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]...
...{3}, & -1 \leq x \leq 1 \\ [5pt]
\frac{2}{3}, & x\geq 1 \\
\end{array}\right.
$](http://www.dsprelated.com/josimages_new/pasp/img1520.png)
In the absence of hard-clipping (
), 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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Stability of Nonlinear Feedback Loops
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Arctangent Spectrum
