McDonald, Andre MVan Wyk, M2019-03-272019-03-272017-08McDonald, A.M. and Van Wyk, M. 2017. Solution of the inverse Frobenius-Perron problem for semi-Markov chaotic maps via recursive Markov state disaggregation. Proceedings of the 25th European Signal Processing Conference (EUSIPCO), Kos Island, Greece, 28 August - 2 September 2017http://www.eurasip.org/Proceedings/Eusipco/Eusipco2017/papers/1570347846.pdfhttp://hdl.handle.net/10204/10864The attached pdf contains the pre-print version of the paper presented at the 25th European Signal Processing Conference (EUSIPCO), Kos Island, Greece, 28 August - 2 September 2017A novel solution of the inverse Frobenius–Perron problem for constructing semi–Markov chaotic maps with prescribed statistical properties is presented. The proposed solution uses recursive Markov state disaggregation to construct an ergodic map with a piecewise constant invariant density function that approximates an arbitrary probability distribution over a compact interval. The solution is novel in the sense that it provides greater freedom, as compared to existing analytic solutions, in specifying the autocorrelation function of the semi–Markov map during its construction. The proposed solution is demonstrated by constructing multiple chaotic maps with invariant densities that provide an increasingly accurate approximation of the asymmetric beta probability distribution over the unit interval. It is demonstrated that normalised autocorrelation functions with components having different rates of decay and which alternate in sign between consecutive delays may be specified. It is concluded that the flexibility of the proposed solution facilitates its application towards modelling of random signals in various contexts.enErgodic systemsFrobenius-PerronChaosRandom signalConference PresentationMcDonald, A. M., & Van Wyk, M. (2017). Solution of the inverse Frobenius-Perron problem for semi-Markov chaotic maps via recursive Markov state disaggregation. http://hdl.handle.net/10204/10864McDonald, Andre M, and M Van Wyk. "Solution of the inverse Frobenius-Perron problem for semi-Markov chaotic maps via recursive Markov state disaggregation." (2017): http://hdl.handle.net/10204/10864McDonald AM, Van Wyk M, Solution of the inverse Frobenius-Perron problem for semi-Markov chaotic maps via recursive Markov state disaggregation; 2017. http://hdl.handle.net/10204/10864 .TY - Conference Presentation AU - McDonald, Andre M AU - Van Wyk, M AB - A novel solution of the inverse Frobenius–Perron problem for constructing semi–Markov chaotic maps with prescribed statistical properties is presented. The proposed solution uses recursive Markov state disaggregation to construct an ergodic map with a piecewise constant invariant density function that approximates an arbitrary probability distribution over a compact interval. The solution is novel in the sense that it provides greater freedom, as compared to existing analytic solutions, in specifying the autocorrelation function of the semi–Markov map during its construction. The proposed solution is demonstrated by constructing multiple chaotic maps with invariant densities that provide an increasingly accurate approximation of the asymmetric beta probability distribution over the unit interval. It is demonstrated that normalised autocorrelation functions with components having different rates of decay and which alternate in sign between consecutive delays may be specified. It is concluded that the flexibility of the proposed solution facilitates its application towards modelling of random signals in various contexts. DA - 2017-08 DB - ResearchSpace DP - CSIR KW - Ergodic systems KW - Frobenius-Perron KW - Chaos KW - Random signal LK - https://researchspace.csir.co.za PY - 2017 T1 - Solution of the inverse Frobenius-Perron problem for semi-Markov chaotic maps via recursive Markov state disaggregation TI - Solution of the inverse Frobenius-Perron problem for semi-Markov chaotic maps via recursive Markov state disaggregation UR - http://hdl.handle.net/10204/10864 ER -