The use of stationarity and nonstationarity in the detection and analysis of neural oscillations

Using available signal (i.e., spectral and time-frequency) analysis methods, it can be difficult to detect neural oscillations because of their continuously changing properties (i.e., nonstationarities) and the noise in which they are embedded. Here, we introduce fractally scaled envelope modulation (FSEM) estimation which is sensitive specifically to the changing properties of oscillatory activity. FSEM utilizes the fractal characteristic of wavelet transforms to produce a compact, two-dimensional representation of time series data where signal components at each frequency are made directly comparable according to the spectral distribution of their envelope modulations. This allows the straightforward identification of neural oscillations and other signal components with an envelope structure different from noise. For stable oscillations, we demonstrate how partition-referenced spectral estimation (PRSE) removes the noise slope from spectral estimates, yielding a level estimate where only peaks signifying the presence of oscillatory activity remain. The functionality of these methods is demonstrated with simulations and by analyzing MEG data from human auditory brain areas. FSEM uncovered oscillations in the 9- to 12-Hz and 15- to 18-Hz ranges whereas traditional spectral estimates were able to detect oscillations only in the former range. FSEM further showed that the oscillations exhibited envelope modulations spanning 3-7 s. Thus, FSEM effectively reveals oscillations undetectable with spectral estimates and allows the use of EEG and MEG for studying cognitive processes when the common approach of stimulus time-locked averaging of the measured signal is unfeasible.