  Neuronal activity in the brain generates synchronous oscillations of the
Local Field Potential (LFP). The traditional analyses of the LFPs are based on
decomposing the signal into simpler components, such as sinusoidal harmonics.
However, a common drawback of such methods is that the decomposition primitives
are usually presumed from the onset, which may bias our understanding of the
signal's structure. Here, we introduce an alternative approach that allows an
impartial, high resolution, hands-off decomposition of the brain waves into a
small number of discrete, frequency-modulated oscillatory processes, which we
call oscillons. In particular, we demonstrate that mouse hippocampal LFP
contain a single oscillon that occupies the $\theta$-frequency band and a
couple of $\gamma$-oscillons that correspond, respectively, to slow and fast
$\gamma$-waves. Since the oscillons were identified empirically, they may
represent the actual, physical structure of synchronous oscillations in
neuronal ensembles, whereas Fourier-defined "brain waves" are nothing but
poorly resolved oscillons.
