Arctangent Nonlinearity
A simple example of an invertible (one-to-one) memoryless nonlinearity is the arctangent mapping:
![$\displaystyle f(x) = \frac{2}{\pi}\arctan(\alpha x), \quad x\in[-1,1]
$](http://www.dsprelated.com/josimages_new/pasp/img1515.png)







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Clipping Nonlinearity
A simple example of an invertible (one-to-one) memoryless nonlinearity is the arctangent mapping: