A system is called linear if it has two mathematical properties: homogeneity and additivity. If you can show that a system has both properties, then you have proven that the system is linear. Likewise, if you can show that a system doesn’t have one or both properties, you have proven that it isn’t linear.
All nonlinear systems, or more precisely, their underlying nonlinearities, produce partials that previously didn’t exist. Depending on the type of nonlinearity, these can be in harmonic relation to the signal, or not.
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