Modeling non-linearities with LaPlace Tranfer functions

Unfortunately there's no simple answer to this question. As soon as a system goes outside the linear region, all bets are off. There are heaps of examples of apparently 'simple' nonlinear systems exhibiting massively complex behaviour that can't be predicted with any formal method. If you want an example, google on Mandelbrot set or Henon maps.

Depending on what you want to do, a couple of techniques that *might* prove useful are piecewise linearisation, which is deriving a linear relationship about a chosen operating point for small deviations, and describing functions which extend frequency domain analysis into the nonlinear regime - slightly.

A practical approach for dealing with nonlinear systems is rigorous system modelling in the time domain, this requires experience, time and patience to get results.

The base of the fourier/laplace transform is linearity. So if youf system is not linear, then you have to look very precise what actually you're doing. A thorough understanding of the involved theory is necessary.

Start with the Schwartz space, where the transform lives in. IMO, the ground to use the laplace transform becomes soft, wobbly and slowly unuseable.

Rene

On approach is to approximate the nonlinear response by the sum of functions (non necessarily linear) for which the LaPlace transform exists.

This is excactly what does not work. A property of the Laplace transform L() :

L(a*A+b*B+c*C)=aL(A)+bL(B)+cL(C) //a,b,c : Constant

Now since the input of the Transform is not linear: { Be f the nonlinear function } f(a*A+b*B) != af(A)+bf(B) //a,b,c : Constant

Then the property above is not true either. Sorry.

Rene

That looks like a differential amplifier. You can develop the 1+tanh function like this:

I understand that this solution does include the nonlinearities in some way but I don't see how this will include the Gain as a function of frequency ?

Thanks for your feedback.

Timo, this is adding harmonics depending on the signal level. So you take your signal to be processed and apply the filter functtion and after each filter step calculate the level and then add those harmonics depending on the envelope and do the next filter stage with the addaed harmonics. those