% Default to the notebook output style % Inherit from the specified cell style. \documentclass[11pt]{article} \usepackage[T1]{fontenc} % Nicer default font (+ math font) than Computer Modern for most use cases \usepackage{mathpazo} % Basic figure setup, for now with no caption control since it's done % automatically by Pandoc (which extracts ![](path) syntax from Markdown). \usepackage{graphicx} % We will generate all images so they have a width \maxwidth. This means % that they will get their normal width if they fit onto the page, but % are scaled down if they would overflow the margins. \makeatletter \def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth \else\Gin@nat@width\fi} \makeatother \let\Oldincludegraphics\includegraphics % Set max figure width to be 80% of text width, for now hardcoded. \renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}} % Ensure that by default, figures have no caption (until we provide a % proper Figure object with a Caption API and a way to capture that % in the conversion process - todo). \usepackage{caption} \DeclareCaptionLabelFormat{nolabel}{} \captionsetup{labelformat=nolabel} \usepackage{adjustbox} % Used to constrain images to a maximum size \usepackage{xcolor} % Allow colors to be defined \usepackage{enumerate} % Needed for markdown enumerations to work \usepackage{geometry} % Used to adjust the document margins \usepackage{amsmath} % Equations \usepackage{amssymb} % Equations \usepackage{textcomp} % defines textquotesingle % Hack from http://tex.stackexchange.com/a/47451/13684: \AtBeginDocument{% \def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code } \usepackage{upquote} % Upright quotes for verbatim code \usepackage{eurosym} % defines \euro \usepackage[mathletters]{ucs} % Extended unicode (utf-8) support \usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document \usepackage{fancyvrb} % verbatim replacement that allows latex \usepackage{grffile} % extends the file name processing of package graphics % to support a larger range % The hyperref package gives us a pdf with properly built % internal navigation ('pdf bookmarks' for the table of contents, % internal cross-reference links, web links for URLs, etc.) \usepackage{hyperref} \usepackage{longtable} % longtable support required by pandoc >1.10 \usepackage{booktabs} % table support for pandoc > 1.12.2 \usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment) \usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout) % normalem makes italics be italics, not underlines % Colors for the hyperref package \definecolor{urlcolor}{rgb}{0,.145,.698} \definecolor{linkcolor}{rgb}{.71,0.21,0.01} \definecolor{citecolor}{rgb}{.12,.54,.11} % ANSI colors \definecolor{ansi-black}{HTML}{3E424D} \definecolor{ansi-black-intense}{HTML}{282C36} \definecolor{ansi-red}{HTML}{E75C58} \definecolor{ansi-red-intense}{HTML}{B22B31} \definecolor{ansi-green}{HTML}{00A250} \definecolor{ansi-green-intense}{HTML}{007427} \definecolor{ansi-yellow}{HTML}{DDB62B} \definecolor{ansi-yellow-intense}{HTML}{B27D12} \definecolor{ansi-blue}{HTML}{208FFB} \definecolor{ansi-blue-intense}{HTML}{0065CA} \definecolor{ansi-magenta}{HTML}{D160C4} \definecolor{ansi-magenta-intense}{HTML}{A03196} \definecolor{ansi-cyan}{HTML}{60C6C8} \definecolor{ansi-cyan-intense}{HTML}{258F8F} \definecolor{ansi-white}{HTML}{C5C1B4} \definecolor{ansi-white-intense}{HTML}{A1A6B2} % commands