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fixed chi2 denominator (added sqrt)

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Jan Benda 2025-03-03 15:29:55 +01:00
parent 8f5e983386
commit 3e42267b20
1 changed files with 2 additions and 1 deletions
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susceptibility1.tex
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@ -685,8 +685,9 @@ describes nonlinear interactions that generate responses at the sum and differen
The second-order susceptibility
\begin{equation}
\label{eq:susceptibility}
\chi_{2}(\omega_{1}, \omega_{2}) = \frac{S_{xss} (\omega_{1},\omega_{2})}{2S_{ss} (\omega_{1}) S_{ss} (\omega_{2})}
\chi_{2}(\omega_{1}, \omega_{2}) = \frac{S_{xss} (\omega_{1},\omega_{2})}{2\sqrt{S_{ss} (\omega_{1}) S_{ss} (\omega_{2})}}
\end{equation}
\note{is the denominator right? What is the unit?}
normalizes the second-order cross-spectrum by the spectral power at the two stimulus frequencies.
% Applying the Fourier transform this can be rewritten resulting in:
% \begin{equation}