Q:

Why is an electronic circuit system should be linear to use Fourier and Laplace transforms?

What I understood is, if we need to analyze a data from a system(such as damped oscillation or an output of an electronic circuit), the system must act in linear fashion to employ Fourier and Laplace transform. Why is it like that? I thought any signal could be decomposed as sinusoid. I mean if one make data acquisition of a system why that data has to be obtained from a linear system to employ Fourier and Laplace transforms?

A:

Because a nonlinear system doesn't benefit from the superposition property, that is essential to use the transforms. Another property that is not valid for nonlinear system is the homogeneity.
The only solution is find the equilibrium point, because for little excursions from this point you have a linear system, and you can approximate the behavior of the system by this way.

