  Real life signals are in general non--stationary and non--linear. The
development of methods able to extract their hidden features in a fast and
reliable way is of high importance in many research fields. In this work we
tackle the problem of further analyzing the convergence of the Iterative
Filtering method both in a continuous and a discrete setting in order to
provide a comprehensive analysis of its behavior. Based on these results we
provide new ideas for efficient implementations of Iterative Filtering
algorithm which are based on Fast Fourier Transform (FFT), and the reduction of
the original iterative algorithm to a direct method.
