On the use of general iterated function systems in signal modelling

The use of iterated function system (IFS) and recurrent iterated function system (RIFS) representations of Markov and hidden Markov processes and dynamical systems as time series models is investigated. Originally devised for use in deterministic fractal image compression schemes, they are introduced as a time-varying, generally nonlinear stochastic data models which entail a new set of inverse problems. It is shown how IFSs, in their most general formulation, offer a framework which, in addition to describing a number of existing Markov models, suggests a range of diverse new ones. Emphasis is placed on a novel model whose RIFS version can be seen as a generalization of hidden Markov models having a greater predictive ability. Parameterization is discussed from both the synthesis and analytical viewpoints. An algorithm for the parameter estimation of the RIFS model is proposed. Comments are made on the relation between RIFS and deterministic chaotic nonlinear systems