  The Iterative Filtering method is a technique aimed at the decomposition of
non-stationary and non-linear signals into simple oscillatory components. This
method, proposed a decade ago as an alternative technique to the Empirical Mode
Decomposition, has been used extensively in many applied fields of research and
studied, from a mathematical point of view, in several papers published in the
last few years. However, even if its convergence and stability are now
established both in the continuous and discrete setting, it is still an open
problem to understand up to what extent this approach can separate two close-by
frequencies contained in a signal.
  In this paper, following the studies conducted on the Empirical Mode
Decomposition and the Synchrosqueezing methods, we analyze in detail the
abilities of the Iterative Filtering algorithm in extracting two stationary
frequencies from a given signal. In particular, after reviewing the Iterative
Filtering technique and its known properties, we present new theoretical
results and numerical evidence showing the ability of this technique in
addressing the fundamental "one or two frequencies" question.
