Supplement II: Signal processing tools

Abstract

Brain waves are commonly treated as if they were the sum of the outputs of a set of neural oscillators, each of which has a constant frequency and variable amplitude. This treatment is based on the assumption that brain dynamics is linear and time-invariant, which is clearly not the case. The advantage conveyed by this assumption is the ease with which linear analysis can be applied to brain waves using, e.g., Fast Fourier Transform (FFT). The disadvantage is the inability of the linear analysis to capture and display the transient dynamics, including nonlinear state transitions by which brains operate.