commit 13fee60e91caeae41fef7130cb3722ae69030e48
Author: surtur <a_mirre@utb.cz>
Date:   Sun Nov 13 21:20:59 2022 +0100

    initial commit

diff --git a/.envrc b/.envrc
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--- /dev/null
+++ b/.envrc
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+use flake
diff --git a/.gitignore b/.gitignore
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--- /dev/null
+++ b/.gitignore
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+.direnv
+.latexmkout
+result
+*.pdf
diff --git a/.latexmkrc b/.latexmkrc
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index 0000000..494f4e5
--- /dev/null
+++ b/.latexmkrc
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+# https://mg.readthedocs.io/latexmk.html#configuration-files
+$pdf_previewer = 'zathura';
diff --git a/LICENSE b/LICENSE
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--- /dev/null
+++ b/LICENSE
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+Creative Commons Legal Code
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+equitable action to disrupt the quiet enjoyment of the Work by the public
+as contemplated by Affirmer's express Statement of Purpose.
+
+3. Public License Fallback. Should any part of the Waiver for anyreason
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+Waiver shall be preserved to the maximum extent permitted taking into
+account Affirmer's express Statement of Purpose. In addition, to the
+extent the Waiver is so judged Affirmer hereby grants to each affected
+person a royalty-free, non transferable, non sublicensable, non exclusive,
+irrevocable and unconditional license to exercise Affirmer's Copyright and
+Related Rights in the Work (i) in all territories worldwide, (ii)for the
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+of copies, and (iv) for any purpose whatsoever, including without
+limitation commercial, advertising or promotional purposes (the
+"License"). The License shall be deemed effective as of the date CC0 was
+applied by Affirmer to the Work. Should any part of the License for any
+reason be judged legally invalid or ineffective under applicable law, such
+partial invalidity or ineffectiveness shall not invalidate the remainder
+of the License, and in such case Affirmer hereby affirms that he or she
+will not (i) exercise any of his or her remaining Copyright and Related
+Rights in the Work or (ii) assert any associated claims and causes of
+action with respect to the Work, in either case contrary to Affirmer's
+express Statement of Purpose.
+
+4. Limitations and Disclaimers.
+
+ a. No trademark or patent rights held by Affirmer are waived, abandoned,
+    surrendered, licensed or otherwise affected by this document.
+ b. Affirmer offers the Work as-is and makes no representations or
+    warranties of any kind concerning the Work, express, implied,
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+ d. Affirmer understands and acknowledges that Creative Commons is not a
+    party to this document and has no duty or obligation with respect to
+    this CC0 or use of the Work.
diff --git a/Makefile b/Makefile
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--- /dev/null
+++ b/Makefile
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+DOCNAME=proto2
+CMD="pdflatex -synctex=1 -file-line-error -interaction=nonstopmode"
+
+.PHONY: $(DOCNAME).pdf all clean
+
+all: $(DOCNAME).pdf
+
+$(DOCNAME).pdf: $(DOCNAME).tex
+	latexmk -pdf -pdflatex=$(CMD) -use-make $(DOCNAME).tex
+
+watch: $(DOCNAME).tex
+	latexmk -pvc -pdf -pdflatex=$(CMD) -use-make $(DOCNAME).tex
+
+clean:
+	# latexmk -CA # -> deprecated
+	latexmk -C
+
+install:
+	cp $(DOCNAME).pdf ${out}/
+
diff --git a/README.md b/README.md
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--- /dev/null
+++ b/README.md
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+# ak9im-proto2
+
+### License
+CC0
diff --git a/flake.lock b/flake.lock
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--- /dev/null
+++ b/flake.lock
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+{
+  "nodes": {
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1668354518,
+        "narHash": "sha256-7A2k/Qmh1j475TRtDHJZLeaQB4BzzRTGl5ibjJaTIaY=",
+        "owner": "nixos",
+        "repo": "nixpkgs",
+        "rev": "74b5398c530d09ee5e4e66e2b6383c2c50c904a6",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nixos",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
+    "root": {
+      "inputs": {
+        "nixpkgs": "nixpkgs"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}
diff --git a/flake.nix b/flake.nix
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--- /dev/null
+++ b/flake.nix
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+{
+  description = "AK9MI proto 2";
+
+  inputs = {
+    nixpkgs.url = "github:nixos/nixpkgs";
+  };
+
+  outputs = {
+    self,
+    nixpkgs,
+    ...
