From 26c84ab358466d727aeac60bb368caaf01322048 Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Mon, 27 May 2013 07:22:49 -0400 Subject: [PATCH] calibcant/theory.tex: Use en-dashes (--) for Wiener-Khinchin This matches the Wikipedia URL ('%E2%80%93' codes for U+2013 EN DASH). --- src/calibcant/main.bib | 2 +- src/calibcant/theory.tex | 7 ++++--- 2 files changed, 5 insertions(+), 4 deletions(-) diff --git a/src/calibcant/main.bib b/src/calibcant/main.bib index e38fda5..d27d06f 100644 --- a/src/calibcant/main.bib +++ b/src/calibcant/main.bib @@ -50,7 +50,7 @@ } @Misc{wikipedia-wiener-khinchin, - title = "{W}iener-{K}hinchin theorem", + title = "{W}iener--{K}hinchin theorem", publisher = "Wikipedia", url = "http://en.wikipedia.org/wiki/Wiener\%E2\%80\%93Khinchin_theorem", day = "TODO", diff --git a/src/calibcant/theory.tex b/src/calibcant/theory.tex index 86ac487..ed602cf 100644 --- a/src/calibcant/theory.tex +++ b/src/calibcant/theory.tex @@ -86,12 +86,13 @@ where $t_T$ is the total time over which data has been aquired. \nomenclature{$\abs{z}$}{Absolute value (or magnitude) of $z$. For complex $z$, $\abs{z}\equiv\sqrt{z\conj{z}}$.} -We also use the Wiener-Khinchin theorem, +We also use the Wiener--Khinchin theorem, which relates the two sided power spectral density $S_{xx}(\omega)$ to the autocorrelation function $r_{xx}(t)$ via \begin{align} S_{xx}(\omega) &= \Four{ r_{xx}(t) } \;, - &\text{(Wiener-Khinchin)\citep{wiener-khinchin}} \label{eq:wiener_khinchin} + &\text{(Wiener--Khinchin)\citep{wiener-khinchin}} + \label{eq:wiener_khinchin} \end{align} \index{Wiener-Khinchin theorem} where $r_{xx}(t)$ is defined in terms of the expectation value @@ -137,7 +138,7 @@ We compute the \PSD\ by plugging \cref{eq:ODHO-xmag} into \end{equation} \index{PSD@\PSD} -Because thermal noise is white (not autocorrelated + Wiener-Khinchin +Because thermal noise is white (not autocorrelated + Wiener--Khinchin Theorem), we can write the one sided thermal power spectral density per unit time as \begin{equation} -- 2.26.2