Modelling of fractal coding schemes

Fractal techniques applied in the area of signal coding suffer from the lack of an analytical description, especially if the question of convergence at the decoder is addressed. For this purpose an expensive eigenvalue calculation of the transformation matrix during the encoding process is necessary which is in general computational infeasible. In this paper the conditional equation for the eigenvalues is determined for a rather general coding scheme. This allows formulation of the probability density function of the largest eigenvalue which in turn determines whether or not the reconstruction converges. These results are not only important for evaluation of the convergence properties of various coding schemes but are also valuable for optimizing their appropriate encoding parameters.