{ "cells": [ { "cell_type": "markdown", "id": "b080b1e2-f275-4677-b719-0ad2752de4e7", "metadata": { "tags": [] }, "source": [ "| [README](README.ipynb) <= | FREQ1 : phaseurs | => [FREQ2](FREQ2_ondes_discretes.ipynb) | $\\|$ | [README](README.ipynb)\n", "|---------------------------|------------------|-----------------------------------|---|---: \n", "\n", "---\n", "# FREQ1 : phaseurs \n", " - [A](#A---Onde-imaginaire-et-partie-r%C3%A9elle) : Onde imaginaire et partie réelle\n", " - [B](#B---Phaseur) : Phaseur \n", " - [C](#C---Repr%C3%A9sentation-IQ:-a(n)-et-b(n)) : Représentation a(n) et b(n)\n", " - [D](#D---a(n),-b(n)-vers-phaseur) : a(n), b(n) vers phaseur\n", " - [E](#E--Repr%C3%A9sentation-avec-ondes-complexes-conjugu%C3%A9es-:-c(n)c(n),-c(%E2%88%92n)c(-n)) : Représentetion c(n) et c(-n)\n", " - [F](#F---Exercices-de-2IMACS-pour-s'entrainer...) : Exercices de 2IMACS\n", " - [G](#G---Somme-partielle-de-Fourier) : Somme partielle de Fourier\n", "---\n", "\n", "Pour tout exécuter cliquez sur le bouton play en haut de ce notebook. Pour exécuter juste une cellule de code :\n", "\n", "> Faites SHIT+ENTER pour exécuter une cellule et passer à la suivante\n" ] }, { "cell_type": "markdown", "id": "c507771d-e706-4c78-a734-c49feea4edd1", "metadata": {}, "source": [ " 1) Peut-être que les représentations \n", " $ \\mathcal{R}\\!\\!\\left[z_n.e^{i.\\omega_n.t}\\right] = \\quad \\quad c_n.e^{i\\omega_n.t} + \\overline{c_n}.e^{-i\\omega_n.t} \\quad \\quad = a_n.cos(\\omega_n.t)+b_n.\\sin(\\omega_n.t) \\quad= A_n.\\cos{(\\omega_n.t+\\varphi_n} )$ \n", "ne vous posent pas de problème : \n", " => sautez direct au [petits exos de 2IMACS](#Exercices-de-2IMACS-pour-s'entrainer...) pour vérifier que tout va bien.\n", " 2) Peut-être que les sommes partielle de Fourier et représentations spectrales ne vous posent pas de problème et \n", " => sautez direct à l'[exercice global](#Exercice-global)\n", " \n", "Peut-être vous avez le temps de revoir tout ça et lisez tout..." ] }, { "cell_type": "markdown", "id": "993812e0-1a02-4cc8-a436-d938c54ad0f5", "metadata": { "tags": [] }, "source": [ "## A - Onde imaginaire et partie réelle\n", "---\n", "\n", "On peut représenter l'onde complexe $t\\mapsto e^{i.\\omega.t}$ (notée en bref $e^{i.\\omega.\\bullet}$) dans le plan complexe (vision phaseur/Fresnel) ou la projeter sur les réels pour obtenir un cosinus.\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "a4dc5d2a-7619-4ffd-b542-89e0bf29dffd", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t=-0.5:0.01:1.1;\n", "f=1;\n", "w = exp(i*2*pi*f*t);\n", "\n", "Zi = 1;\n", "\n", "plot(t,real(Zi*w),'b');\n", "grid on; hold on;\n", "plot(t,imag(Zi*w),'r');\n", "\n", "xlabel('temps [s]');\n", "legend([\"partir reelle\";\"partir imaginaire\"]);\n" ] }, { "cell_type": "markdown", "id": "81d576a0-1e59-4df1-96b4-aedeef239a60", "metadata": {}, "source": [ "On comprend parfaitement ici la formule d'Euler appliquée à l'onde complexe : $e^{i\\omega.t}=\\cos(i\\omega.t) + i.\\sin(\\omega.t)$. \n", "Le cosinus est la partie réelle d'un nombre complexe qui tourne sur le cercle unité :\n", "\n", "\n", " " ] }, { "cell_type": "markdown", "id": "1d866a90-57df-4f08-99af-db718a1ba8eb", "metadata": { "tags": [] }, "source": [ "## B - Phaseur\n", "---\n", "Un phaseur $z$ est un nombre complexe qui va être multiplié à l'onde complexe $e^{i\\omega\\bullet}$.