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"Saturation" or "clipping" function: clip(x)=min(max(x, -1), 1)

The context where I encountered this is LTI (linear time-invariant) system analysis (in classic control theory).

I tried to take its laplace transformation and mix it into the system's transfer function as usual, but soon figured out that I can't perform the inverse laplace transformation once it's mixed in.

Fortunately, an analytically accurate solution is not necessary. So I figured I need a simple yet effective function that does pretty much the same as clip(x), with a simpler Laplace Transformed form.

Or... Are there any simpler ways of doing it (other than doing an discrete-time simulation)?

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clip() is not a LTI filter (it's not linear). So I don't understand how you'd expect to use Laplace/Fourier here.

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  • $\begingroup$ That's the point -- is there a "good enough" approximation to it that CAN be laplace'd? $\endgroup$ – smilekzs Jun 16 '13 at 1:37
  • $\begingroup$ No. I think you are missing the point of Laplace/Fourier transform in this context. They are primary related to the temporal characterization of a filter. Eg, if you have a memoryless filter, it must be linear and its Laplace transform is trivial (a constant). That would be the only approximation. $\endgroup$ – leonbloy Jun 16 '13 at 14:02
  • $\begingroup$ Only in very special cases (for very restricted input signals), you could approximate the effect of memoryless alinear filter by a linear filter with memory: eg, saturation "produces/enhances" high frecuencies $\endgroup$ – leonbloy Jun 16 '13 at 14:05
  • $\begingroup$ Ah I see. So basically waveshapers are of a different kind from LTI filters. Thanks! $\endgroup$ – smilekzs Jun 17 '13 at 14:46

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