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.

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