and environments needed by pandoc snippets % extracted from the output of `pandoc -s` \providecommand{\tightlist}{% \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} \DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} % Add ',fontsize=\small' for more characters per line \newenvironment{Shaded}{}{} \newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}} \newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}} \newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} \newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} \newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}} \newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} \newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} \newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}} \newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}} \newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} \newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}} \newcommand{\RegionMarkerTok}[1]{{#1}} \newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}} \newcommand{\NormalTok}[1]{{#1}} % Additional commands for more recent versions of Pandoc \newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}} \newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} \newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}} \newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}} \newcommand{\ImportTok}[1]{{#1}} \newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}} \newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} \newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}} \newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}} 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\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} \expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} \expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}} \def\PYZbs{\char`\\} \def\PYZus{\char`\_} \def\PYZob{\char`\{} \def\PYZcb{\char`\}} \def\PYZca{\char`\^} \def\PYZam{\char`\&} \def\PYZlt{\char`\<} \def\PYZgt{\char`\>} \def\PYZsh{\char`\#} \def\PYZpc{\char`\%} \def\PYZdl{\char`\$} \def\PYZhy{\char`\-} \def\PYZsq{\char`\'} \def\PYZdq{\char`\"} \def\PYZti{\char`\~} % for compatibility with earlier versions \def\PYZat{@} \def\PYZlb{[} \def\PYZrb{]} \makeatother % Exact colors from NB \definecolor{incolor}{rgb}{0.0, 0.0, 0.5} \definecolor{outcolor}{rgb}{0.545, 0.0, 0.0} % Prevent overflowing lines due to hard-to-break entities \sloppy % Setup hyperref package \hypersetup{ breaklinks=true, % so long urls are correctly broken across lines colorlinks=true, urlcolor=urlcolor, linkcolor=linkcolor, citecolor=citecolor, } % Slightly bigger margins than the latex defaults \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} \begin{document} \maketitle \section{Analyse non paramétrique du signal de la flute}\label{analyse-non-paramuxe9trique-du-signal-de-la-flute} Nous allons commencer par afficher le signals /TODO mettre des labels X/Y avec unités et des titres à toutes les figure \begin{Verbatim}[commandchars=\\\{\}] {\color{incolor}In [{\color{incolor}46}]:} \PY{k}{using} \PY{n}{WAV} \PY{n}{s}\PY{p}{,} \PY{n}{fs} \PY{o}{=} \PY{n}{wavread}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{.