A direct analytical demonstration of the essential equivalence of detrended fluctuation analysis and spectral analysis of RR interval variability

Detrended fluctuation analysis (DFA) of heart rate variability appears to yield improved prognostic power in cardiovascular disease, through calculation of the fractal scaling exponent alpha. We have recently used Taylor series approximations to propose that DFA is closely related to standard spectral analysis measures. We now present a direct analytical approach using integration and explicit expressions for the steps involved in DFA. This demonstrates clearly how DFA corresponds to standard spectral analysis.