+  }: let
+    supportedSystems = ["x86_64-linux" "x86_64-darwin"];
+    forAllSystems = nixpkgs.lib.genAttrs supportedSystems;
+
+    courseCode = "ak9im";
+    documentName = "proto2";
+    pname = courseCode + "_" + documentName;
+    version = "0.0.1";
+
+    pkgs = forAllSystems (system: nixpkgs.legacyPackages.${system});
+    nixpkgsFor = forAllSystems (
+      system:
+        import nixpkgs {
+          inherit system;
+          overlays = [self.overlays.default];
+        }
+    );
+  in rec {
+    formatter = forAllSystems (
+      system:
+        nixpkgsFor.${system}.alejandra
+    );
+
+    overlays.default = with pkgs;
+      final: prev: {
+        watcher = with final;
+          writeScriptBin "watch" ''
+            out=".latexmkout"
+            mkdir "$out"
+            latexmk \
+              -pvc \
+              -outdir="$out" \
+              -pdf \
+              -pdflatex="pdflatex -synctex=1 -file-line-error -interaction=nonstopmode" \
+              -use-make ${documentName}.tex
+            rm -r "$out"
+          '';
+
+        buildLatex = with final;
+        with pkgs;
+          stdenv.mkDerivation {
+            inherit pname version;
+
+            src = lib.cleanSource ./.;
+
+            nativeBuildInputs = with pkgs; [
+              (texlive.combine {
+                inherit
+                  (texlive)
+                  scheme-medium
+                  authblk
+                  multirow
+                  hyperref
+                  blindtext
+                  etoolbox
+                  topiclongtable
+                  ;
+              })
+              gnumake
+            ];
+
+            buildPhase = ''
+              latexmk \
+              -pdf \
+              -pdflatex="pdflatex -file-line-error -interaction=nonstopmode" \
+              -use-make ${documentName}.tex
+            '';
+            installPhase = ''
+              install -Dm444 -t $out ${documentName}.pdf
+            '';
+          };
+      };
+
+    packages = forAllSystems (system: {
+      inherit (nixpkgsFor.${system}) watcher buildLatex;
+
+      default = nixpkgsFor.${system}.watcher;
+    });
+
+    defaultPackage =
+      forAllSystems (system: self.packages."${system}".buildLatex);
+
+    apps = forAllSystems (system: rec {
+      watch = {
+        type = "app";
+        program = "${self.packages."${system}".watcher}/bin/watch";
+      };
+      buildLatex = {
+        type = "app";
+        program = "${self.packages."${system}".buildLatex}";
+      };
+      # default = buildLatex;
+      default = watch;
+    });
+
+    devShells = with pkgs;
+      forAllSystems (system: let
+        pkgs = import nixpkgs {
+          inherit system;
+          overlays = [self.overlays.default];
+        };
+
+        nativeBuildInputs = with pkgs; [
+          (texlive.combine {
+            inherit
+              (texlive)
+              scheme-medium
+              authblk
+              multirow
+              hyperref
+              blindtext
+              etoolbox
+              topiclongtable
+              ;
+          })
+          gnumake
+        ];
+
+        watcher = pkgs.writeShellScriptBin "watcher" ''
+          out=".latexmkout"
+          mkdir "$out"
+          latexmk \
+            -pvc \
+            -outdir="$out" \
+            -pdf \
+            -pdflatex="pdflatex -synctex=1 -file-line-error -interaction=nonstopmode" \
+            -use-make ${documentName}.tex
+          rm -r "$out"
+        '';
+      in {
+        default = nixpkgsFor.${system}.mkShell {
+          name = "${pname}-" + version;
+          shellHook = ''
+            echo " -- in ${pname} dev shell..."
