{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Etude de l'influence de l'amplitude et de la période pour un signal périodique (version professeur)" ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ ":download:`Télécharger le pdf <./signal_periodique_professeur.pdf>`\n", "\n", ":download:`Télécharger le notebook <./signal_periodique_professeur.ipynb>`\n", "\n", ":download:`Lancer le notebook sur binder (lent) `" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous allons étudier un signal sinusoïdal. Un tel signal se répète identique à lui-même tous les 2 $\\pi$, au bout d'une durée T (période en s).\n", "\n", "Son évolution au cours du temps t se traduit par la fonction mathématique : A.sin((2$\\pi$/T).t) \n", "\n", "où A est l'amplitude\n", "\n", "Comme le temps t ne peut pas être continu, il faut le discrétiser, c'est à dire calculer t pour des valeurs entières, multiples d'une petite durée appelée *période d'échantillonnage* et notée Te.\n", "\n", "Te doit être suffisamment petit par rapport à T. \n", "\n", "Ce qui donne l'expression mathématique suivante : A.sin((2$\\pi$/T).i.Te) \n", "\n", "Avec i prenant des valeurs entières." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "# cette fonction permet d'afficher un graphique \n", "# à un emplacement précis de la fenêtre graphique. \n", "# Ainsi, on peut afficher plusieurs sous-graphiques \n", "# sur la même fenêtre.\n", "\n", "def affichage_graphique(n,y,l,yl) :\n", "# Déclaration du nombre d'emplacements dans la fenêtre \n", " plt.subplot(3,1,n) \n", "# Affichage de la courbe\n", " plt.plot(t,y,'k-',lw=1,label=n) \n", " # Impose les bornes min et max sur l'axe des ordonnées\n", " plt.ylim(-2,2) \n", " plt.grid()\n", " plt.xlabel('t (s)')\n", " plt.ylabel(yl)\n", " plt.legend()\n", "\n", "# Déclaration des variables\n", "Ymax=1 # amplitude en m\n", "T=1 # période en s\n", "Te=0.01 # période d'échantillonnage en s\n", "# Création des listes (vides) qui contiendront les valeurs \n", "# du temps et des amplitudes\n", "t=[] \n", "y1=[] \n", "\n", "# Boucle permettant de parcourir toutes les valeurs du temps \n", "# discrétisé.\n", "for i in range (0,1000) : \n", "# La méthode append permet de rajouter une valeur en fin \n", "# de la liste t\n", " t.append(i*Te) \n", "# la fonction sinus est contenue dans la bibliothèque numpy\n", "# la constante pi est contenue dans la bibliothèque numpy\n", " y1.append(Ymax*np.sin((2*np.pi/T)*i*Te)) \n", " \n", "\n", "# création du graphique \n", "\n", "# création de la fenêtre graphique\n", "plt.figure(2,figsize=(10,12)) \n", "# appel de la fonction gérant l'affichage du sous-graphique\n", "affichage_graphique(1,y1,\"courbe de référence\",\"y1 (m)\") \n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Etude préalable :**\n", "\n", "En tenant compte des renseignements donnés lignes 24, 25 et 33 répondez aux questions suivantes :\n", "1. Combien d'échantillons temporels aura-t-on?\n", "2. Par quel calcul simple aurait-on pu prévoir la durée du signal créé?\n", "3. Par quel calcul simple aurait-on pu prévoir le nombre de périodes affichées?\n", "4. Combien d'échantillons temporels a-t-on par période?\n", "\n", "Réponses :\n", "1. 1000 (voir boucle)\n", "2. durée = nb d'échantillons * Te = 1000 * 0.01 = 10 s\n", "3. nb périodes = durée / T = 10/1 = 10 périodes\n", "4. T/Te = 1/0.01 = 100 échantillons temporels par période" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous souhaitons étudier l'influence des paramètres A et T sur l'évolution temporelle du signal sinusoïdal.\n", "\n", "Pour cela, nous avons déjà écrit en lignes 25 et 37 du programme ci-dessous, la création d'un signal sinusoïdal de référence noté y1.\n", "\n", "Nous avons également déjà déclaré les listes y2 et y3 sur les lignes de code 26 et 27.\n", "\n", "Sur le modèle de la ligne 37, compléter la ligne 38 de manière à créer un signal sinusoïdal nommé y2 d'amplitude deux fois plus grande que y1.\n", "\n", "Puis, toujours sur le même modèle, compléter la ligne 39 de manière à créer un signal sinusoïdal nommé y3 de période deux fois plus grande que y1.\n", "\n", "Nous souhaitons de plus, afficher ces trois signaux en trois graphiques situés l'un au-dessous de l'autre. Nous allons pour cela utiliser la méthode plt.subplot(nombre de lignes, nombre de colonnes, index) de la bibliothèque matplotlib.pyplot as plt.\n", "\n", "L'affichage est géré par une fonction nommée affichage_graphique qui a besoin d'un certain nombre de paramètres (fournis entre parenthèses) pour fonctionner correctement.\n", "\n", "Sur le modèle de la ligne 43, écrire la ligne de code nécessaire à l'affichage de y2.\n", "\n", "Puis, toujours sur le modèle de la ligne 43, écrire la ligne de code nécessaire à l'affichage de y3." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "def affichage_graphique(n,y,l,yl) :\n", "# Déclaration du nombre d'emplacements dans la fenêtre\n", " plt.subplot(3,1,n) \n", "# Affichage de la courbe\n", " plt.plot(t,y,'k-',lw=1,label=n) \n", "# Impose les bornes min et max sur l'axe des ordonnées\n", " plt.ylim(-2,2) \n", " plt.grid()\n", " plt.xlabel('t (s)')\n", " plt.ylabel(yl)\n", " plt.legend()\n", "\n", "# Déclaration des variables\n", "Ymax=1 # amplitude en m\n", "T=1 # période en s\n", "Te=0.01 # période d'échantillonnage en s\n", "\n", "# Création des listes (vides) qui contiendront les valeurs\n", "# du temps et des amplitudes\n", "t=[] \n", "y1=[] \n", "y2=[]\n", "y3=[]\n", "\n", "# Boucle permettant de parcourir toutes les valeurs du temps discrétisé.\n", "for i in range (0,1000) : \n", "# La méthode append permet de rajouter une valeur en fin de la liste t\n", " t.append(i*Te) \n", "# la fonction sinus est contenue dans la bibliothèque numpy\n", "# la constante pi est contenue dans la bibliothèque numpy\n", "# On aurait pu aussi utiliser la bibliothèque math pour y avoir accés\n", "# à l'aide des fonctions math.sin() et math.pi\n", " y1.append(Ymax*np.sin((2*np.pi/T)*i*Te)) \n", " y2.append(2*Ymax*np.sin((2*np.pi/T)*i*Te))\n", " y3.append(Ymax*np.sin((2*np.pi/(2*T))*i*Te))\n", "\n", " # création de la fenêtre graphique\n", "plt.figure(2,figsize=(10,12)) \n", "affichage_graphique(1,y1,\"courbe de référence\",\"y1 (m)\")\n", "affichage_graphique(2,y2,\"amplitude doublée\",\"y2 (m)\")\n", "affichage_graphique(3,y3,\"période doublée\",\"y3 (m)\")\n", "\n", "plt.show()" ] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 4 }