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Clipping Nonlinearity

A simple example of a noninvertible (many-to-one) memoryless nonlinearity is the clipping nonlinearity, well known to anyone who records or synthesizes audio signals. In normalized form, the clipping nonlinearity is defined by

$\displaystyle f(x) = \left\{\begin{array}{ll} -1, & x\leq -1 \\ [5pt] x, & -1 \leq x \leq 1 \\ [5pt] 1, & x\geq 1 \\ \end{array} \right. \protect$ (7.17)

Since the clipping nonlinearity abruptly transitions from linear to hard-clipped in a non-invertible, heavily aliasing manner, it is usually desirable to use some form of soft-clipping before entering the hard-clipping range.


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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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