\n", "\n", "$A\\cos\\left(\\omega.t+\\varphi\\right) \\quad=\\quad \\mathcal{R}\\!\\!\\left[z.e^{i.\\omega.t}\\right]$ \n", "\n", "En représentation polaire $z=A.e^{i\\varphi}$ :\n", " - le module $A=|z|$ aura un effet d'amplification de l'onde \n", " - l'argument $\\varphi=\\arg(z)$ aura un effet de rotation d'un ampgle $\\varphi$ radians.\n", "\n", "Pour les produits complexes, les modules se multiplient et les arguments s'ajoutent (comme les arguments d'une exponentielle : d'où l'idée d'Euler de la notation $e^{i\\theta}$).\n", "\n", "$\\mathcal{R}\\!\\!\\left[z.e^{i.\\omega.t}\\right] = \\mathcal{R}\\!\\!\\left[A.e^{i\\varphi}.e^{i.\\omega.t}\\right] = \\mathcal{R}\\!\\!\\left[A.e^{i.(\\omega.t+\\varphi)}\\right] = A.\\mathcal{R}\\!\\!\\left[e^{i.(\\omega.t+\\varphi)}\\right] = A.\\cos(\\omega.t+\\varphi)$ \n", "\n", "\n", "L'onde multipliée aura ainsi un déphasage de $\\varphi$ par rapport à l'onde de base $e^{i\\omega\\bullet}$ e tune amplitude A\n", "\n" ] }, { "cell_type": "markdown", "id": "f700d797-c525-4426-a9df-acefd7328694", "metadata": { "tags": [] }, "source": [ "### Exercice phaseur de cosinus et de sinus\n", "Le phaseur appelé $z_I$ pour **In phase** (avec le cosinus), qui donnera les $a(n)$ des Séries de Fourier, est celui qui permet d'obtenir un **cosinus en partie réelle** : \n", "$z_I=1$ car la partie réelle de $e^{i\\omega.t}$ est déjà un cosinus. \n", "Car $1=1.e^{i.0}$ ce qui fait bien une amplitude 1 et une phase nulle pous $cos(\\omega.t)$\n", "\n", "Le phaseur appelé $z_Q$ pour **Quadrature** (avec le cosinus), qui donnera les b(n) des SdF, est celui qui permet d'obtenir un **sinus en partie réelle**.\n", "\n", "À vous de trouver la valeur du phaseur $z_Q$ donnant un sinus en partie réelle.\n", "\n", "La valeur proposée `Zq = 2j+1` n'est pas la bonne car $2i+1 = \\sqrt{3}.e^{i.\\textrm{atan}(2)}$ donne :\n", " - une amplitude $\\sqrt{3}$ trop grande. \n", "- une phase qui n'est pas le $-\\frac{\\pi}{2}$ voulu car le sinus est bien en retard sur le cos : $\\sin(\\omega.t)=\\cos(\\omega.t-\\frac{\\pi}{2})$\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "916b9ccf-a1c9-43cc-83f2-e59e06d2da51", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# A VOUS DE TROUVER Zq = ? donnant le sinus\n", "Zq = 2j+1; # Modifiez ce nombre complexe et SHIFT + ENTREE pour voir\n", "\n", "t = 0:0.01:0.9; w = exp(i*2*pi*f*t);\n", "subplot(121);\n", "plot(real(Zi*w),imag(Zi*w),'b'); hold on;\n", "plot(real(Zq*w),imag(Zq*w),'r'); grid on;\n", "plot(real(Zi),imag(Zi),'ob'); xlabel('reels');\n", "plot(real(Zq),imag(Zq),'or'); ylabel('imag.');\n", "\n", "axis(\"square\");\n", "subplot(122);\n", "plot(t,real(Zi*w),'b'); hold on;\n", "plot(t,real(Zq*w),'r'); grid on;\n", "plot(0,real(Zi),'ob'); \n", "plot(0,real(Zq),'or'); \n", "\n", "axis(\"square\");\n" ] }, { "cell_type": "markdown", "id": "e8931c55-79b1-4505-ac6e-c9cd78ec118b", "metadata": { "tags": [] }, "source": [ "#### Corrigé\n", "Déroulez la cellule pour avoir la