+          '';
+
+          nativeBuildInputs = with pkgs; [
+            (texlive.combine {
+              inherit
+                (texlive)
+                scheme-full
+                multirow
+                hyperref
+                blindtext
+                etoolbox
+                topiclongtable
+                ;
+            })
+            gnumake
+          ];
+
+          packages = with nixpkgsFor.${system}; [
+            watcher
+
+            gnumake
+            alejandra
+          ];
+        };
+      });
+  };
+}
diff --git a/meta.sty b/meta.sty
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+\newcommand{\doctitle}{Protokol 2}
+\newcommand{\authorname}{Adam Mirre}
+
+\newcommand{\faculty}{Fakulta Aplikované Informatiky}
+\newcommand{\shortfaculty}{FAI}
+\newcommand{\uni}{Univerzita Tomáše Bati ve Zlíně}
+\newcommand{\coursecode}{AK9IM}
+\newcommand{\subject}{Výpočet impulsní funkce pomocí korelační analýzy}
+\newcommand{\acyear}{2022}
diff --git a/proto2.tex b/proto2.tex
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+% vim: tw=0 wrap
+\documentclass[12pt,a4paper]{article}
+\usepackage{geometry}
+ \geometry{
+ a4paper,
+ top=18mm,
+ bottom=19mm,
+ }
+% \usepackage{lmodern}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage[slovak]{babel}
+\usepackage{pdfpages}
+\usepackage[fleqn]{amsmath}
+\usepackage{amssymb}
+\usepackage{amsfonts}
+% \usepackage{fontspec}
+% \usefonttheme[onlymath]{serif}
+% \usepackage{lstfiracode}
+% \setmonofont{Fira Code Retina}
+% \setmonofont{Fira Code Retina}[
+  % Contextuals=Alternate  % Activate the calt feature
+% ]
+\usepackage{bookmark}
+\usepackage{multirow}
+\usepackage{graphicx}
+\usepackage{textcomp}
+\usepackage{hyperref}
+\usepackage{etoolbox}
+\usepackage{longtable}
+\usepackage{meta}
+\usepackage[affil-it]{authblk}
+
+\date{\today}
+\title{\coursecode{}\\\subject{}}
+\author[1]{\authorname{} (\href{https://git.dotya.ml/wanderer}{wanderer})}
+
+\begin{document}
+\affil{\shortfaculty{} UTB ve Zlíně, Informační technologie - Kybernetická bezpečnost}
+
+\maketitle
+% \pagebreak
+
+\renewcommand{\figurename}{Obrázok}
+\renewcommand{\tablename}{Tabuľka}
+\renewcommand{\listtablename}{Zoznam tabuliek}
+\renewcommand{\listfigurename}{Zoznam grafov}
+\renewcommand{\contentsname}{Obsah}
+
+\newpage
+\tableofcontents
+\listoftables
+\listoffigures
+\pagebreak
+
+% \section{Zadanie}
+\input{task}
+\newpage
+
+\section{Vypracovanie}
+\input{solution}
+
+\end{document}
diff --git a/res/autocorrelation_u.jpg b/res/autocorrelation_u.jpg
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diff --git a/res/samplecount.png b/res/samplecount.png
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diff --git a/res/signal_u.jpg b/res/signal_u.jpg
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diff --git a/res/signal_y.jpg b/res/signal_y.jpg
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diff --git a/res/step_response.png b/res/step_response.png
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diff --git a/solution.tex b/solution.tex
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+Jazyky zvolené pre vypracovanie práce boli Go a Python. Pseudonáhodné dáta
+reprezentujúce signál boli vygenerované programom Matlab -
+Simulink\footnotemark{}.
+\\
+\\
+Kód je dostupný na nasledujúcom odkaze:\\
+\url{https://git.dotya.ml/wanderer/ak9im/src/branch/development/p2}.
+\\
+Kód tohto protokolu je dostupný na nasledujúcom odkaze:\\
+\url{https://git.dotya.ml/wanderer/ak9im-proto2}.
+
+\footnotetext{Matlab bol používaný na systéme Arch Linux (btw\texttrademark)
+\href{https://bbs.archlinux.org/viewtopic.php?id=277970}{po}
+\href{https://bbs.archlinux.org/viewtopic.php?pid=2051175#p2051175}{prekonaní}
+\href{https://uk.mathworks.com/matlabcentral/answers/1798895-invalid-cross-device-link-18-when-saving-a-file-on-arch-linux}{viacerých}
+\href{https://www.mathworks.com/matlabcentral/answers/93703-why-do-i-receive-host-id-error-after-selecting-a-license-file-during-installation}{problémov}
+s~inštaláciou, aktiváciou, QT + Wayland, \texttt{libfreetype.so} a inými.}
+
+\subsection{Spojitý model}
+\begin{equation*}
+  G(s) = \frac{1}{2s^2 + 5s + 1}
+\end{equation*}
+
+\subsection{Simulinkové schéma pre simuláciu pseudonáhodného signálu}
+\begin{figure}[ht]
+  \centering
+  \includegraphics[width=.80\textwidth]{res/model}
+  \caption{Simulinkové schéma pre simuláciu pseudonáhodného signálu}
+  \label{fig:model}
+\end{figure}
+Pre potreby tohto protokolu boli vygenerované nové dáta (neboli použité dáta
+vygenerované pre protokol 1).
