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Signal systems cheatsheet plots #1

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Update signals-and-systems-cheatsheet.tex
started 4 FTs
fs446 committed Nov 4, 2020
commit 28c302f565022dda7c6e6953aa737a537e07ca9b
27 changes: 25 additions & 2 deletions signals-and-systems-cheatsheet.tex
Original file line number Diff line number Diff line change
@@ -10,6 +10,7 @@
}
\date{\today}

\usepackage{trfsigns}

\begin{document}
\maketitle
@@ -21,9 +22,20 @@ \subsection{Fundamental Signals}
\subsection{Laplace Transform}

\subsection{Fourier Series (FS)}
%
\begin{align*}
X[\mu] = \int\limits_{0}^{T_0} x(t) \e^{-\im (\frac{2\pi}{T_0} \mu) t}\mathrm{d}t
\qquad
x(t) = \frac{1}{T_0}\sum\limits_{\mu=-\infty}^{+\infty} X[\mu] \e^{+\im (\frac{2\pi}{T_0} \mu) t}
\end{align*}

\subsection{Fourier Transform (FT)}

%
\begin{align*}
X(\omega) = \int\limits_{-\infty}^{+\infty} x(t) \e^{-\im \omega t}\mathrm{d}t
\qquad
x(t) = \int\limits_{-\infty}^{+\infty} X(\omega) \e^{+\im \omega t}\mathrm{d}\omega
\end{align*}



@@ -34,9 +46,20 @@ \subsection{Fundamental Signals}
\subsection{z-Transform}

\subsection{Discrete-Time Fourier Transform (DTFT)}
%
\begin{align*}
X(\Omega) = \sum\limits_{k=-\infty}^{+\infty} x[k] \e^{-\im \Omega k}
\qquad
x[k] = \frac{1}{2\pi}\int\limits_{0}^{2\pi} X(\Omega) \e^{+\im \Omega k}\mathrm{d}\Omega
\end{align*}

\subsection{Discrete Fourier Transform (DFT)}

%
\begin{align*}
X[\mu] = \sum\limits_{k=0}^{N-1} x[k] \e^{-\im (\frac{2\pi}{N} \mu) k}
\qquad
x[k] = \frac{1}{N}\sum\limits_{\mu=0}^{N-1} X[\mu] \e^{+\im (\frac{2\pi}{N} \mu) k}
\end{align*}

\section{Changelog}
\begin{description}