WIP - exercise 4

6 files changed, 276 insertions, 3 deletions

diff --git a/Makefile b/Makefile
index dd8d149..e1ab442 100644
--- a/Makefile
+++ b/Makefile
@@ -5,7 +5,7 @@ LATEXMK = latexmk -pdf -silent -synctex=1
 LATEXMK_PVC = $(LATEXMK) -pvc
 
 ALL_CHAPTERS = $(BUILD_DIR)/chapter00.pdf $(BUILD_DIR)/chapter01.pdf $(BUILD_DIR)/chapter02.pdf $(BUILD_DIR)/chapter03.pdf $(BUILD_DIR)/chapter04.pdf $(BUILD_DIR)/chapter05.pdf
-ALL_EXERCISES = $(BUILD_DIR)/exercise00.pdf $(BUILD_DIR)/exercise01.pdf $(BUILD_DIR)/exercise02.pdf $(BUILD_DIR)/exercise03.pdf
+ALL_EXERCISES = $(BUILD_DIR)/exercise00.pdf $(BUILD_DIR)/exercise01.pdf $(BUILD_DIR)/exercise02.pdf $(BUILD_DIR)/exercise03.pdf $(BUILD_DIR)/exercise04.pdf $(BUILD_DIR)/exercise05.pdf
 ALL_SVGS = $(BUILD_DIR)/svg/ch01_EM_Spectrum_Properties.pdf $(BUILD_DIR)/svg/ch01_Electromagnetic-Spectrum.pdf $(BUILD_DIR)/svg/ch01_NetworkTopologies.pdf $(BUILD_DIR)/svg/ch03_Conv_Corr_Auto.pdf $(BUILD_DIR)/svg/ch04_win_blackman.pdf $(BUILD_DIR)/svg/ch04_win_hamming.pdf $(BUILD_DIR)/svg/ch04_win_hann.pdf $(BUILD_DIR)/svg/ch04_win_rect.pdf $(BUILD_DIR)/svg/ch04_win_tri.pdf $(BUILD_DIR)/svg/ch04_win_gauss.pdf
 COMMON_DEPS = common/settings.tex common/titlepage.tex common/acronym.tex common/imprint.tex DCS.bib
 
diff --git a/exercise04/exercise04.tex b/exercise04/exercise04.tex
new file mode 100644
index 0000000..27551d4
--- /dev/null
+++ b/exercise04/exercise04.tex
@@ -0,0 +1,100 @@
+% SPDX-License-Identifier: CC-BY-SA-4.0
+%
+% Copyright (c) 2020 Philipp Le
+%
+% Except where otherwise noted, this work is licensed under a
+% Creative Commons Attribution-ShareAlike 4.0 License.
+%
+% Please find the full copy of the licence at:
+% https://creativecommons.org/licenses/by-sa/4.0/legalcode
+
+\phantomsection
+\addcontentsline{toc}{section}{Exercise 4}
+\section*{Exercise 4}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{question}[subtitle={Sampling Periodic Signals}]
+	\begin{equation*}
+		u(t) = \SI{2}{V} \cos\left(2\pi \SI{2}{MHz} t + \SI{60}{\degree}\right)
+	\end{equation*}
+	The signal is sampled with a sampling period of $T_S = \SI{125}{\nano\second}$. The first sample taken is $u(t = 0)$.
+	
+	\begin{tasks}
+		\task
+		Plot the function from $t = 0$ to $t = \SI{1}{\micro\second}$!
+		
+		\task
+		Calculate the samples $n = 0 \dots 8$!
+		
+		\task
+		What is the DTFT of the signal?
+		
+		Hints:
+		\begin{equation*}
+			\begin{split}
+				x[n] = e^{-j a n} &= \underline{X}_{\frac{2\pi}{T_S}}\left(e^{-j T_S \omega}\right) = 2 \pi \cdot \delta \left(\omega + a\right) \\
+				\cos\left(b\right) &= \frac{1}{2} \left(e^{j b} + e^{-j b}\right)
+			\end{split}
+		\end{equation*}
+		
+		\task
+		Can the DFT directly applied to the signal? If yes, determine the smallest $N$ and give the values of all $\underline{U}[k]$!
+		
+		\task
+		What is the longest possible sampling period? What must be considered at this sampling period?
+		
+		\task
+		Now, the sampling period is changed to $T_S = \SI{0.5}{\micro\second}$. There is no anti-aliasing filter. The reconstruction filter is an ideal low-pass filter with a cut-off frequency of \SI{50}{kHz}. Give the reconstructed output function in the time domain! Give an explanation in the frequency domain!
+	\end{tasks}
+\end{question}
+
+\begin{solution}
+	\begin{tasks}
+	\end{tasks}
+\end{solution}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\begin{question}[subtitle={Sampling Non-Periodic Signals}]
+%	\begin{tasks}
+%	\end{tasks}
+%\end{question}
+%
+%\begin{solution}
+%	\begin{tasks}
+%	\end{tasks}
+%\end{solution}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{question}[subtitle={Quantization}]
+	The signal of task 1b) is now quantized. The quantizer has $8$ discrete values. These values are equally distributed between \SI{-2}{V} and \SI{2}{V}. Prior to sampling, the original time-continuous signal passed through an ideal low-pass filter with a cut-off frequency of \SI{4}{MHz}.
+	
+	\begin{tasks}
+		\task
+		Define a mapping from the value-continuous samples to the value-discrete samples!
+		
+		\task
+		The value-discrete samples are now pulse-code modulated. How many bits are required?
+		
+		\task
+		Determine the quantization error for each value-discrete sample! How much is the signal-to-noise ratio?
+		
+		\task
+		3 bits are a very poor resolution. How many bits are appropriate for the quantizer to obtain the best signal-to-noise ratio? Effects of the window filter are neglected. Assume that the signal has passed through a processing chain with a total gain of \SI{25}{dB} and noise figure of \SI{12}{dB} prior to quantization. The input of the quantizer has an impedance of \SI{50}{\ohm}. % 14 bits
+	\end{tasks}
+\end{question}
+
+\begin{solution}
+	\begin{tasks}
+	\end{tasks}
+\end{solution}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\begin{question}[subtitle={Decibel}]
+%	\begin{tasks}
+%	\end{tasks}
+%\end{question}
+%
+%\begin{solution}
+%	\begin{tasks}
+%	\end{tasks}
+%\end{solution}
diff --git a/exercise05/exercise05.tex b/exercise05/exercise05.tex
new file mode 100644
index 0000000..0591f3c
--- /dev/null
+++ b/exercise05/exercise05.tex
@@ -0,0 +1,25 @@
+% SPDX-License-Identifier: CC-BY-SA-4.0
+%
+% Copyright (c) 2020 Philipp Le
+%
+% Except where otherwise noted, this work is licensed under a
+% Creative Commons Attribution-ShareAlike 4.0 License.
+%
+% Please find the full copy of the licence at:
+% https://creativecommons.org/licenses/by-sa/4.0/legalcode
+
+\phantomsection
+\addcontentsline{toc}{section}{Exercise 5}
+\section*{Exercise 5}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\begin{question}[subtitle={Decibel}]
+%	\begin{tasks}
+%	\end{tasks}
+%\end{question}
+%
+%\begin{solution}
+%	\begin{tasks}
+%	\end{tasks}
+%\end{solution}
diff --git a/main/DCS.tex b/main/DCS.tex
index b4bebd6..8804df7 100644
--- a/main/DCS.tex
+++ b/main/DCS.tex
@@ -86,12 +86,12 @@
 
