The Fourier transform and spectral analysis are employed to estimate the fractal dimension and explore the fractal parameter relations of urban growth and form using mathematical experiments and empirical analyses. Based on the models of urban density, two kinds of fractal dimensions of urban form can be evaluated with the scaling relations between the wave number and the spectral density. One ...

Analysis of the Fractal Dimension of the EEG appears to be a good approach for the computation of biomarkers for dementia. Several Fractal Dimension algorithms have been used in the EEG analysis of cognitive and sleep disorders. The aim of this paper is to find an accurate Fractal Dimension algorithm that can be applied to the EEG for computing reliable biomarkers, specifically, for the assessm...

In terms of the present short-term load forecasting(STLF) methods, whether the linear or the nonlinear, neither could meet the STLF requirements better with the rapid developments of electrical power systems and electrical power markets, and so a novel STLF method was proposed based on fractal theory in this paper. Firstly, the paper investigated the fractal characteristics of power system load...

Detection of deep and hidden mineralization using the surface geochemical data is a challenging subject in the mineral exploration. In this work, a novel scenario based on the spectrum–area fractal analysis (SAFA) and the principal component analysis (PCA) has been applied to distinguish and delineate the blind and deep Mo anomaly in the Dalli Cu–Au porphyry mineralization area. The Dalli miner...

Estimations of the local roughness of Digital Elevation Models (DEMs) have been used both for a better geological understanding of terrain structures and for a more accurate DEM interpolation leading to higher resolution terrain maps. This work investigates two fractal dimension estimators for the characterization of the roughness of DEMs: the power spectrum estimator and the wavelet-based esti...

BACKGROUND: This study presents an analysis of trabecular bone structure in standard radiographs using Fourier transforms and principal components analysis (PCA) to identify contributions to hip fracture risk. METHODS: Radiographs were obtained from 26 hip fracture patients and 24 controls. They were digitised and five regions of interest (ROI) were identified from the femoral head and neck for...

Non-linear parameters obtained from heart rate variability (HRV) analysis has recently been recognized to provide valuable information for physiological interpretation of heart rate fluctuation. Among the numerous non-linear parameters related to the fractal behaviour of the HRV signal, two classes have gained wide interest in the last years: the beta exponent based on the 1/f-like relationship...

Stochastic fractal signals can be characterized by the Hurst coefficient H, which is related to the exponents of various power-law statistics characteristic of these processes. Two techniques widely used to estimate H are spectral analysis and detrended fluctuation analysis (DFA). This paper examines the analytical link between these two measures and shows that they are related through an integ...