Rényi divergence as an improved generalised fractal dimension for signal and fractal analysis.

The Generalised Fractal Dimension (GFD) is widely used to analyse the scaling properties of multi-fractal signals. However, its reliance on a uniform distribution baseline limits its sensitivity to subtle structural variations. This study introduces Renyi divergence as an enhanced alternative, providing greater sensitivity by quantifying deviations from uniformity. A mathematical relationship between GFD and Renyi divergence is established, demonstrating how the latter offers a more detailed characterisation of multi-fractal structures. To improve computational efficiency, the Renyi divergence spectrum is approximated using a generalised logistic function, ensuring analytical tractability without compromising accuracy. The method's effectiveness is illustrated through an example showing that Renyi divergence can distinguish signals that appear nearly identical under GFD analysis. These findings position Renyi divergence as a valuable extension of GFD, with potential applications in anomaly detection, signal classification, and multi-fractal analysis. [ABSTRACT FROM AUTHOR]