added missing parts of the number one

Assignment1_211.tex

@@ -121,13 +121,26 @@ Quirin Ecker, k12310122 \\
 \noindent \rule[0.8em]{\textwidth}{0.12mm}\\[-0.5em]
 %=======================================================================================
 
-\begin{aufgabe}
+\begin{aufgabe}{}
 
 	\begin{enumerate}
-		\item add back in
-		\item add back in
-		\item add back in
-		\item add back in
+		\item figure: \\
+			\includegraphics[width=0.95\textwidth]{fig/aufgabe1_a.png}
+
+		\item
+			\begin{gather*}
+				\Omega_3 = 2 \pi \frac{3.5}{64} \\
+				\Omega_4 = \frac{9}{64}
+			\end{gather*}
+		\item
+			\begin{gather*}
+				\frac{\Omega_3}{2 \pi} = \frac{3.5}{64} = \frac{7}{128} \\
+				N_{0,3} = 128 \\
+				\frac{\Omega_4}{2 \pi} = \frac{9}{64 \cdot 2 \pi} = \frac{9}{128 \pi} \\
+				\implies \text{Irational because of $\pi$} \\
+				\implies \text{Not periodic} \\
+			\end{gather*}
+		\item (see assignment2\_1.m)
 		\item (see assignment2\_1.m)
 		\item table:
 			\begin{table}[h]
@@ -146,16 +159,14 @@ Quirin Ecker, k12310122 \\
 				\label{tab:energy_power}
 			\end{table}
 	\end{enumerate}
-
 \end{aufgabe}
 
-\begin{aufgabe}
+\begin{aufgabe}{}
 
 	\begin{enumerate}
 		\item $|x[n]| + |h[n]| - 1 = 5 + 4 - 1 = 8$
 		\item
 			\begin{gather*}
-
 A=
 \begin{bmatrix}
 3 & 0 & 0 & 0\\
@@ -174,8 +185,7 @@ x=
 3\\
 4\\
 1
-\end{bmatrix}
-
+\end{bmatrix} \\
 Ax=
 \begin{bmatrix}
 6\\
@@ -189,10 +199,9 @@ Ax=
 \end{bmatrix}
 			\end{gather*}
 	\end{enumerate}
-
 \end{aufgabe}
 
-\begin{aufgabe}
+\begin{aufgabe}{}
 
 	\begin{enumerate}
 		\item $L_y = |x[n]| + |h[n]| - 1 = 50 + 3 - 1 = 52$
@@ -201,10 +210,9 @@ Ax=
 		\item figure: \\
 			\includegraphics[width=0.95\textwidth]{fig/aufgabe3_cd.png}
 	\end{enumerate}
-
 \end{aufgabe}
 
-\begin{aufgabe}
+\begin{aufgabe}{}
 
 	\begin{enumerate}
 		\item (see assignment2\_4.m)
@@ -212,11 +220,10 @@ Ax=
 			\includegraphics[width=0.95\textwidth]{fig/aufgabe4_b.png}
 		\item The magnitued seems to be repeating and the phase response seems to be mirrored accross the x and y axis.
 	\end{enumerate}
-
 \end{aufgabe}
 
 
-\begin{aufgabe}
+\begin{aufgabe}{}
 
 	\begin{enumerate}
 		\item (siehe assignment2\_5.m)
@@ -226,10 +233,6 @@ Ax=
 		\item original energy: 41343 \\ reverb energy: 2069.0506 \\ rir energy: $9.9997 \cdot 10^{3}$ \\
 			explanation: The rir energy is less than one which would explain why the outcoming signal is smaller than the original, because convulution scales proportionally.
 	\end{enumerate}
-
-
-
-
 \end{aufgabe}
 
 \end{document}