réponse. " ] }, { "cell_type": "markdown", "id": "797f158a-a033-41e7-ba37-b20b447aa4f7", "metadata": {}, "source": [ "Le phaseur est donc un vecteur du plan complexe représenté à l'instant $t=0$. Ce vecteur tourne en étant multiplié par $e^{i\\omega t}$ créant une onde complexe dont la partie réelle est le signal réel représenté. En représentation I, Q le phaseur est décomposé en :\n", "* Phaseur \"In phase\" : $z_I = 1.e^{i 0} \\quad= 1$ (bleu) est sur l'axe réel vers la droite ($A_2=1, \\varphi_2=0$) : sa projection sur les réels donne $\\cos{\\omega t}$\n", "* Phaseur \"in Quadrature\" : $z_Q = 1.e^{-i\\frac{\\pi}{2}} \\quad = -i$ (rouge) est **vers le bas !** sur l'axe imaginaire ($A_1=1, \\varphi_1=-\\frac{\\pi}{2}$) : sa projection sur les réels donne $\\sin(\\omega t)$\n", "\n", "Il fallait donc mettre `Zq = -j` dans le code Octave" ] }, { "cell_type": "markdown", "id": "7879c059-e058-4bfc-822d-e92eebbb6891", "metadata": { "tags": [] }, "source": [ "## C - Représentation IQ: a(n) et b(n)\n", "---\n", "\n", "On peut représenter n'importe quelle onde déphasée et amplifiée sous forme d'un cosinus + un sinus.\n", "\n", "En télécom c'est la représentation IQ et ce sont nos fameux coefficient $a(n)$ et $b(n)$ d'une série de Fourier : \n", "$A.cos(\\omega.t+\\varphi) = a.\\cos(\\omega.t) + b.\\sin(\\omega.t) = a.\\mathcal{R}\\!\\!\\left[z_I.e^{i\\omega.t} \\right] + b . \\mathcal{R}\\!\\!\\left[z_Q.e^{i\\omega.t}\\right] = \\mathcal{R}\\!\\!\\left[(a.z_I + b.z_Q).e^{i\\omega.t} \\right]$" ] }, { "cell_type": "markdown", "id": "29dff1d7-4986-404d-8800-642124711f5b", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "Pour les séries de Fourier on utilise des pulsations multiples d'une pulsation fondamentale $\\omega_0$ et pour chaque multiple de rang $n$ de pulsation $\\omega_n = n.\\omega_0$ on aura une onde déphasée représentée par deux coefficients $a(n)$ et $b(n)$ :\n", "\n", "$A_n . cos(\\omega_n.t+\\varphi_n) = a(n).\\cos(\\omega_n.t) + b(n).\\sin(\\omega_n.t)= a(n).\\mathcal{R}\\!\\!\\left[z_I.e^{i\\omega.t} \\right] + b(n) . \\mathcal{R}\\!\\!\\left[z_Q.e^{i\\omega.t}\\right] = \\mathcal{R}\\!\\!\\left[(a(n).z_I + b(n).z_Q).e^{i\\omega.t} \\right]$" ] }, { "cell_type": "markdown", "id": "5174d55e-51fd-440f-b00b-9acc261fd0e3", "metadata": { "tags": [] }, "source": [ "### Exercice a(n), b(n) -> amplitude,phase\n", " - Savoir afficher un signal\n", " - Savoir mesurer une amplitude, phase sur un graphique\n", "\n", "**Diable !** les valeurs `666` ne sont pas les bonnes...\n", "À vous de :\n", " - construire et afficher le signal $a(n).\\cos(\\omega_n.t) + b(n).\\sin(\\omega_n.t)$\n", " - faire les mesures sur le graphique (comme sur un ocsilloscope : mesure du temps d'un pic, mesure de la période etc.)\n", " - estimer/calculer $A(n)$ et $\\varphi(n)$" ] }, { "cell_type": "code", "execution_count": 4, "id": "a21c3ab9-4b56-4af9-9355-f74960004af7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "an = 1.7321\n", "bn = -1\n", "A_n = 666\n", "Phi_n = 0.0047171\n" ] } ], "source": [ "%% Exemple de somme IQ ou a(n) b(n)\n", "F0 = 2 ; w0=2*pi*F0; % fréquence fondamentale d'une série de Fourier\n", "n = 1; wn = n*w0; % rang de la composante n\n", "an = sqrt(3)/n % coefs de Fourier\n", "bn = (-1)^n/n\n", "\n", "%% VOTRE CODE qui affiche la composante de rang n.