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.