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Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic
1Digital Signal Processing Research Group, University College Dublin, Belfield, Dublin 4, Ireland.
Summary
Detrended fluctuation analysis (DFA) and spectral analysis are shown to be equivalent methods for characterizing stochastic fractal signals using the Hurst coefficient (H). This finding holds for both synthesized and physiological data, confirming their long-term correlation properties.
Area of Science:
- Complex Systems Analysis
- Signal Processing
- Physiological Data Analysis
Background:
- Stochastic fractal signals exhibit long-term correlations, often quantified by the Hurst coefficient (H).
- Estimating H is crucial for understanding processes across various scientific domains.
- Spectral analysis and Detrended Fluctuation Analysis (DFA) are prominent methods for H estimation.
Purpose of the Study:
- To establish the analytical relationship between spectral analysis and DFA for Hurst coefficient estimation.
- To compare the performance of spectral analysis and DFA as H estimators.
- To validate the derived relationship using both synthesized and real-world physiological data.
Main Methods:
- Derivation of an integral transform linking spectral density and DFA measures.
- Numerical simulations using synthesized fractal signals.
- Application of the derived relationship to physiological heartbeat R-R interval data.
Main Results:
- An analytical integral transform was identified connecting spectral analysis and DFA.
- Both methods demonstrated similar performance in estimating H for synthesized signals based on mean square error.
- DFA measures derived via the spectral density integral transform closely matched direct DFA estimates for R-R interval data.
Conclusions:
- Spectral analysis and DFA provide equivalent characterizations of stochastic signals with long-term correlations.
- The established analytical link is robust, applying to both ideal and non-ideal fractal properties.
- This equivalence simplifies the analysis and interpretation of fractal dynamics in complex systems.