Talk:Kramers–Kronig relation

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Since the Kramers-Kroning dispersion relations relate to so many topics in signal theory and physics, a more general discussion might be appropriate.

Why not start with a general causal transfer function and use this to show the relations.

Specific examples for such a transfer function \chi such as filter, susceptibilities, etc. could be listed at the end of the article.

ben

Personally, I would prefer stating the relations as \chi(\omega)=\frac{1}{\pi} P \int_{-\infty}^{\infty} d\omega' \frac{\chi'(\omega')}{\omega-\omega'}

ben

May be

{\rm Im}[\chi(\omega)]=\frac{1}{\pi}~ {-}\!\!\!\!\!\!\int_{0}^{\infty} {\rm d}\Omega \frac{{\rm Re}[\chi(\Omega)]}{\omega-\Omega}

would look better? Is the current version equivalent of this?

--dima 23:28, 8 August 2006 (UTC)

[edit] Toll

Why did somebody remove the reference to the important article by Toll? It didn't hurt, did it, to have a pointer to causality and Kramers-Kronig? (It took Kronig to 1942 before he saw the connection clearly). --P.wormer 10:47, 23 February 2007 (UTC)

I had rewritten the article without paying too much attention to the existing references -- pls revert my changes if for the better. Chuck Yee 09:35, 24 February 2007 (UTC)

there is a mistake in the integrations of the first two equations: the argument in chi1 and chhi2 should be w' and no w.

[edit] WikiProject class rating

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:57, 10 November 2007 (UTC)