From periodic/aperiodic to static/dynamic: rethinking the decomposition of neural power spectra

The power spectrum of electrophysiological signals exhibits both narrowband peaks and a broadband 1/f-like slope. The two are routinely treated as separable components: a "periodic" foreground and an "aperiodic" background; and each has been related to behaviour, cognition, and clinical status. This paper argues, and illustrates with simulations and case studies, that the boundary between the two is less sharp than the standard decomposition assumes: non-stationary amplitude modulation of an oscillation can inflate the apparent spectral trend (whereas clean periodic modulation does not, its sidebands being absorbed into the peak), and a broadband process viewed through any narrow band produces an envelope that mimics amplitude modulation. The two phenomena are mirror images of the same underlying property, that the temporal envelope and the spectral slope are coupled. I show what this means in practice with a set of illustrative scenarios and three case studies (a simulated alpha lateralisation paradigm, an auditory oddball ERP, and simultaneous scalp EEG and ECoG under rest and propofol sedation). I argue that the question "is the observed change a change in the aperiodic component" cannot in general be answered from time-series analysis alone, and that the temporal envelope of detected oscillations carries information that the static power spectrum loses. I ultimately argue that the conventional periodic/aperiodic partition of neural power spectra conflates a more fundamental distinction: between processes whose amplitude is stationary over the analysis window and processes whose amplitude changes. Transferring the dichotomy from the spectral domain to the time domain, from periodic/aperiodic to static/dynamic, reveals structure that the power spectrum alone cannot recover.