  Detrend fluctuation analysis (DFA) has become a choice method for effective
analysis of a broad variety of nonstationary signals. We show in the present
article that, provided the nonstationary fluctuations occur at a large enough
time scale, an alternative approach can be obtained by using the Fourier series
of the signal. More specifically, signal reconstructions considering Fourier
series with increasing number of higher spectral components are subtracted from
the signal, while the dispersion of such a difference is calculated. The slope
of the loglog representation of the dispersions in terms of the time scale
(reciprocal of the frequency) is calculated and used for the characterization
of the signal. The detrend action in this methodology is performed by the early
incorporation of the low frequency spectral components in the signal
representation. The application of the spectral DFA to the analysis of heart
rate variability data has yielded results which are similar to those obtained
by traditional DFA. Because of the direct relationship with the spectral
content of the analyzed signal, the spectral DFA may be used as a complementary
resource for characterization and analysis of some types of nonstationary
signals.
