236 lines
5.6 KiB
TeX
236 lines
5.6 KiB
TeX
\documentclass[12pt,a4paper,austrian]{article}
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\usepackage{graphicx}
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\usepackage[austrian, english]{babel}
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\usepackage[utf8]{inputenc}
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%\usepackage{listings}
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\usepackage{multirow}
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\usepackage{epstopdf}
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\usepackage{amsmath}
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\usepackage{amssymb} % fuer Mengen \N, Q, C, R
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\graphicspath{{./fig/}}
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%% Satzspiegel
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\setlength{\hoffset}{-1in} \setlength{\textwidth}{18cm}
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\setlength{\oddsidemargin}{1.5cm}
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\setlength{\evensidemargin}{1.5cm}
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\setlength{\marginparsep}{0.7em}
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\setlength{\marginparwidth}{0.5cm}
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\setlength{\voffset}{-1.9in}
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\setlength{\headheight}{12pt}
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\setlength{\topmargin}{2.6cm}
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\addtolength{\topmargin}{-\headheight}
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\setlength{\headsep}{3.5cm}
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\addtolength{\headsep}{-\topmargin}
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\addtolength{\headsep}{-\headheight}
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\setlength{\textheight}{27cm}
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%% How should floats be treated?
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\setlength{\floatsep}{12 pt plus 0 pt minus 8 pt}
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\setlength{\textfloatsep}{12 pt plus 0pt minus 8 pt}
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\setlength{\intextsep}{12 pt plus 0pt minus 8 pt}
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\tolerance2000
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\emergencystretch20pt
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%% Text appearence
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% English text
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\newcommand{\eg}[1]%
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{\selectlanguage{english}\textit{#1}\selectlanguage{austrian}}
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\newcommand{\filename}[1]
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{\begin{small}\texttt{#1}\end{small}}
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\newcommand\IFT{\unitlength1mm\begin{picture}(10,2) \put (1,1)
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{\circle{1.7}} \put(2,1){\line(1,0){5}} \put(8,1)
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{\circle*{1.7}}\end{picture}}
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\newcommand\FT{\unitlength1mm\begin{picture}(10,2) \put (1,1)
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{\circle*{1.7}} \put(2,1){\line(1,0){5}} \put(8,1)
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{\circle{1.7}}\end{picture}}
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% A box for multiple choice problems
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\newcommand{\choicebox}{\fbox{\rule{0pt}{0.5ex}\rule{0.5ex}{0pt}}}
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\newenvironment{wahrfalsch}%
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{\bigskip\par\noindent\makebox[1cm][c]{richtig}\hspace{3mm}\makebox[1cm][c]{falsch}
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\begin{list}%
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{\makebox[1cm][c]{\choicebox}\hspace{3mm}\makebox[1cm][c]{\choicebox}}%
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{\setlength{\labelwidth}{2.31 cm}\setlength{\labelsep}{3mm}
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\setlength{\leftmargin}{2.61 cm}\setlength{\listparindent}{0pt}
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\setlength{\itemindent}{0pt}}%
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}
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{\end{list}}
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\newcounter{theaufgabe}\setcounter{theaufgabe}{1}
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\newenvironment{aufgabe}[1]%
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{\bigskip\par\noindent\begin{nopagebreak}
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\textsf{\textbf{\arabic{theaufgabe}.\thinspace Exercise}}\quad
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\textsf{\textit{#1}}\\*[1ex]%
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\stepcounter{theaufgabe}\hspace{2ex}\end{nopagebreak}}
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{\par\pagebreak[2]}
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% Innerhalb der Aufgaben erfolgt die weitere Unterteilung mittels einer
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% enumerate Umgebung, die allerdings a), b),... zaehlen soll.
