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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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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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