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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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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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