  Adaptive Local Iterative Filtering (ALIF) is a currently proposed novel
time-frequency analysis tool. It has been empirically shown that ALIF is able
to separate components and overcome the mode-mixing problem. However, so far
its convergence is still an open problem, particularly for highly nonstationary
signals, due to the fact that the kernel associated with ALIF is
non-translational invariant, non-convolutional and non-symmetric. Our first
contribution in this work is providing a convergence analysis of ALIF. From the
practical perspective, ALIF depends on a robust frequencies estimator, based on
which the decomposition can be achieved.
  Our second contribution is proposing a robust and adaptive decomposition
method for noisy and nonstationary signals, which we coined the
Synchrosqueezing Iterative Filtering Technique (SIFT). In SIFT, we apply the
synchrosqueezing transform to estimate the instantaneous frequency, and then
apply the ALIF to decompose a signal. We show numerically the ability of this
new approach in handling highly nonstationary signals.
