Precision and Accuracy of Length and Variance Fractal Dimensions Computed from Fractional Self-Affine Signals

Abstract

- Many digital signal processing algorithms are based on mono-scale analysis. Since the reshuffling of any data value does not change the probability distribution, the sense of correlation or covariance in the data is lost, especially when dealing with self-affine time series. An alternative approach is to use poly-scale analysis. This paper describes two poly-scale algorithms: the length fractal dimension and variance fractal dimension and evaluates their accuracy and precision. First, we generate white Gaussian noise and fractal Brownian motion using the concepts of fractional Brownian motion and the discrete Fourier transform. Next, we evaluate the performance of these measures. Since many processes are nonstationary, we also present a stationarity-frame detection technique based on the One-Way ANOVA and Bartlett tests. Our results show that these poly-scale techniques can always be used as reliable tools for different purposes in self-affine data analysis. sure that the generator transient does not affect our data. Next, we investigate two methods to synthesize two classes of fractional noise with known fractal properties. We further describe two statistical tests, the One-Way ANOVA and Bartlett tests, to determine the appropriate stationarity frame of the synthesized time series. We evaluate the