main.tex

\documentclass[10pt,a4paper,twoside]{book}

\input{style}

\usepackage[
  left=2.5cm, % inner
  right=2.5cm, % outer
  top=2.5cm,
  bottom=3cm,
  %showframe,
  ]{geometry}

\usepackage{xr} % cross-referencing 
\makenoidxglossaries

% Comandi pratici

% d nell'integrale e i rispettivi usi
\newcommand{\dl}{\de l}
\newcommand{\dr}{\de r}
\newcommand{\dxi}{\de \xi}
\newcommand{\drho}{\de \rho}

% d nell'integrale con differenziale vettoriale
\newcommand{\dxx}{\de \x}
\newcommand{\dyy}{\de \y}
\newcommand{\dsig}{\de \sigg}

\allowdisplaybreaks[4] % Consente di rompere equazioni su più pagine

% MIDA1 acronym
\newacronym{sp}{SP}{Stochastic Process}
\newacronym{ssp}{SSP}{Stationary Stochastic Process}
\newacronym{ma}{MA}{Moving Average}
\newacronym{ar}{AR}{Auto Regressive}
\newacronym{arx}{ARX}{Auto Regressive with Exogenous Input}
\newacronym{arma}{ARMA}{Auto Regressive Moving Average}
\newacronym{armax}{ARMAX}{Auto Regressive Moving Average with Exogenous Input}
\newacronym{mse}{MSE}{Mean Square Error}
\newacronym{wn}{WN}{White Noise}
\newacronym{pem}{PEM}{Prediction Error Minimization}

% MIDA2 acronym
\newacronym{tf}{TF}{Transfer Function}
\newacronym{ss}{SS}{State-Space}
\newacronym{ir}{IR}{Impulse Response}
\newacronym{bb}{BB}{Black-Box}
\newacronym{wb}{WB}{White-Box}
\newacronym{gb}{GB}{Gray-Box}
\newacronym{kf}{KF}{Kalman Filter}
\newacronym{dre}{DRE}{Difference Riccati Equation}
\newacronym{are}{ARE}{Algebraic Riccati Equation}
\newacronym{sem}{SEM}{Simulation Error Method}

%c ommon used operator
\DeclareMathOperator{\WN}{WN}

\begin{document}

\frontmatter

\pagestyle{empty}

% TITLE PAGE

\hypertarget{mytitlepage}{} % set the hypertarget
\bookmark[dest=mytitlepage,level=chapter]{Title Page} % add the bookmark

\vspace*{\fill}
\begin{center}
	{\large \textsc{Lecture Notes of}}\\
	
  \vspace*{0.4cm}
	
  {\Huge
  \textsc{Model Identification}\\
	\vspace*{0.4cm}
	\textsc{and Data Analysis}}\\
	\vspace*{0.4cm}
	{\huge \textsc{Module 2}}\\
	
  \vspace*{1cm}
	
  {\large {From Professor Sergio Savaresi's lectures}}\\
	
  \vspace*{1cm}
	
  {\large
  Author\\
  \vspace*{0.1cm}
  \textsc{Edoardo Morassutto}\\
  
  \vspace*{0.4cm}
  
  Contributors\\
  \vspace*{0.1cm}
  \textsc{Marco Donadoni}\\
  \textsc{Cosimo Russo}\\
  \textsc{Federico Cazzola}\\
  
  \vspace*{0.4cm}
	
  Reviewed for the 2022 edition of the course by\\
  \vspace*{0.1cm}
  \textsc{Andrea Bosisio}\\

  \vspace*{0.4cm}
  
  Document formatting by\\
  \vspace*{0.1cm}
  \textsc{Teo Bucci}}\\
	
  \vspace*{1cm}
	
  Politecnico di Milano\\A.Y. 2021/2022
\end{center}
\vspace*{\fill}
\clearpage

% COPYRIGHT PAGE

\hypertarget{mycopyright}{} % set the hypertarget
\bookmark[dest=mycopyright,level=chapter]{Copyright Page} % add the bookmark
\input{firstpages/copyright}
\clearpage

% PREFACE

% \hypertarget{mypreface}{} % set the hypertarget
% \bookmark[dest=mypreface,level=chapter]{Preface} % add the bookmark
% \input{firstpages/preface}
% \clearpage

% CONTENTS

\cleardoublepage
\pagestyle{toc}
\hypertarget{mytoc}{} % set the hypertarget
\bookmark[dest=mytoc,level=chapter]{\contentsname} % add the bookmark
\tableofcontents
\cleardoublepage

% MAIN MATTER

\pagestyle{fancy}
\mainmatter

%%TIKZ

\usetikzlibrary{matrix,shapes.geometric}

\tikzstyle{block}      = [draw, rectangle, inner sep=6pt]
\tikzstyle{every node} = [font=\small]
\tikzstyle{sum}        = [draw, circle, inner sep=3pt, minimum size =0.1cm]

% Cross
\tikzset{cross/.style={cross out, draw=black, minimum size=2*(#1-\pgflinewidth), inner sep=0pt, outer sep=0pt},
  %default radius will be 1pt.
  cross/.default={0.1cm}}