\n", "\n", "%% VOTRE mesure graphique de l'amplitude et de la phase.\n", "A_n = 666 % mesure de l'amplitude\n", "Phi_n =pi/666 % mesure de la phase " ] }, { "cell_type": "markdown", "id": "b9dbf920-0179-43a2-8708-70980ad05b33", "metadata": { "tags": [] }, "source": [ "#### Corrigé de l'exercice\n", "\n", "Déroulez la cellule pour voir" ] }, { "cell_type": "code", "execution_count": 5, "id": "d13c94a0-5278-40ed-b249-53669b612f2f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "an = 1.7321\n", "bn = -1\n", "A_n = 2\n", "Phi_n = 0.50265\n", "Phi_n_deg = 28.800\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%% Exemple de somme IQ ou a(n) b(n)\n", "F0 = 2 ; w0=2*pi*F0; % fréquence fondamentale d'une série de Fourier\n", "n = 1; wn = n*w0; % rang de la composante n\n", "an = sqrt(3)/n % coefs de Fourier\n", "bn = (-1)^n/n\n", "\n", "%% VOTRE CODE qui affiche la composante de rang n.\n", "T0 = 1/F0;\n", "t = -0.5:0.01:T0;\n", "plot(t,an*cos(wn*t)+bn*sin(wn*t));\n", "grid on;\n", "xlabel(\"temps [s]\")\n", "ylabel(\"signal [V]\")\n", "%% VOTRE mesure graphique de l'amplitude et de la phase.\n", "A_n = 2 % mesure de l'amplitude\n", "% Le maximum (-tm,2) est en avance de l'instant 0 à environ \n", "tm = -0.04; \n", "hold on; plot(tm,2,'or');\n", "% L'écart de temps par rapport à 0 est donc\n", "Dt = 0 - tm;\n", "% ce qui fait un déphasage Dt/T0 * 2pi\n", "Phi_n =Dt/T0*2*pi % mesure de la phase v[rad]\n", "Phi_n_deg = Phi_n * 180/pi % en degrés\n", "% déphasage positif car l'onde est en avance sur le cosinus" ] }, { "cell_type": "markdown", "id": "9b267ab8-2098-475e-aceb-7b1661a3d2c6", "metadata": { "tags": [] }, "source": [ "## D - a(n), b(n) vers phaseur\n", "---\n", "Dans une somme $a(n).\\cos(\\omega_n.t) + b(n).\\sin(\\omega_n.t)$ il suffit de faire la somme des phaseurs pour avoir la représentation IQ :\n", "\n", "$a(n).\\mathcal{R}\\left(z_I.e^{i.\\omega_n.t}\\right) + b(n).\\mathcal{R}\\left(z_Q.e^{i.\\omega_n.t}\\right) = \\mathcal{R}\\left(\\overbrace{(a(n).z_I+b(n).z_Q)}^{z_n}.e^{i.\\omega_n.t}\\right)$\n", "\n", "\n", "On décompose alors $z_n = a(n).z_I + b(n).z_Q = a(n) -i. b(n)$ pour obtenir $s(t) = a(n).\\cos(\\omega_n.t) + b(n).\\sin(\\omega_n.t)= \\mathcal{R}\\left(z_n.e^{i.\\omega_n.t}\\right)$" ] }, { "cell_type": "markdown", "id": "4815c343-4365-49d2-81b1-13b6b382c90b", "metadata": { "tags": [] }, "source": [ "Ajouter deux ondes, c'est ajouter leurs phaseurs et inversement :\n", "\n", " \n", " \n", " \n", " \n", "
\\( \\begin{array}{c} y(t) = \\overbrace{A.e^{i\\varphi}}^{\\text{phaseur } z_y}.e^{i.\\omega t} \\in \\mathbb{C} \\\\ s(t) = \\mathcal{R}\\left(y(t)\\right) \\in \\mathbb{R} = A\\cos(\\omega t + \\varphi) \\\\ \\\\ \\mathcal{R}\\left(y_1(t)=z_1.e^{i\\omega t}\\right) = A_1\\cos(\\omega t + \\varphi_1) \\\\ \\mathcal{R}\\left(y_2(t)=z_2.e^{i\\omega t}\\right) = A_2\\cos(\\omega t + \\varphi_2) \\\\ y(t) = y_1(t) + y_2(t) = \\underbrace{(z_1+z_2)}_{z}.e^{i\\omega t} \\in \\mathbb{C} \\\\ \\\\ z = z_1 + z_2 \\text{ constantes complexes}\\\\\\mathcal{R}\\left(y=y_1+y2\\right) = \\mathcal{R}\\left(y_1\\right) + \\mathcal{R}\\left(y_2\\right) \\\\ A\\cos(\\omega t + \\varphi) = A_2\\cos(\\omega t + \\varphi_2) + A_1\\cos(\\omega t + \\varphi_1) \\end{array} \\)
