A fast box counting algorithm for determining the fractal dimension of sampled continuous functions

Abstract

An adaptation of the box counting algorithm to samples of a continuous signal is given. An iterative scheme is combined with an exploitation of continuity to yield a fast method. This reduces the algorithm's complexity from quadratic to linear. The method is applied to speech segments; in this context it is faster than morphological filtering and Hurst analysis, and has comparable performance. The new algorithm is also suitable to be parallelized. It is applied to calculation of the dimension of fricative phonemes and automatic segmentation of speech into periodic/noiselike segments. This dimension value may be used instead of zero crossing rate in some applications.<>