  Oscillating-gradient spin-echo diffusion-weighted magnetic resonance imaging
(OGSE-DWI) has been promoted as a promising technique for studying the
microstructure of complex hydrated matter in the frequency domain. The target
of the OGSE-DWI technique is the spectral density of molecular diffusion,
$u_{2}(\omega)$, which is predicted to obey a set of asymptotic universality
relations that are linked to the global organisation of the sample. So, in
principle the complex microstructure of a medium can be classified by measuring
the spectral density in its low- and high-frequency limits. However, due to
practical limitations on the spectral resolution and range of the technique, it
is not possible to directly sample the spectral density with OGSE-DWI. Rather,
information about the spectral density can be obtained only indirectly through
the quantities $U_{kk}$ & $U_{k0}$, which are filtered representations of
$u_{2}(\omega)$. The purpose of this study is to investigate how the universal
behaviour of $u_{2}(\omega)$ emerges in the asymptotic behaviour of OGSE-DWI
signal.
