title: A comparative analysis of spectral exponent estimation techniques for 1/f(β) processes with applications to the analysis of stride interval time series.
abstract: BACKGROUND
  The time evolution and complex interactions of many nonlinear systems, such as in the human body, result in fractal types of parameter outcomes that exhibit self similarity over long time scales by a power law in the frequency spectrum S(f)=1/f(β). The scaling exponent β is thus often interpreted as a "biomarker" of relative health and decline.
  
  
  METHODS
  This paper presents a thorough comparative numerical analysis of fractal characterization techniques with specific consideration given to experimentally measured gait stride interval time series. The ideal fractal signals generated in the numerical analysis are constrained under varying lengths and biases indicative of a range of physiologically conceivable fractal signals. This analysis is to complement previous investigations of fractal characteristics in healthy and pathological gait stride interval time series, with which this study is compared.
  
  
  RESULTS
  The results of our analysis showed that the averaged wavelet coefficient method consistently yielded the most accurate results.
  
  
  METHODS
  Class dependent methods proved to be unsuitable for physiological time series. Detrended fluctuation analysis as most prevailing method in the literature exhibited large estimation variances.
  
  
  CONCLUSIONS
  The comparative numerical analysis and experimental applications provide a thorough basis for determining an appropriate and robust method for measuring and comparing a physiologically meaningful biomarker, the spectral index β. In consideration of the constraints of application, we note the significant drawbacks of detrended fluctuation analysis and conclude that the averaged wavelet coefficient method can provide reasonable consistency and accuracy for characterizing these fractal time series.
authors.affiliation: Department of Electrical and Computer Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA.
authors.forename: Alexander
authors.initials: A
authors.lastname: Schaefer
authors.affiliation: Department of Physical Therapy, University of Pittsburgh, Pittsburgh, PA 15260, USA.
authors.forename: Jennifer S
authors.initials: JS
authors.lastname: Brach
authors.affiliation: Department of Medicine, Division of Geriatrics, University of Pittsburgh, Pittsburgh, PA 15261, USA.
authors.forename: Subashan
authors.initials: S
authors.lastname: Perera
authors.affiliation: Department of Electrical and Computer Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA. Electronic address: esejdic@ieee.org.
authors.forename: Ervin
authors.initials: E
authors.lastname: Sejdić
mesh_terms: D000465:Algorithms; D001696:Biomechanical Phenomena; D003198:Computer Simulation; D016208:Databases, Factual; D017709:Fractals; D005684:Gait / Q000502:physiology*; D006801:Humans; D008124:Locomotion / Q000502:physiology; D008954:Models, Biological; D019636:Neurodegenerative Diseases / Q000503:physiopathology; D012044:Regression Analysis; D013995:Time
keywords: 1/f process; Detrended fluctuation analysis; Fractals; Gait; Self similarity; Stride intervals; Time series analysis; Wavelets