# Parseval's theorem

From Glossary of Meteorology

Revision as of 16:34, 25 April 2012 by imported>Perlwikibot

## Parseval's theorem

A theorem relating the product of two functions to the products of their Fourier series components.

If the functions are There is an analogous theorem for Fourier transforms.

*f*(*x*) and*F*(*x*), and their Fourier series components have respective amplitudes*a*_{n},*b*_{n}and*A*_{n},*B*_{n}, Parseval's theorem states that under certain general conditions

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact [email protected]. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.