}\PY{l+s}{.}\PY{l+s}{/}\PY{l+s}{f}\PY{l+s}{l}\PY{l+s}{u}\PY{l+s}{t}\PY{l+s}{e}\PY{l+s}{i}\PY{l+s}{r}\PY{l+s}{c}\PY{l+s}{a}\PY{l+s}{m}\PY{l+s}{.}\PY{l+s}{w}\PY{l+s}{a}\PY{l+s}{v}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{p}{;} \PY{n}{s} \PY{o}{=} \PY{n}{vec}\PY{p}{(}\PY{n}{s}\PY{p}{)}\PY{p}{;} \PY{n}{t} \PY{o}{=} \PY{p}{(}\PY{l+m+mi}{0} \PY{o}{:} \PY{l+m+mi}{1} \PY{o}{:} \PY{n}{size}\PY{p}{(}\PY{n}{s}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{)}\PY{o}{/}\PY{n}{fs}\PY{p}{;} \PY{n}{fs} \PY{o}{=} \PY{n}{floor}\PY{p}{(}\PY{k+kt}{Int}\PY{p}{,} \PY{n}{fs}\PY{p}{)}\PY{p}{;} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] {\color{incolor}In [{\color{incolor}47}]:} \PY{k}{using} \PY{n}{Plots} \PY{n}{plot}\PY{p}{(}\PY{n}{t}\PY{p}{,} \PY{n}{s}\PY{p}{,} \PY{n}{title}\PY{o}{=}\PY{l+s}{\PYZdq{}}\PY{l+s}{S}\PY{l+s}{o}\PY{l+s}{n}\PY{l+s}{ }\PY{l+s}{d}\PY{l+s}{e}\PY{l+s}{ }\PY{l+s}{f}\PY{l+s}{l}\PY{l+s}{u}\PY{l+s}{t}\PY{l+s}{e}\PY{l+s}{\PYZdq{}}\PY{p}{,}\PY{n}{label}\PY{o}{=}\PY{p}{[}\PY{l+s}{\PYZdq{}}\PY{l+s}{S}\PY{l+s}{i}\PY{l+s}{g}\PY{l+s}{n}\PY{l+s}{a}\PY{l+s}{l}\PY{l+s}{\PYZdq{}}\PY{p}{]}\PY{p}{)} \end{Verbatim} \texttt{\color{outcolor}Out[{\color{outcolor}47}]:} \begin{center} \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_2_0.pdf} \end{center} { \hspace*{\fill} \\} Regardons des trames. La taille de trame reste classique : de l'ordre de 20ms. \begin{Verbatim}[commandchars=\\\{\}] {\color{incolor}In [{\color{incolor}48}]:} \PY{k}{using} \PY{n}{LinearAlgebra} \PY{n}{t\PYZus{}s} \PY{o}{=} \PY{l+m+mi}{5} \PY{c}{\PYZsh{}s} \PY{n}{trame\PYZus{}period} \PY{o}{=} \PY{l+m+mf}{0.01} \PY{c}{\PYZsh{}s} \PY{n}{i\PYZus{}s} \PY{o}{=} \PY{n}{floor}\PY{p}{(}\PY{k+kt}{Int}\PY{p}{,} \PY{n}{t\PYZus{}s}\PY{o}{*}\PY{n}{fs}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{)} \PY{n}{i\PYZus{}e} \PY{o}{=} \PY{n}{floor}\PY{p}{(}\PY{k+kt}{Int}\PY{p}{,} \PY{n}{i\PYZus{}s}\PY{o}{+}\PY{n}{trame\PYZus{}period}\PY{o}{*}\PY{n}{fs}\PY{p}{)} \PY{n}{t\PYZus{}trame} \PY{o}{=} \PY{n}{t}\PY{p}{[}\PY{n}{i\PYZus{}s}\PY{o}{:}\PY{n}{i\PYZus{}e}\PY{p}{]} \PY{n}{s\PYZus{}trame} \PY{o}{=} \PY{n}{s}\PY{p}{[}\PY{n}{i\PYZus{}s}\PY{o}{:}\PY{n}{i\PYZus{}e}\PY{p}{]} \PY{n}{plot}\PY{p}{(}\PY{n}{t\PYZus{}trame}\PY{p}{,} \PY{n}{s\PYZus{}trame}\PY{p}{)} \end{Verbatim} \texttt{\color{outcolor}Out[{\color{outcolor}48}]:} \begin{center} \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_4_0.pdf} \end{center} { \hspace*{\fill} \\} On cherche maintenant la fréquence du fondamental. Comme il s'agit d'un instrument à vent, on choisit notre interval de fréquence. \begin{Verbatim}[commandchars=\\\{\}] {\color{incolor}In [{\color{incolor}49}]:} \PY{k}{using} \PY{n}{WORLD} \PY{n}{floor\PYZus{}freq} \PY{o}{=} \PY{l+m+mi}{300} \PY{c}{\PYZsh{}Hz} \PY{n}{ceil\PYZus{}freq} \PY{o}{=} \PY{l+m+mi}{800} \PY{c}{\PYZsh{}Hz} \PY{n}{f0}\PY{p}{,} \PY{n}{timeaxis} \PY{o}{=} \PY{n}{harvest}\PY{p}{(}\PY{n}{s}\PY{p}{,} \PY{n}{fs}\PY{p}{,} \PY{n}{HarvestOption}\PY{p}{(}\PY{n}{floor\PYZus{}freq}\PY{p}{,} \PY{n}{ceil\PYZus{}freq}\PY{p}{,} \PY{n}{trame\PYZus{}period}\PY{p}{)}\PY{p}{)}\PY{p}{;}\PY{c}{\PYZsh{}floor