Power Laws

More generally,

so that the spectral bandwidth of is times that of , in general.

In summary, the spectrum at the output of the square-law nonlinearity can be written as

This illustrates the great value of series expansions for nonlinearities. In audio signal processing systems, it is essential to keep track of the spectral representation of all output signals, since we hear directly in terms of signal spectra.^T.4

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written by 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.