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Cubic Soft-Clipper Spectrum

The cubic soft-clipper, like any polynomial nonlinearity, is defined directly by its series expansion:

$\displaystyle f(x) = \left\{\begin{array}{ll}
-\frac{2}{3}, & x\leq -1 \\ [5pt]
x-\frac{x^3}{3}, & -1 \leq x \leq 1 \\ [5pt]
\frac{2}{3}, & x\geq 1 \\
\end{array} \right.
$ (7.19)

In the absence of hard-clipping ( $ \left\vert x\right\vert\leq1$ ), bandwidth expansion is limited to a factor of three. This is the slowest aliasing rate obtainable for an odd nonlinearity. Note that smoothing the ``corner'' in the clipping nonlinearity can reduce the severe bandwidth expansion associated with hard-clipping.


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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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