" ] }, { "cell_type": "markdown", "id": "48d25556-de1e-43f2-aa66-aadfa46bc39d", "metadata": { "tags": [] }, "source": [ "### Exercice a(n), b(n) vers phaseur\n" ] }, { "cell_type": "markdown", "id": "cba3bec1-3097-47fa-ba4e-d7ad43c0fd3f", "metadata": { "tags": [] }, "source": [ "\n", " 1) Retrouvez le phaseur de l'exercice précédent à partir de a(n), b(n)\n", " 2) Afficher : les représentations a(n), b(n) \"rouge\" et phaseur \"noir\" doivent coller.\n", " 3) Retrouver l'amplitude et phase (environ 2 et +29 degrés) à partir de $z_n$. " ] }, { "cell_type": "code", "execution_count": 4, "id": "997fb6f6-0229-4737-9d3a-ca69d009e958", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "An = 0.732051 \t et on doit avoir environ 2\n", "Phase = 125.264390 (deg) \t et on doit avoir environ +29 degrés\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(t,an*cos(wn*t)+bn*sin(wn*t),'r'); hold on\n", "\n", "%% 1 - VOTRE CODE zn = f(an,bn)\n", "Zi = 1; \n", "Zq = -i; % fameux signe - du phaseur Q\n", "zn = an + bn;\n", "\n", "%% 2- VOTRE affichage du signal temporel \n", "% Restez bien réels !\n", "plot(t,t,'k'); \n", "% le rouge et le noir ne s'épousent-ils pas ?\n", "grid on;\n", "xlabel(\"temps [s]\")\n", "ylabel(\"signal [V]\")\n", "\n", "%% 3 - VOTRE calcul de l'amplitue et phase à partir de zn.\n", "% pour les complexes : abs (module), angle(argument), real ,imag\n", "A_n = real(zn) ;\n", "Phi_n = acos(bn/an);\n", "printf(\"An = %f \\t et on doit avoir environ 2\\n\",A_n)\n", "printf(\"Phase = %f (deg) \\t et on doit avoir environ +29 degrés\\n\",Phi_n*180/pi)" ] }, { "cell_type": "markdown", "id": "34e0989a-6f8c-4ad7-978f-4d88b6be9bbc", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Corrigé\n", "\n", "Déroulez la cellule cachée ici\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "25880151-c495-4f84-8859-61475eea8472", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "an = 1.7321\n", "bn = -1\n", "zn = 1.7321 + 1.0000i\n", "Phi_n = -0.52360\n", "Phi_n = 0.52360\n", "An = 2.000000 \t et on doit avoir environ 2\n", "Phase = 30.000000 (deg) \t et on doit avoir environ +29 degrés\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "an\n", "bn\n", "t=0:0.01:2;\n", "plot(t,an*cos(wn*t)+bn*sin(wn*t),'r-o'); hold on;\n", "\n", "%% 1 - VOTRE CODE zn = f(an,bn)\n", "Zi=1; Zq = -i;\n", "zn = an*Zi + bn * Zq ; %on ajoute les phaseurs\n", "zn = an -i* bn % ce qui donne le fameux signe - !\n", "\n", "%% 2- VOTRE affichage du signal temporel \n", "% Restez bien réels !\n", "plot(t,real(zn*exp(i*wn*t)),'k'); \n", "% le rouge et le noir ne s'épousent-ils pas ?\n", "grid on;\n", "xlabel(\"temps [s]\")\n", "ylabel(\"signal [V]\")\n", "\n", "%% 3 - VOTRE calcul de l'amplitue et phase à partir de zn.\n", "% pour les complexes : abs (module), angle(argument), real ,imag\n", "A_n = abs(zn) ;\n", "Phi_n = atan(bn/an) % est faux ! => piège du Zq = -i \n", "Phi_n = angle(zn) \n", "printf(\"An = %f \\t et on doit avoir environ 2\\n\",A_n)\n", "printf(\"Phase = %f (deg) \\t et on doit avoir environ +29 degrés\\n\",Phi_n*180/pi)" ] }, { "cell_type": "markdown", "id": "b1ed6a78-636b-4ac8-91bf-74a6a0255c78", "metadata": { "tags": [] }, "source": [ "## E- Représentation avec ondes complexes conjuguées : $c(n)$, $c(-n)$ \n", "---\n", "\n", "La partie réelle d'une onde complexe peut être obtenue par la **somme de deux conjugués** $e^{i.