What is wrong in Katz's method? Comments on: "A note on fractal dimensions of biomedical waveforms"

On the November issue of this journal, Raghavendra and Dutt showed that the method proposed by Katz for computing the fractal dimension of waveforms, invariably underestimates the true dimension. This was not completely unexpected because also Esteller et al. reported that it largely underestimates the fractal dimension of data generated by Weierstrass cosine functions. However, what appears strikingly surprising in the work of Raghavendra and Dutt is that the Katz's method practically provides the same estimate, an almost constant value close to 1, even when applied to fractional Brownian motions with true dimension between 1.0 and 1.5. Unlike the Weierstrass cosine functions, fractional Brownian motions are realistic models of several physiological processes. Thus, the results of Raghavendra and Dutt imply that the Katz's method is unable to properly describe the fractal properties of most real biomedical signals. The Katz's method is popular in biological sciences. At the end of 2009 it has been cited by at least 152 papers, according to Google Scholar. The analysis of Raghavendra and Dutt naturally raises a question for the many readers of this journal interested in evaluating the fractal structure of biomedical signals: what is wrong in the Katz's method? This letter answers the question, explaining the poor performances reported previously, and proposes a correction to a fundamental flaw.