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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

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

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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[How to cite and copy this work] 
``Physical Audio Signal Processing for Virtual Musical Instruments and Digital Audio Effects'', by Julius O. Smith III, (December 2005 Edition).
Copyright © 2006-07-01 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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