\\omega_n.t}$ et $e^{-i.\\omega_n.t}$ : car $2.\\mathcal{R}(z) = z + \\overline{z}$\n", "> On fait apparaître une **fréquence négative -$\\omega_n$**, car ce sont des **ondes imaginaires qui s'ajoutent pour donner une onde réelle**.\n", "\n", "Ainsi pour une composante de rang n d'une série nous avons 4 représentations : \n", "\n", "$ \\mathcal{R}\\!\\!\\left[z_n.e^{i.\\omega_n.t}\\right] = \\quad \\quad c_n.e^{i\\omega_n.t} + \\overline{c_n}.e^{-i\\omega_n.t} \\quad \\quad = a_n.cos(\\omega_n.t)+b_n.\\sin(\\omega_n.t) \\quad= A_n.\\cos{(\\omega_n.t+\\varphi_n} )$" ] }, { "cell_type": "markdown", "id": "8252353b-6c6c-4c49-a19f-9d20034d6404", "metadata": { "tags": [] }, "source": [ "Les composantes d'une série de Fourier étant des ondes complexes, on peut les représenter en phaseur, IQ et aussi en somme de conjugués car :\n", "\n", "$s(t) = \\mathcal{R}\\left(z.e^{i\\omega t}\\right) = \\frac{z.e^{i\\omega t} + \\overline{z.e^{i\\omega t}}}{2} = \\underbrace{\\frac{z}{2}}_{c(n)}.e^{i\\omega t} + \\underbrace{\\frac{\\overline{z}}{2}}_{c(-n)}.e^{-i\\omega t}$\n", "\n", "Remarquez que pour qu'une onde soit réelle dans la représentation complexe $c(n).e^{i n \\omega_0 t}+c(-n).e^{-i n \\omega_0 t}$ ***pour tout t***, il faut que $c(n).e^{i n \\omega_0 t}$ soit le conjugué de $c(-n).e^{-i n \\omega_0 t}$ ce qui impose :\n", " - f réelle, $\\forall t \\quad \\implies \\quad c(n)=\\overline{c(-n)}, \\forall n$\n", " - $\\exists t \\;|\\; f(t)$ imaginaire $\\implies \\quad \\exists n \\;|\\; c(n)\\neq\\overline{c(-n)}$\n", "\n" ] }, { "cell_type": "markdown", "id": "3d6b6642-8e03-452e-9260-a2a60eab3689", "metadata": { "tags": [] }, "source": [ "### Exercice\n", "Donnez la représentation en c(n) de l'onde précédente.\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "e45a238c-d52a-41a3-9425-6984a8eff5f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "an = 1.7321\n", "bn = -1\n", "zn = 1.7321 + 1.0000i\n", "Phi_n = 0.52360\n", "c_moins_n = -1.7321\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "an\n", "bn\n", "zn = an -i* bn \n", "A_n = abs(zn) ;\n", "Phi_n = angle(zn)\n", "\n", "%% VOTRE CODE cn=\n", "c_n = an;\n", "c_moins_n = -an\n", "\n", "t=0:0.01:2;\n", "plot(t,A_n*cos(wn*t+Phi_n),'g'); hold on;\n", "plot(t,real(zn*exp(i*wn*t)),'k'); \n", "plot(t,an*cos(wn*t)+bn*sin(wn*t),'ro');\n", "\n", "%% VOTRE affichage de la représentation en c(n) en \"bleu avec des +\"\n", "% le rouge et le noir, le vert et le bleu ne s'épousent-ils pas ?