+
+\newpage
+\subsection{Perióda vzorkovania}
+\begin{figure}[ht]
+  \centering
+  \includegraphics[width=.80\textwidth]{res/step_response}
+  \caption{Prechodová charakteristika modelu podľa \texttt{step(1, [2 5 1])}}
+  \label{fig:stepresponse}
+\end{figure}
+
+Prechodová charakteristika zobrazená na obrázku~\ref{fig:stepresponse} bola
+získaná príkazom \texttt{step(1 [2 5 1])} v Matlabe. V amplitúde nadobúda
+stabilne hodnotu $1$ po cca.~30 sekundách, perióda vzorkovania na výstupoch
+\textit{u} a \textit{y} bola teda podľa zadania zvolená na 3s (aktívna časť =
+10 vzoriek $\rightarrow 30s / 10 = 3s$). Minimálny počet vzoriek bol predpísaný
+na 250, dĺžka vzorkovania bola preto nastavená na 750s.
+
+
+\newpage
+\subsection{Vybudenie sústavy pseudonáhodným signálom}
+Sústava zobrazená na obrázku~\ref{fig:model} bola vybudená pseudonáhodným
+signálom s rovnomerným (\textit{uniform}) rozložením hodnôt v intervale
+$<-1;1>$. Vzorkovaním signálu bolo získaných celkom 251 hodnôt.
+
+\begin{figure}[ht]
+  \centering
+  \includegraphics[width=.35\textwidth]{res/samplecount}
+  \caption{Počet vzoriek zachytených na výstupoch \textit{u} a \textit{y}}
+  \label{samplecount}
+\end{figure}
+
+
+\subsection{Uloženie zachytených vzoriek do CSV}
+Kvôli ďalšiemu spracovávaniu dát v Pythone bolo nutné dostať vzorky z Matlabu
+do CSV súboru. To sa dalo našťastie celkom jednoducho vykonať nasledujúcimi
+príkazmi:
+
+\begin{figure}[h]
+  \centering
+  \begin{varwidth}{\linewidth}
+    \begin{verbatim}
+     >> % matlab command prompt
+     >> cd <project location>
+     >> m = [out.u, out.y]
+     >> writematrix(m, 'data/m.csv')
+    \end{verbatim}
+  \end{varwidth}
+  \caption{Uloženie dát do CSV súboru}
+\end{figure}
+
+Najskôr sme sa premiestnili do \texttt{<project location>}, následne sme si so
+zachytených vzoriek (jednorozmerné polia rovnakej dĺžky) vytvorili
+\textit{maticu}. Túto maticu sme nakoniec zapísali príkazom
+\texttt{writematrix} \footnote{V predošlom protokole sa vyskytovala chyba,
+keďže som poznamenal, že bol použitý príkaz \texttt{matrixwrite}} do želaného
+súboru.
+
+Súbor bolo dodatočne potrebné manuálne upraviť - pridať mu CSV "hlavičku" s
+názvami stĺpcov, aby ho bolo možné za pomoci knižnice
+\href{https://pandas.pydata.org/}{\texttt{Pandas}} bez problémov spracovať.
