diff --git a/Communication Systems/communication_systems.tex b/Communication Systems/communication_systems.tex index 9a7c038..30503d8 100644 --- a/Communication Systems/communication_systems.tex +++ b/Communication Systems/communication_systems.tex @@ -5,7 +5,7 @@ % @Author: Noah Huetter % @Date: 2019-09-24 17:26:28 % @Last Modified by: noah -% @Last Modified time: 2019-10-03 14:59:32 +% @Last Modified time: 2019-10-03 15:04:03 % --------------------------------------------------------------------------- \documentclass[a4paper, fontsize=8pt, landscape, DIV=1]{scrartcl} @@ -615,12 +615,20 @@ \pagebreak \section{Math} % --------------------------------------------------------------------------- + \subsection{General} \begin{empheq}{align*} &\cos(a)\cos(b) + \sin(a)\sin(b) = \cos(a-b) \\ &\sinc(x) = \frac{\sin(\pi x)}{\pi x} \\ &\sin(x) = \frac{e^{ix}-e^{-ix}}{2i} \quad \cos(x) = \frac{e^{ix}+e^{-ix}}{2} \end{empheq} + \subsection{Fourier Transform} + \begin{empheq}{align*} + \rect\left(\frac{t}{T}\right) &\laplace T\sinc(fT) \\ + \sinc\left(\frac{t}{T}\right) &\laplace T\rect(fT) \\ + \end{empheq} + + \end{multicols*}