\n", "\n", "grid on;\n", "xlabel(\"temps [s]\")\n", "ylabel(\"signal [V]\")\n" ] }, { "cell_type": "markdown", "id": "4f763d9e-7611-4d7a-8fca-ea4994eb0024", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Corrigé\n", "\n", "Déroulez la cellule cachée ici" ] }, { "cell_type": "code", "execution_count": 7, "id": "2f7875e4-800e-4339-b0c0-c92c215277df", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "an = 1.7321\n", "bn = -1\n", "zn = 1.7321 + 1.0000i\n", "Phi_n = 0.52360\n", "c_n = 0.86603 + 0.50000i\n", "c_n = 0.86603 + 0.50000i\n", "c_moins_n = 0.86603 - 0.50000i\n", "c_moins_n = 0.86603 - 0.50000i\n", "energie_imaginaire = 0\n", "energie_reelle = 403.00\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "an\n", "bn\n", "zn = an -i* bn \n", "A_n = abs(zn) ;\n", "Phi_n = angle(zn)\n", "\n", "%% VOTRE CODE cn=\n", "c_n = zn/2\n", "c_n= an/2-i*bn/2\n", "c_moins_n = conj(c_n)\n", "c_moins_n = an/2+i*bn/2\n", "\n", "\n", "t=0:0.01:2;\n", "plot(t,A_n*cos(wn*t+Phi_n),'g'); hold on;\n", "plot(t,real(zn*exp(i*wn*t)),'k'); \n", "plot(t,an*cos(wn*t)+bn*sin(wn*t),'ro');\n", "\n", "%% VOTRE affichage de la représentation en c(n) en \"bleu avec des +\"\n", "% le rouge et le noir, le vert et le bleu ne s'épousent-ils pas ?\n", "s_n = c_n*exp(i*wn*t);;\n", "s_moins_n = c_moins_n*exp(-i*wn*t);\n", "s = s_n + s_moins_n;\n", "plot(t, s,'b+')\n", "grid on;\n", "xlabel(\"temps [s]\")\n", "ylabel(\"signal [V]\")\n", "\n", "%% VOTRE CODE qui vérifie que le signal est bien réel \n", "s_i = imag(s); % on extrait la partie imaginaire et réelle\n", "s_r = real(s); %\n", "\n", "% On calcule la norme 2 par produit scalaire\n", "energie_imaginaire = s_i*transpose(s_i)\n", "energie_reelle = s_r*transpose(s_r)\n" ] }, { "cell_type": "markdown", "id": "740c98ff-6117-440d-a5da-6f9e546f539f", "metadata": { "tags": [] }, "source": [ "#### Bonus dans le plan complexe\n", "On peut visualiser le phaseur qui tourne et les deux ondes complexes conjuguées qui s'ajoutent pour faire sa partie réelle." ] }, { "cell_type": "code", "execution_count": 8, "id": "768df3b4-6c3d-4af4-83a1-5763780fad32", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = 0:0.01:0.1; \n", "w = exp(i*wn*t);\n", "\n", "%cercle unité\n", "plot(cos(0:0.1:2*pi), sin(0:0.1:2*pi), 'k--'); hold on ;\n", "\n", "plot(real(zn*w),imag(zn*w),'k'); % zn \n", "plot(real(c_n*w),imag(c_n*w),'b'); % c(n) \n", "plot(real(c_moins_n*exp(-i*wn*t)),\n", " imag(c_moins_n*exp(-i*wn*t)),'r'); % c(-n) \n", "\n", "plot([0, real(zn)],[0,imag(zn)],'ok'); \n", "plot(real(c_n),imag(c_n),'ob'); \n", "plot(real(c_moins_n),imag(c_moins_n),'or'); \n", "\n", "xlabel('reels');\n", "ylabel('imag.');\n", "legend([\"cercle unite\";\"z(n)\";\"c(n)\";\"c(-n)\"])\n", "axis(\"square\");\n", "grid on;" ] }, { "cell_type": "markdown", "id": "e22a23c9-a36b-4f55-b609-2d3a8c763a59", "metadata": { "tags": [] }, "source": [ "## F - Exercices de 2IMACS pour s'entrainer...\n", "---" ] }, { "cell_type": "markdown", "id": "fff66e5f-d855-4b3d-bca5-a143ef92db25", "metadata": { "tags": [] }, "source": [ "### Exercice : Phaseur vers IQ et A$\\varphi$\n", "> Exercice [Ch2-Ex2.2 a)](https://moodle.insa-toulouse.fr/mod/resource/view.php?id=24741#page=35) : \n", "> Dans l'expression $(1+j).e^{i.10.t}$, vous retrouvez un phaseur $(1+j)$ qu'il est facile de décomposer en IQ (attention au signe !). \n", "> Dans le plan complexe l'amplitude $A$ et la phase $\\phi$ se retrouvent facilement en écrivant le phaseur en coordonnées polaires : $i+j = \\sqrt{2}.e^{i.