Time-frequency fading

Abstract: We are interested in the problem of attenuating time-frequency regions,
for example when a disturbance signal is well localized in the
time-frequency plane. We approach this problem from the point of view of
time-frequency filtering, by formulating the optimization problem in the
signal domain in order to avoid the difficulties related to the phase,
and by proposing algorithmically efficient solutions.

The formulation of the problem allows to precisely control the level of
attenuation, by adjusting a trade-off between the energy in the areas to
be attenuated and the approximation error outside these areas. The
problem admits an analytical solution that involves the notion of Gabor
multipliers. The dominant eigenvectors of these operators have
remarkable time-frequency localization properties and the decay of their
eigenvalues allows the use of reduced-rank approximations. We propose
algorithms whose efficiency is based on these approximations, as well as
on randomized decomposition algorithms and on non-overlapping properties
of the time-frequency regions to be attenuated.