and ceil freq, period} \PY{n}{plot}\PY{p}{(}\PY{n}{timeaxis}\PY{p}{,} \PY{n}{f0}\PY{p}{)} \end{Verbatim} \texttt{\color{outcolor}Out[{\color{outcolor}49}]:} \begin{center} \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_6_0.pdf} \end{center} { \hspace*{\fill} \\} On observe des vibratos, par exemple un gros vibrato vers 5s, un "fa". La fréquence du son ne correspond pas exactement à la fréquence du fondamental. On a une modulation de fréquence. /TODO étudier cette modulation de fréquence Regardons un zoom sur un vibrato. /TODO fft du petit bout de signal \begin{Verbatim}[commandchars=\\\{\}] {\color{incolor}In [{\color{incolor}50}]:} \PY{n}{number\PYZus{}trame} \PY{o}{=} \PY{l+m+mi}{100} \PY{c}{\PYZsh{} trames on each side of t\PYZus{}s} \PY{n}{i\PYZus{}s} \PY{o}{=} \PY{n}{floor}\PY{p}{(}\PY{k+kt}{Int}\PY{p}{,} \PY{n}{t\PYZus{}s}\PY{o}{*}\PY{n}{fs}\PY{o}{\PYZhy{}}\PY{n}{number\PYZus{}trame}\PY{o}{*}\PY{n}{trame\PYZus{}period}\PY{o}{*}\PY{n}{fs}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{)} \PY{n}{i\PYZus{}e} \PY{o}{=} \PY{n}{floor}\PY{p}{(}\PY{k+kt}{Int}\PY{p}{,} \PY{n}{i\PYZus{}s}\PY{o}{+}\PY{l+m+mi}{2}\PY{o}{*}\PY{n}{number\PYZus{}trame}\PY{o}{*}\PY{n}{trame\PYZus{}period}\PY{o}{*}\PY{n}{fs}\PY{p}{)} \PY{n}{t\PYZus{}trame} \PY{o}{=} \PY{n}{t}\PY{p}{[}\PY{n}{i\PYZus{}s}\PY{o}{:}\PY{n}{i\PYZus{}e}\PY{p}{]} \PY{n}{s\PYZus{}trame} \PY{o}{=} \PY{n}{s}\PY{p}{[}\PY{n}{i\PYZus{}s}\PY{o}{:}\PY{n}{i\PYZus{}e}\PY{p}{]} \PY{n}{f0}\PY{p}{,} \PY{n}{timeaxis} \PY{o}{=} \PY{n}{harvest}\PY{p}{(}\PY{n}{s\PYZus{}trame}\PY{p}{,} \PY{n}{fs}\PY{p}{,} \PY{n}{HarvestOption}\PY{p}{(}\PY{n}{floor\PYZus{}freq}\PY{p}{,} \PY{n}{ceil\PYZus{}freq}\PY{p}{,} \PY{n}{trame\PYZus{}period}\PY{p}{)}\PY{p}{)}\PY{p}{;}\PY{c}{\PYZsh{}floor and ceil freq, period} \PY{n}{plot}\PY{p}{(}\PY{n}{timeaxis}\PY{o}{.+}\PY{n}{t\PYZus{}trame}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,} \PY{n}{f0}\PY{p}{)} \end{Verbatim} \texttt{\color{outcolor}Out[{\color{outcolor}50}]:} \begin{center} \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_8_0.pdf} \end{center} { \hspace*{\fill} \\} On va s'intéresser maintenant au spectrogramme. \TODO On choisit une fenêtre XXXX car XXX \begin{Verbatim}[commandchars=\\\{\}] {\color{incolor}In [{\color{incolor}53}]:} \PY{c}{\PYZsh{}\PYZpc{}matplotlib inline} \PY{k}{using} \PY{n}{DSP}\PY{p}{,} \PY{n}{PyPlot} \PY{n}{trame\PYZus{}period} \PY{o}{=} \PY{l+m+mf}{0.01} \PY{c}{\PYZsh{}s} \PY{n}{overlap} \PY{o}{=} \PY{l+m+mf}{0.001}\PY{c}{\PYZsh{}s} \PY{n}{S} \PY{o}{=} \PY{n}{spectrogram}\PY{p}{(}\PY{n}{s}\PY{p}{,} \PY{n}{convert}\PY{p}{(}\PY{k+kt}{Int}\PY{p}{,} \PY{n}{trame\PYZus{}period}\PY{o}{*}\PY{n}{fs}\PY{p}{)}\PY{p}{,} \PY{n}{convert}\PY{p}{(}\PY{k+kt}{Int}\PY{p}{,} \PY{n}{overlap}\PY{o}{*}\PY{n}{fs}\PY{p}{)}\PY{p}{;} \PY{n}{fs}\PY{o}{=}\PY{n}{fs}\PY{p}{,} \PY{n}{window}\PY{o}{=}\PY{n}{hanning}\PY{p}{)} \PY{n}{t} \PY{o}{=} \PY{n}{time}\PY{p}{(}\PY{n}{S}\PY{p}{)} \PY{n}{f} \PY{o}{=} \PY{n}{freq}\PY{p}{(}\PY{n}{S}\PY{p}{)} \PY{n}{imshow}\PY{p}{(}\PY{n}{reverse}\PY{p}{(}\PY{n}{log10}\PY{o}{.