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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]
$

where normally $ \alpha\gg 1$. This function is graphed for $ \alpha=10$ in Fig.6.21. (Recall that $ \arctan(x)$ is defined as the angle whose tangent is $ x$. Only angles between $ -\pi /2$ and $ \pi /2$ are needed to cover all real values of $ x$.)
Figure 6.21: Arctangent nonlinearity.
\includegraphics[width=3in]{eps/atanex}

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