DSPRelated.com
Free Books

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.
$ (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.


Next Section:
Stability of Nonlinear Feedback Loops
Previous Section:
Arctangent Spectrum