new theoretical expression is given for the dynamic thresholds in presence of the stochastic variable, providing a fair prediction of the thresholds found in finite-precision simulations. These dynamic thresholds are found to depend on the increase rate and are independent on the initial value of the parameter, both in simulations and in theory.

In this paper we investigate the degradation of the statistic properties of chaotic maps as consequence of their implementation in a digital media such as Digital Signal Processors (DSP), Field Programmable Gate Arrays (FPGA) or Application-Specific Integrated Circuits (ASIC). In these systems, binary floating-and fixed-point are the numerical representations available. Fixed-point representation is preferred over floating-point when speed, low power and/or small circuit area are necessary. Then, in this paper we compare the degradation of fixed-point binary precision version of chaotic maps with the one obtained by using floating point 754-IEEE standard, to evaluate the feasibility of their FPGA implementation. The specific period that every fixed-point precision produces was investigated in previous reports. Statistical characteristics are also relevant, it has been recently shown that it is convenient to describe the statistical characteristic using both, causal and non-causal quantifiers. In this paper we complement the period analysis by characterizing the behavior of these maps from an statistical point of view using cuantifiers from information theory. Here, rather than reproducing an exact replica of the real system, the aim is to meet certain conditions related to the statistics of systems.

In this paper we investigate the degradation of the statistic properties of chaotic maps as consequence of their implementation in a digital media such as Digital Signal Processors (DSP), Field Programmable Gate Arrays (FPGA) or Application-Specific Integrated Circuits (ASIC). In these systems, binary floating-and fixed-point are the numerical representations available. Fixed-point representation is preferred over floating-point when speed, low power and/or small circuit area are necessary. Then, in this paper we compare the degradation of fixed-point binary precision version of chaotic maps with the one obtained by using floating point 754-IEEE standard, to evaluate the feasibility of their FPGA implementation. The specific period that every fixed-point precision produces was investigated in previous reports. Statistical characteristics are also relevant, it has been recently shown that it is convenient to describe the statistical characteristic using both, causal and non-causal quantifiers. In this paper we complement the period analysis by characterizing the behavior of these maps from an statistical point of view using cuantifiers from information theory. Here, rather than reproducing an exact replica of the real system, the aim is to meet certain conditions related to the statistics of systems.

In this work we comment some conclusions derived from the analysis of recent proposals in the field of chaos-based cryptography. These observations remark a number of major problems detected in some of those schemes under examination. Therefore, this paper is a list of what to avoid and to pay special attention to when considering chaos as source of new strategies to conceal and protect information.

This paper deals with a family of interesting 2 D-quadratic maps proposed by Sprott, in his seminal paper [1], related to "chaotic art". Our main interest about these maps is their great potential for using them in digital electronic applications because they present multiple chaotic attractors depending on the selected point in the parameter's space. Only results for the analytical representation of these maps have been published in the open literature. Consequently, the objective of this paper is to extend the analysis to the digital version, to make possible the hardware implementation in a digital medium, like field programmable gate arrays (FPGA) in fixed-point arithmetic. Our main contributions are: (a) the study of the domains of attraction in fixed-point arithmetic, in terms of period lengths and statistical properties; (b) the determination of the threshold of the bus width that preserves the integrity of the domain of attraction and (c) the comparison between two quantifiers based on respective probability distribution functions (PDFs) and the well known maximum Lyapunov exponent (MLE) to detect the above mentioned threshold.