deletions | additions       diff --git a/subsection_The_Signal_Distortion_The__.tex b/subsection_The_Signal_Distortion_The__.tex  index 2adac72..43b08a9 100644  --- a/subsection_The_Signal_Distortion_The__.tex  +++ b/subsection_The_Signal_Distortion_The__.tex 
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\begin{equation}\label{eqn:Pobs_from_Lorentz_profile}  P_{\rm obs} = \dfrac{P_{\rm act}}{1 + \left( \dfrac{2 b}{\Gamma_{\rm act}} \right)^2}.  \end{equation}  Clearly, unless $b = 0$, $P_{\rm obs} < P_{\rm act}$. Likewise, non-central encounters will distort the profile full-width/half-max, giving a full-width/half-max $\Gamma_{\rm obs}$. Having passed through its minimum at the devil's closest approach distance, the observed pressure signal reaches half its value at a time $t = \frac{1}{2} \Gamma_{\rm obs}^\prime = \frac{1}{2} \Gamma_{\rm obs}/\upsilon$ by definition. At this time, the center of the devil is a radial distance from the barometer $r(t = \Gamma_{\rm obs}^\prime/2) = \sqrt{b^2 + \left( \frac{1}{2} \Gamma_{\rm obs} \right)^2}$ and $P(r) = \frac{1}{2} P_{\rm obs} = \frac{1}{2} \dfrac{P_{\rm act}}{1 + \left( 2 b /\Gamma_{\rm act} \right)^2} = \dfrac{P_{\rm act}}{1 + \left( 2r(\Gamma_{\rm obs}^\prime/2)/\Gamma_{\rm act} \right)^2 }$. Solving for $\Gamma_{\rm obs}$ gives $\Gamma_{\rm obs}^2 = \Gamma_{\rm act}^2 + \left( 2b \right)^2$. and the profile width observed in the time series $\Gamma_{\rm obs}^\prime > \Gamma_{\rm act}^\prime$, as pointed out by \citet{Ellehoj_2010} and \citet{Lorenz_2014}. These effects represent the signal distortion induced by the miss distance effect.