Representation of discrete sequences with three-dimensional iterated function systems

Abstract

Several recent papers have shown the ability of iterated function system (IFS) models to represent discrete sequences where the attractor of an IFS is self-affine either in R/sup 2/ or R/sup 3/ or is piece-wise self-affine in R/sup 2/. We extend the piece-wise self-affine IFS model from R/sup 2/ to R/sup 3/ and we call this model the piece-wise hidden-variable fractal model. This extension permits the representation of discrete sequences with a fractal model that is general and flexible. This new model is presented and a constrained inverse algorithm for identification of the model parameters is given. Examples of this model to seismic data and speech data are then presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>