 \input{../chapter04/content_ch04.tex}
 \clearpage
-%\input{../exercise04/exercise04.tex}
+\input{../exercise04/exercise04.tex}
 \clearpage
 
 \input{../chapter05/content_ch05.tex}
 \clearpage
-%\input{../exercise05/exercise05.tex}
+\input{../exercise05/exercise05.tex}
 \clearpage
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/main/exercise04.tex b/main/exercise04.tex
new file mode 100644
index 0000000..1002d6e
--- /dev/null
+++ b/main/exercise04.tex
@@ -0,0 +1,74 @@
+% SPDX-License-Identifier: CC-BY-SA-4.0
+%
+% Copyright (c) 2020 Philipp Le
+%
+% Except where otherwise noted, this work is licensed under a
+% Creative Commons Attribution-ShareAlike 4.0 License.
+%
+% Please find the full copy of the licence at:
+% https://creativecommons.org/licenses/by-sa/4.0/legalcode
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Configuration
+\def\thekindofdocument{Exercise}
+\def\thesubtitle{Chapter 4: Sampling and Time-Discrete Signals and Systems}
+\def\therevision{1}
+\def\therevisiondate{2020-05-26}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Header
+\input{../common/settings.tex}
+
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Title Page
+\pagenumbering{Alph}
+\pagestyle{empty}
+
+% Title Page
+\input{../common/titlepage.tex}
+\newpage
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Preface
+\pagenumbering{arabic}
+\pagestyle{headings}
+
+% Inhaltsverzeichnis
+%\tableofcontents
+%\newpage
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Content
+
+\setcounter{chapter}{4}
+
+\input{../exercise04/exercise04.tex}
+\clearpage
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Appendix
+
+\begin{appendix}
+
+\chapter{Solutions}
+
+\printsolutions
+\clearpage
+
+\end{appendix}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Nachtrag
+
+% Imprint
+\input{../common/imprint.tex}
+\newpage
+
+% To Do
+\pagenumbering{alph}
+%\listoftodos
+
+\end{document}
diff --git a/main/exercise05.tex b/main/exercise05.tex
new file mode 100644
index 0000000..5cf47b4
--- /dev/null
+++ b/main/exercise05.tex
@@ -0,0 +1,74 @@
+% SPDX-License-Identifier: CC-BY-SA-4.0
+%
+% Copyright (c) 2020 Philipp Le
+%
+% Except where otherwise noted, this work is licensed under a
+% Creative Commons Attribution-ShareAlike 4.0 License.
+%
+% Please find the full copy of the licence at:
+% https://creativecommons.org/licenses/by-sa/4.0/legalcode
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Configuration
+\def\thekindofdocument{Exercise}
+\def\thesubtitle{Chapter 3: Modulation}
+\def\therevision{1}
+\def\therevisiondate{2020-05-26}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Header
+\input{../common/settings.tex}
+
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Title Page
+\pagenumbering{Alph}
+\pagestyle{empty}
+
+% Title Page
+\input{../common/titlepage.tex}
+\newpage
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Preface
+\pagenumbering{arabic}
+\pagestyle{headings}
+
+% Inhaltsverzeichnis
+%\tableofcontents
+%\newpage
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Content
+
+\setcounter{chapter}{5}
+
+\input{../exercise05/exercise05.tex}
+\clearpage
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Appendix
+
+\begin{appendix}
+
+\chapter{Solutions}
+
+\printsolutions
+\clearpage
+
+\end{appendix}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Nachtrag
+
+% Imprint
+\input{../common/imprint.tex}
+\newpage
+
+% To Do
+\pagenumbering{alph}
+%\listoftodos
+
+\end{document}