An Algorithmic Approach for Signal Measurement Using Symbolic Dynamics of Tent Map

Abstract

Abstract-The symbolic time series generated by a unimodal chaotic map starting from any initial condition creates a binary sequence that contains information about the initial condition. A binary sequence of a given length generated this way has a one-toone correspondence with a given range of the input signal. This can be used to construct analogue to digital converters (ADC). However, in actual circuit realizations, component imperfections and ambient noise result in deviations in the map function from the ideal, which, in turn, can cause significant error in signal measurement. In this paper, we propose ways of circumventing these problems through an algorithmic procedure that takes into account the non-idealities. The most common form of nonideality-reduction in the height of the map function-alters the partitions that correspond to each symbolic sequence. We show that it is possible to define the partitions correctly if the height of the map function is known. We also propose a method to estimate this height from the symbolic sequence obtained. We demonstrate the efficacy of the proposed algorithm with simulation as well as experiment. With this development, practical ADCs utilizing chaotic dynamics may become reality.

Digital System Performance Enhancement of a Tent Map-Based ADC for Monitoring Photovoltaic Systems

“…By achieving this, further signal processing could be performed on the FPGA, producing a low-cost DAQ system (the set-up is presented in Figure 3). Principal conclusions drawn from this research were: the algorithm was able to improve the effective resolution of the TM-based ADC; implementing the algorithm as a real-time, digital, compensation system was possible; the algorithm was as effective as the algorithm proposed by Basu et al [21]; the difference values that require calculating can be estimated using fewer hardware resources; and the sensitivity analysis highlighted the need for an investigation into high accuracy µ estimation, when employing the compensation algorithm for higher staged TM-based ADCs.…”

“…A more accurate initial condition estimation method was proposed by Basu et al [21] who calculated the effective difference between the voltage levels for ideal and non-ideal µ that each bit of the ADC output represented. However, this approach was more complex and challenging to implement as a digital system, as the algorithm involved calculating floating point numbers, using multiplication and division, for n iterations (n is the ADC resolution) and requires more computational overhead than the previous two examples [21].…”

“…The aim of this paper is to evaluate a novel algorithm of estimating the initial conditions of a TM-based ADC when the mean µ is known. Similar to the algorithm proposed by Basu et al [21], this algorithm determines the difference between the voltage levels that each bit represents for the actual and ideal µ. However, the proposed algorithm requires less computational overhead enabling a simpler digital system implementation.…”

Parameter estimation for 1D PWL chaotic maps using noisy dynamics

“…Among the 1D PWL maps, the tent map (both symmetric and skew), the zigzag map and Bernoulli shift map are the are the common examples, as these maps are widely used in various areas of application. First, we consider symmetric tent map T (x n ) [3] to observe the behaviour of noise-affected chaotic dynamics and investigate the properties of the noisy iterates reflecting upon the maps fixed points and the parameter. Later we adapt the estimation technique for the other 1D PWL maps.…”

“…In particular, certain maps belonging to this class are extensively studied and applied for their uniformly dense chaotic behaviour over a wide range of parametric values, referred to as 'robust chaos' [1]. Such maps have therefore received considerable attention for use in applications involving physical implementations [2][3][4][5][6].…”