}\PY{p}{(}\PY{n}{power}\PY{p}{(}\PY{n}{S}\PY{p}{)}\PY{p}{)}\PY{p}{,} \PY{n}{dims}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{,} \PY{n}{extent}\PY{o}{=}\PY{p}{[}\PY{n}{first}\PY{p}{(}\PY{n}{t}\PY{p}{)}\PY{p}{,} \PY{n}{last}\PY{p}{(}\PY{n}{t}\PY{p}{)}\PY{p}{,} \PY{n}{first}\PY{p}{(}\PY{n}{f}\PY{p}{)}\PY{p}{,} \PY{n}{last}\PY{p}{(}\PY{n}{f}\PY{p}{)}\PY{p}{]}\PY{p}{,} \PY{n}{aspect}\PY{o}{=}\PY{l+s}{\PYZdq{}}\PY{l+s}{a}\PY{l+s}{u}\PY{l+s}{t}\PY{l+s}{o}\PY{l+s}{\PYZdq{}}\PY{p}{)} \end{Verbatim} The analogue of IPython's \texttt{\%matplotlib} in Julia is to use the \href{https://github.com/stevengj/PyPlot.jl}{PyPlot package}, which gives a Julia interface to Matplotlib including inline plots in IJulia notebooks. (The equivalent of \texttt{numpy} is already loaded by default in Julia.) Given PyPlot, the analogue of \texttt{\%matplotlib inline} is \texttt{using PyPlot}, since PyPlot defaults to inline plots in IJulia. To enable separate GUI windows in PyPlot, analogous to \texttt{\%matplotlib}, do \texttt{using PyPlot; pygui(true)}. To specify a particular gui backend, analogous to \texttt{\%matplotlib gui}, you can either do \texttt{using PyPlot; pygui(:gui); using PyPlot; pygui(true)} (where \texttt{gui} is \texttt{wx}, \texttt{qt}, \texttt{tk}, or \texttt{gtk}), or you can do \texttt{ENV["MPLBACKEND"]=backend; using PyPlot; pygui(true)} (where \texttt{backend} is the name of a Matplotlib backend, like \texttt{tkagg}). For more options, see the PyPlot documentation. \begin{Verbatim}[commandchars=\\\{\}] {\color{incolor}In [{\color{incolor} }]:} \PY{n}{Zoom} \PY{n}{sur} \PY{n}{notre} \PY{n}{vibrato} \PY{n}{que} \PY{n}{l}\PY{o}{\PYZsq{}}\PY{n}{on} \PY{n}{voit} \PY{n}{un} \PY{n}{peu} \end{Verbatim} \begin{Verbatim}[commandchars=\\\{\}] {\color{incolor}In [{\color{incolor}52}]:} \PY{n}{S} \PY{o}{=} \PY{n}{spectrogram}\PY{p}{(}\PY{n}{s\PYZus{}trame}\PY{p}{,} \PY{n}{convert}\PY{p}{(}\PY{k+kt}{Int}\PY{p}{,} \PY{n}{trame\PYZus{}period}\PY{o}{*}\PY{n}{fs}\PY{p}{)}\PY{p}{,} \PY{n}{convert}\PY{p}{(}\PY{k+kt}{Int}\PY{p}{,} \PY{n}{overlap}\PY{o}{*}\PY{n}{fs}\PY{p}{)}\PY{p}{;} \PY{n}{fs}\PY{o}{=}\PY{n}{fs}\PY{p}{,} \PY{n}{window}\PY{o}{=}\PY{n}{hanning}\PY{p}{)} \PY{n}{t} \PY{o}{=} \PY{n}{time}\PY{p}{(}\PY{n}{S}\PY{p}{)} \PY{n}{f} \PY{o}{=} \PY{n}{freq}\PY{p}{(}\PY{n}{S}\PY{p}{)} \PY{n}{imshow}\PY{p}{(}\PY{n}{reverse}\PY{p}{(}\PY{n}{log10}\PY{o}{.}\PY{p}{(}\PY{n}{power}\PY{p}{(}\PY{n}{S}\PY{p}{)}\PY{p}{)}\PY{p}{,} \PY{n}{dims}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{,} \PY{n}{extent}\PY{o}{=}\PY{p}{[}\PY{n}{first}\PY{p}{(}\PY{n}{t}\PY{p}{)}\PY{o}{.+}\PY{n}{t\PYZus{}trame}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,} \PY{n}{last}\PY{p}{(}\PY{n}{t}\PY{p}{)}\PY{o}{.+}\PY{n}{t\PYZus{}trame}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{,} \PY{n}{first}\PY{p}{(}\PY{n}{f}\PY{p}{)}\PY{p}{,} \PY{n}{last}\PY{p}{(}\PY{n}{f}\PY{p}{)}\PY{p}{]}\PY{p}{,} \PY{n}{aspect}\PY{o}{=}\PY{l+s}{\PYZdq{}}\PY{l+s}{a}\PY{l+s}{u}\PY{l+s}{t}\PY{l+s}{o}\PY{l+s}{\PYZdq{}}\PY{p}{)} \end{Verbatim} \begin{center} \adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_12_0.png} \end{center} { \hspace*{\fill} \\} \begin{Verbatim}[commandchars=\\\{\}] {\color{outcolor}Out[{\color{outcolor}52}]:} PyObject \end{Verbatim} % Add a bibliography block to the postdoc \end{document}