From: W. Trevor King <wking@tremily.us>
Date: Fri, 24 May 2013 16:29:51 +0000 (-0400)
Subject: calibcant/theory.tex: Add 'i' to nomenclature and move omega entry up
X-Git-Tag: v1.0~134
X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=6014513b4a8c18fd417eb5f53ed45f38ae7a9d5c;p=thesis.git

calibcant/theory.tex: Add 'i' to nomenclature and move omega entry up

The nomenclature entries should follow their first use.

Thanks Mom!
---

diff --git a/src/calibcant/theory.tex b/src/calibcant/theory.tex
index cfd035e..ea0977a 100644
--- a/src/calibcant/theory.tex
+++ b/src/calibcant/theory.tex
@@ -32,13 +32,18 @@ During the non-contact phase of calibration,
 In the following analysis, we use the unitary, angular frequency
 Fourier transform normalization
 \begin{equation}
-  \Four{x(t)} \equiv \frac{1}{\sqrt{2\pi}} \iInfInf{t}{x(t) e^{-i \omega t}}\;.
+  \Four{x(t)} \equiv \frac{1}{\sqrt{2\pi}} \iInfInf{t}{x(t) e^{-i \omega t}}\;,
 \end{equation}
+where $\omega$ is the angular frequency and $i\equiv\sqrt{-1}$ is the
+imaginary unit.
+%
 \nomenclature{\Four{s(t)}}{Fourier transform of the time-series
   $s(t)$.
   $s(f) = \Four{s(t)}
-   \equiv \frac{1}{\sqrt{2\pi}} \iInfInf{t}{s(t) e^{-i \omega t}}$
+   \equiv \frac{1}{\sqrt{2\pi}} \iInfInf{t}{s(t) e^{-i \omega t}}$.
   }\index{Fourier transform}
+\nomenclature{$i$}{Imaginary unit $i\equiv\sqrt{-1}$.}
+\nomenclature{$\omega$}{Angular frequency (radians per second).}
 
 We also use the following theorems (proved elsewhere):
 \begin{align}
@@ -78,7 +83,6 @@ where $t_T$ is the total time over which data has been aquired.
   \begin{equation}
     \PSD(g, w) \equiv \normLimT 2 \magSq{ \Four{g(t)}(\omega) }
   \end{equation}}
-\nomenclature{$\omega$}{Angular frequency (radians per second)}
 \nomenclature{$\abs{z}$}{Absolute value (or magnitude) of $z$.  For
   complex $z$, $\abs{z}\equiv\sqrt{z\conj{z}}$.}