+
+
+\newpage
+\subsection{Získané signály}
+\begin{figure}[ht]
+  \centering
+  \includegraphics[width=.77\textwidth]{res/signal_u}
+  \caption{Náhodne vygenerovaný signál pred aplikáciou filtra - u}
+  \label{fig:signalorig}
+\end{figure}
+
+\begin{figure}[ht]
+  \centering
+  \includegraphics[width=.77\textwidth]{res/signal_y}
+  \caption{Náhodne vygenerovaný signál po aplikácii filtra - y}
+  \label{fig:signalfiltered}
+\end{figure}
+
+\newpage
+\subsection{Štatistické charakteristiky\ 1.\ a\ 2.\ rádu}
+Vypočítali sme štatistické charakteristiky prvého a druhého rádu, ktorými sú:
+\begin{itemize}
+  \item stredná hodnota pre u, y (viď tabuľka~\ref{table:stats})
+  \item rozptyl pre u, y (viď tabuľka~\ref{table:stats})
+  \item koeficient korelácie (viď tabuľka~\ref{table:stats})
+  \item kovariančná matica (viď tabuľka~\ref{table:covmatrix})
+  \item autokorelačná funkcia pre u, y (obr.~\ref{fig:autocorrelation-u},~\ref{fig:autocorrelation-y})
+  \item vzájomne korelačná funkcia (obr.~\ref{fig:mutualcorrelation-uy},~\ref{fig:mutualcorrelation-yu})
+\end{itemize}
+
+
+\newpage
+\subsection{Korelácia}
+\subsubsection{Autokorelačná funkcia u}
+\begin{figure}[ht]
+  \centering
+  \includegraphics[width=.77\textwidth]{res/autocorrelation_u}
+  \caption{Autokorelačná funkcia u}
+  \label{fig:autocorrelation-u}
+\end{figure}
+
+\subsubsection{Autokorelačná funkcia y}
+\begin{figure}[ht]
+  \centering
+  \includegraphics[width=.77\textwidth]{res/autocorrelation_y}
+  \caption{Autokorelačná funkcia y}
+  \label{fig:autocorrelation-y}
+\end{figure}
+
+\newpage
+\subsubsection{Vzájomne korelačná funkcia}
+\begin{figure}[ht]
+  \centering
+  \includegraphics[width=.77\textwidth]{res/mutual_correlation_uy}
+  \caption{Vzájomne korelačná funkcia uy}
+  \label{fig:mutualcorrelation-uy}
+\end{figure}
+
+\begin{figure}[ht]
+  \centering
+  \includegraphics[width=.77\textwidth]{res/mutual_correlation_yu}
+  \caption{Vzájomne korelačná funkcia yu}
+  \label{fig:mutualcorrelation-yu}
+\end{figure}
+
+
+\newpage
+\subsection{Štatistické charakteristiky - súhrn}
+
+\begin{table}[!hbt]
+  \centering
+  \begin{tabular}{r|cc}
+     & \textbf{u} & \textbf{y} \\
+    \hline
+    \textbf{u} & 0.30774141 & -0.00436625 \\
+    \textbf{y} & -0.00436625 & 0.01241115 \\
+  \end{tabular}
+
+  \caption{Kovariančná matica}
+  \label{table:covmatrix}
+\end{table}
+
+Zo zaznamenaných dát signálov sme spočítali odhady stredných hodnôt a
+rozptylov.
+V~tabuľke~\ref{table:stats} môžeme vidieť výrazné posuny signálu po prechode
+filtrom oproti pôvodnému signálu ako v strednej hodnote tak v rozptyle.
+
+
+\begin{table}[!hbt]
+  \centering
+  \begin{tabular}{r|cc}
+     & \textbf{u} & \textbf{y} \\
+    \hline
+    \textbf{$\hat{\mu}_{u,y}$ (stredná hodnota)} & -0.0016865221052993265 & 0.0030596815877553443 \\
+      \textbf{$\hat{\sigma}^{2}_{u,y}$ (rozptyl)} & 0.3077414110318535 & 0.012411153945455982 \\
+    \textbf{$\hat{r}(U,Y)$ (koeficient korelácie)} & \multicolumn{2}{c}{-0.07064959453763188} \\
+  \end{tabular}
+
+  \caption{Súhrn štatistických charakteristík}
+  \label{table:stats}
+\end{table}
+
+Hodnota koeficientu korelácie je mierne záporná, čo znamená jemný náznak
+tvrdenia, že signály spolu nesúvisia, resp. vzhľadom na to ako blízko je
+daná záporná hodnota 0 ide skôr o preukázanie neexistencie súvisu.
+
+
+
+\newpage
+\section{Záver}
+
diff --git a/task.tex b/task.tex
new file mode 100644
index 0000000..765236a
--- /dev/null
+++ b/task.tex
@@ -0,0 +1 @@
+\includepdf[pages=-]{res/zadani2.pdf}