Sign in

username:

password:



Not a member?

Search Online Books



Search tips

Free Online Books

Sponsor

Industry's highest performing at the lowest power DSPs now as low as $5.00*
Start development today!
*volume pricing for 10ku

Chapters

See Also

Embedded SystemsFPGAElectronics

Physical Audio Signal Processing
    Digital Waveguide Models
       Nonlinear Elements
          Memoryless Nonlinearities
             Power Law Spectrum

Chapter Contents:

Search Physical Audio Signal Processing

  

Book Index | Global Index

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

  

Power Law Spectrum

More generally,

$\displaystyle x^k(n) \;\longleftrightarrow\; \underbrace{(X\ast X \ast \cdots \ast X)}_{\mbox{$k$\ times}}(\omega) $

so that the spectral bandwidth of $ x^k(n)$ is $ k$ times that of $ x(n)$, in general.

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

$\displaystyle Y(\omega) = X(\omega) + \alpha (X\ast X)(\omega) $

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.7.20

Previous: Square Law Series Expansion
Next: Arctangent Spectrum

Order a Hardcopy of Physical Audio Signal Processing

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.


Comments

No comments yet for this page


Add a Comment
You need to login before you can post a comment (best way to prevent spam). ( Not a member? )