On the efficient prediction of fractal signals

A novel prediction scheme for self-affine fractal signals is presented. The signal is modeled by self-affine linear mappings, whose contraction factors are assumed to follow an auto-regressive (AR) process. In this way, the highly nonlinear time evolution of the fractal signal is captured by the linear AR process of the contraction factors, thereby exploiting the simplicity and ease of computation inherent in the AR model. An adaptive version of the proposed scheme is applied in simulations using the Weierstrass-Mandelbrot cosine fractal, as well as, in practice, using real radar sea clutter data