Why is not Fourier Transform Good for Non-linear Processes I was reading through slides about Hilbert Huang Transform. In slide 14, which talks about the motivations of a new method instead of Fourier Transform (FT), the author provides those two reasons in addition to other reasons


Physical processes are mostly nonstationary.
Physical processes are mostly nonlinear. 


I understand the first reason, where the FT cannot locate the frequencies in time. However, I do not understand why the FT does not work for the nonlinear processes. Based on my understanding, the FT is a method to decompose the signal into different and simple components. Why does condition of non-linearity play a role here? 

My first thought for reasoning that assumption, was that we cannot represent a non-linearity in the signal by a linear combinations of sinusoids. However, I think sinusoids themselves will handle the non-linearity.
Because complex exponentials $e^{\jmath \omega t}$, which are results of Fourier transform, are the eigenfunctions for linear, time invariant (LTI) systems. See eigenfunction of LTI. Also see this answer on SP.SE.

Thus, Fourier transform is useful for analyzing linear (not suitable for non-linear one) time invariant (can be intepreted as stationnary) system.