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modelisationanalysespectrale/rossignol/nonParametrique/notebook.tex
hschindler ba48cde99b commit julia du sale
2019-10-02 14:36:08 +02:00

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% 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
}
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% 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.)
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\usepackage{longtable} % longtable support required by pandoc >1.10
\usepackage{booktabs} % table support for pandoc > 1.12.2
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\title{Analyse-Non-Param-Flute}
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\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}{;}
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\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}47}]:} \PY{k}{using} \PY{n}{Plots}
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\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 <matplotlib.image.AxesImage object at 0x7fac9988bb38>
\end{Verbatim}
% Add a bibliography block to the postdoc
\end{document}
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