By Topic

Generalized harmonic analysis for distributions

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)

Generalized harmonic analysis in the sense of Wiener is extended to the framework of Schwartz distributions. The approach seems mathematically and physically more transparent than the classical scheme, since every distribution possesses a Fourier transform so that the use of integrated Fourier transforms is avoided. A generalized Wiener-Khintchine representation is given which agrees well with the intuitive concept of the power spectrum. The latter is shown to be a tempered measure, in general, whose support is contained in the support of the Fourier transform of the signal. The correlation functional and power spectrum of filtered distributional signals is derived for a class of generalized filter impulse responses, which includes those that have bounded support or correspond to stable rational transfer functions. As an illustration, the form of the correlation functional and power spectrum for periodic and almost-periodic distributions and for delta-pulse trains occurring in sampled-data systems is given, and a deterministic white noise signal is constructed.

Published in:

Information Theory, IEEE Transactions on  (Volume:21 ,  Issue: 6 )