% double border
\tikzstyle{double border} = [double, double distance=0.5mm]
% pattern in border
\newcounter{tmp}
\newif\ifpathisclosed
\tikzset{dashed border/.style={
    preaction={decoration={contour lineto closed, contour distance=2pt},
      decorate,
    },
    postaction={
      insert path={%
        \pgfextra{%
          \pgfinterruptpath
          \path[pattern=north west lines, pattern color=black,even odd rule]
          \mySecondList \myList
          ;
        \endpgfinterruptpath}
    }},
}}
\def\pgfdecoratedcontourdistance{0pt}
\pgfset{
  decoration/contour distance/.code=%
\pgfmathsetlengthmacro\pgfdecoratedcontourdistance{#1}}
\pgfdeclaredecoration{contour lineto closed}{start}{%
  \state{start}[
  next state=draw,
  width=0pt,
  persistent precomputation=\let\pgf@decorate@firstsegmentangle\pgfdecoratedangle]{%
    %\xdef\myList{}\xdef\mySecondList{}%
    \setcounter{tmp}{0}%
    \global\pathisclosedfalse%
    \pgfpathmoveto{\pgfpointlineattime{.5}
      {\pgfqpoint{0pt}{\pgfdecoratedcontourdistance}}
    {\pgfqpoint{\pgfdecoratedinputsegmentlength}{\pgfdecoratedcontourdistance}}}%
  }%
  \state{draw}[next state=draw, width=\pgfdecoratedinputsegmentlength]{%
    \ifpgf@decorate@is@closepath@%
      \pgfmathsetmacro\pgfdecoratedangletonextinputsegment{%
      -\pgfdecoratedangle+\pgf@decorate@firstsegmentangle}%
    \fi
    \pgfmathsetlengthmacro\pgf@decoration@contour@shorten{%
    -\pgfdecoratedcontourdistance*cot(-\pgfdecoratedangletonextinputsegment/2+90)}%
    \pgfpathlineto
    {\pgfpoint{\pgfdecoratedinputsegmentlength+\pgf@decoration@contour@shorten}
    {\pgfdecoratedcontourdistance}}%
    \stepcounter{tmp}%
    \pgfcoordinate{muemmel\number\value{tmp}}{\pgfpoint{\pgfdecoratedinputsegmentlength+\pgf@decoration@contour@shorten}
    {\pgfdecoratedcontourdistance}}%
    \pgfcoordinate{feep\number\value{tmp}}{\pgfpoint{\pgfdecoratedinputsegmentlength}{0pt}}%
    \ifnum\value{tmp}=1\relax%
     \pgfcoordinate{muemmel0}{\pgfpoint{0pt}{\pgfdecoratedcontourdistance}}%
     \pgfcoordinate{feep0}{\pgfpoint{0pt}{0pt}}%
     \xdef\myList{(muemmel\number\value{tmp})}%
     \xdef\mySecondList{(feep\number\value{tmp})}%
    \else
     \xdef\myList{\myList -- (muemmel\number\value{tmp})}%
     \xdef\mySecondList{(feep\number\value{tmp}) -- \mySecondList}%
    \fi
    \ifpgf@decorate@is@closepath@%
      \pgfpathclose
      \global\pathisclosedtrue%
    \fi
  }%
  \state{final}{%\typeout{\myList,\mySecondList}%
    \ifpathisclosed%
      \xdef\myList{\myList -- cycle}%
      \xdef\mySecondList{\mySecondList -- cycle}%
      %\typeout{closed \mySecondList \myList }
    \else
      %\typeout{\number\value{tmp}}%
      \xdef\myList{(muemmel0) -- \myList -- cycle}%
      \xdef\mySecondList{\mySecondList -- (feep0) --}%
      %\typeout{not closed \mySecondList \myList }%
    \fi
  }%
}
\tikzset{
  contour/.style={
    decoration={
      name=contour lineto closed,
      contour distance=#1
    },
decorate}}

% pattern
\tikzset{
  hatch distance/.store in=\hatchdistance,
  hatch distance=10pt,
  hatch thickness/.store in=\hatchthickness,
  hatch thickness=0.2pt
}
\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{flexible hatch}
{\pgfqpoint{0pt}{0pt}}
{\pgfqpoint{\hatchdistance}{\hatchdistance}}
{\pgfpoint{\hatchdistance-1pt}{\hatchdistance-1pt}}%
{
  \pgfsetcolor{\tikz@pattern@color}
  \pgfsetlinewidth{\hatchthickness}
  \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{\hatchdistance}{\hatchdistance}}
  \pgfusepath{stroke}
}

%\tikzstyle{input} = [coordinate]
%\tikzstyle{output} = [coordinate]
%\tikzstyle{pinstyle} = [pin edge={to-,thin,black}]

\input{lectures/2022_04_06}
\input{lectures/2022_04_07}
\input{lectures/2022_04_11}
\input{lectures/2022_04_12}
\input{lectures/2022_04_14}
\input{lectures/2022_04_20}
\input{lectures/2022_04_21}
\input{lectures/2022_04_27}
\input{lectures/2022_05_02}
\input{lectures/2022_05_09}
\input{lectures/2022_05_12}

\glsaddall
\printnoidxglossary[type=\acronymtype,title=Glossary, toctitle=Glossary, nonumberlist]
\cleardoublepage

\end{document}

%Aliasing errors occur when components of a signal are above the Nyquist frequency (Nyquist theory states that the sampling frequency must be at least two times the highest frequency component of the signal) or one half the sample rate.