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\renewcommand{\labelenumi}{\alph{enumi})}
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\renewcommand{\labelenumii}{\arabic{enumii})}
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% A box to tick for everything which has to done
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\newcommand{\abgabe}{\marginpar{$\Box$}}
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% Margin paragraphs on the left side
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\reversemarginpar
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% Language for listings
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%\lstset{language=Vhdl,
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% basicstyle=\small\tt,
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% keywordstyle=\tt\bf,
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% commentstyle=\sl}
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% No indention
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\setlength{\parindent}{0.0cm}
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% Don't number sections
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\setcounter{secnumdepth}{0}
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%% Beginning of the text
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\begin{document}
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\selectlanguage{austrian}
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\pagestyle{plain}
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%=== This is the header section ============================================================
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\thispagestyle{empty}
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\noindent
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\begin{minipage}[b][4cm]{1.0\textwidth}
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\begin{center}
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\begin{bf}
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\begin{large} Digitale Signalverarbeitung SS 2025/26 -- 2.~Aufgabe\end{large} \\
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\vspace{0.3cm}
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\begin{Large} Analog Signals and Systems \end{Large} \\
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\vspace{0.3cm}
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\end{bf}
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\begin{large}
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Gruppennummer 211 \\
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Manuel Illmayer, k12308149 \\
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Quirin Ecker, k12310122 \\
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\end{large}
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\end{center}
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\end{minipage}
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\noindent \rule[0.8em]{\textwidth}{0.12mm}\\[-0.5em]
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%=======================================================================================
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\begin{aufgabe}
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\begin{enumerate}
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\item add back in
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\item add back in
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\item add back in
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\item add back in
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\item (see assignment2\_1.m)
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\item table:
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\begin{table}[h]
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\centering
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\begin{tabular}{|c|c|c|}
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\hline
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Signal & Energy & Power \\
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\hline
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$x_1[n]$ & 37 & -- \\
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$x_2[n]$ & 48.0394 & -- \\
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$x_3[n]$ & 1152 & 4.4825 \\
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$x_4[n]$ & 128.9565 & -- \\
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\hline
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\end{tabular}
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\caption{Energy and Power Values}
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\label{tab:energy_power}
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\end{table}
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\end{enumerate}
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\end{aufgabe}
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\begin{aufgabe}
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\begin{enumerate}
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\item $|x[n]| + |h[n]| - 1 = 5 + 4 - 1 = 8$
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\item
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\begin{gather*}
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A=
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\begin{bmatrix}
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3 & 0 & 0 & 0\\
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-1 & 3 & 0 & 0\\
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2 & -1 & 3 & 0\\
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0 & 2 & -1 & 3\\
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1 & 0 & 2 & -1\\
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0 & 1 & 0 & 2\\
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0 & 0 & 1 & 0\\
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0 & 0 & 0 & 1
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\end{bmatrix},
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\qquad
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x=
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\begin{bmatrix}
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2\\
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3\\
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4\\
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1
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\end{bmatrix}
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Ax=
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\begin{bmatrix}
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6\\
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7\\
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13\\
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5\\
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9\\
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5\\
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4\\
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1
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\end{bmatrix}
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\end{gather*}
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\end{enumerate}
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\end{aufgabe}
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\begin{aufgabe}
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\begin{enumerate}
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\item $L_y = |x[n]| + |h[n]| - 1 = 50 + 3 - 1 = 52$
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\item (see assignment2\_3.m)
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\item see d)
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\item figure: \\
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\includegraphics[width=0.95\textwidth]{fig/aufgabe3_cd.png}
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\end{enumerate}
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\end{aufgabe}
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\begin{aufgabe}
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\begin{enumerate}
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\item (see assignment2\_4.m)
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\item Phase Response is very small in the realm of $10^{-15}$. The signal contians multiple bigger spikes. \\
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\includegraphics[width=0.95\textwidth]{fig/aufgabe4_b.png}
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\item The magnitued seems to be repeating and the phase response seems to be mirrored accross the x and y axis.
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\end{enumerate}
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\end{aufgabe}
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\begin{aufgabe}
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\begin{enumerate}
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\item (siehe assignment2\_5.m)
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\item (siehe assignment2\_5.m)
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\item figure: \\
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\includegraphics[width=0.95\textwidth]{fig/aufgabe5_c.png}
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\item original energy: 41343 \\ reverb energy: 2069.0506 \\ rir energy: $9.9997 \cdot 10^{3}$ \\
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explanation: The rir energy is less than one which would explain why the outcoming signal is smaller than the original, because convulution scales proportionally.
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\end{enumerate}
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\end{aufgabe}
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\end{document}
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