Introduction to Multifractal Detrended Fluctuation Analysis in Matlab
By Espen Alexander Fürst Ihlen. Front. Physio., 2012
875 citations recorded by the source corpus.
Fractal structures are found in biomedical time series from a wide range of physiological phenomena. The multifractal spectrum identifies the deviations in fractal structure within time periods with large and small fluctuations. The present tutorial is an introduction to multifractal detrended fluctuation analysis (MFDFA) that estimates the multifractal spectrum of biomedical time series. The tutorial presents MFDFA step-by-step in an interactive Matlab session. All Matlab tools needed are available in Introduction to MFDFA folder at the website www.ntnu.edu/inm/geri/software. MFDFA are introduced in Matlab code boxes where the reader can employ pieces of, or the entire MFDFA to example time series. After introducing MFDFA, the tutorial discusses the best practice of MFDFA in biomedical signal processing. The main aim of the tutorial is to give the reader a simple self-sustained guide to the implementation of MFDFA and interpretation of the resulting multifractal spectra.
Subfields: Economics and Econometrics, Molecular Biology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c0e67131d479feff9010557c79268282254db4e4
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Citations in the corpus
- Multifractality in combustion noise: predicting an impending combustion instability (2014, neutral): “(A 3) For q= 0, the structure function is defined as Ihlen (2012): F0w = exp ( 1 2nw nw∑ i=1 log ( 1 w w∑ t=1 (yi(t)− ȳi)2 )) .”
- Multifractal Detrended Fluctuation Analysis of Streamflow in the Yellow River Basin, China (2015, background): “Ihlen [36] concluded that the time series had a long left tail when it was insensitive to local fluctuations with small magnitudes, and would have a long right tail when it was insensitive to the larger magnitudes of local fluctuations.”
- p-exponent and p-leaders, Part II: Multifractal Analysis. Relations to Detrended Fluctuation Analysis (2015, neutral): “[23,63,64], always perform an integration of the data, X(t) → ∫ t X(s)ds, as a preliminary step (hence implicitly assuming that for the integrated data, h > 0).”