\\frac{\\pi}{4}}$." ] }, { "cell_type": "code", "execution_count": 9, "id": "ef053a8a-72f7-4ba2-a500-8a71d2f81049", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w = 0.66600\n", "A = 0.66600\n", "phi = 2 pi / 3\n", "z = 1 + 1i\n", "a = 0.66600\n", "b = 0.66600\n", "c_n = 0.66600\n", "c_moins_n = 0.66600\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## VOS VALEURS manquantes à la place de \"0.666\"\n", "clear all;\n", "w = 0.666 % pulsation [rad/s]\n", "A = 0.666 % amplitude [V] \n", "phi = 0.666 *pi; % phase [rad]\n", "printf(\"phi = 2 pi / %.0f\\n\",2*pi/phi)\n", "z = 1+j % phaseur [V] complexe\n", "a = 0.666 % I in phase ou a(n) [V]\n", "b = 0.666 % Q Quadrature ou b(n) [V]\n", "c_n = 0.666 % c(n) [V] complexe\n", "c_moins_n = 0.666 % c(-n) [V] complexe \n", "\n", "\n", "f=w/2/pi; T = 1/f; t=-T/2:T/20:T/2;\n", "plot(t,real(z*exp(i*w*t)), \"k\"); hold on;\n", "plot(t,A*cos(w*t+phi), \"ro\"); \n", "plot(t,a*cos(w*t)+b*sin(w*t), \"b+\");\n", "plot(t,c_n*exp(i*w*t)+c_moins_n*exp(-i*w*t), \"gd\");\n", "plot(t,cos(w*t),'k--');\n", "tm = -phi/2/pi*T;\n", "plot([0,tm,tm],[1,1,A],\"k->\")\n", "text(tm,0.9,[\"Dt=1/\",num2str(T/abs(tm)),\".T\"])\n", "grid on;\n", "legend([\"phaseur\";\"ampli., phase\";\"a(n),b(n)\";\"c(n),c(-n)\";\"cos\"])\n" ] }, { "cell_type": "markdown", "id": "a94d0433-0d17-4a66-9ebd-e9b70794cfe6", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Corrigé\n", "\n", "Déroulez la cellule cahcée ici" ] }, { "cell_type": "code", "execution_count": 10, "id": "09f06abf-988f-4f91-85de-536c618ff440", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w = 10\n", "A = 1.4142\n", "phi = 2 pi / 8\n", "z = 1 + 1i\n", "a = 1\n", "b = -1\n", "c_n = 0.50000 + 0.50000i\n", "c_moins_n = 0.50000 - 0.50000i\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## CORRIGÉ\n", "w = 10 % pulsation [rad/s]\n", "A = sqrt(2) % amplitude [V] \n", "phi = pi/4 ; % phase [rad]\n", "printf(\"phi = 2 pi / %.0f\\n\",2*pi/phi)\n", "z = 1+j % phaseur [V] complexe\n", "a = 1 % I in phase ou a(n) [V]\n", "b = -1 % Q Quadrature ou b(n) [V]\n", "c_n = 1/2 + j/2 % c(n) [V] complexe\n", "c_moins_n = 1/2 - j/2 % c(-n) [V] complexe \n", "\n", "\n", "f=w/2/pi; T = 1/f; t=-T/2:T/20:T/2;\n", "plot(t,real(z*exp(i*w*t)), \"k\"); hold on;\n", "plot(t,A*cos(w*t+phi), \"ro\"); \n", "plot(t,a*cos(w*t)+b*sin(w*t), \"b+\");\n", "plot(t,c_n*exp(i*w*t)+c_moins_n*exp(-i*w*t), \"gd\");\n", "plot(t,cos(w*t),'k--');\n", "tm = -phi/2/pi*T;\n", "plot([0,tm,tm],[1,1,A],\"k->\")\n", "text(tm,0.9,[\"Dt=1/\",num2str(T/abs(tm)),\".T\"])\n", "grid on;\n", "legend([\"phaseur\";\"ampli., phase\";\"a(n),b(n)\";\"c(n),c(-n)\";\"cos\"])\n" ] }, { "cell_type": "markdown", "id": "f79c109c-993b-403b-9a74-22343aca8760", "metadata": { "tags": [] }, "source": [ "### Exercice : A$\\varphi$ vers Phaseur et IQ \n", "> Exercice [Ch2-Ex4 a)](https://moodle.insa-toulouse.fr/mod/resource/view.php?id=24741#page=35) : \n", "> * Dans $\\frac{1}{2}e^{i.2\\pi.t+\\frac{\\pi}{3}}$, trouvez le phaseur en factorisant ce qui est constant dans le temps pour avoir la forme $Z.e^{i.\\omega.t}$ avec $Z=\\rho.e^{i.\\varphi}\\in\\mathbb{C}$ le phaseur et $\\omega\\in\\mathbb{R}$ la pulsation en rad/s \n", "> * Passez ce phaseur de la représentation polaire à la forme $R+i.I$ et trouvez ainsi le I (ou $a_n$) et le Q (ou $b_n$) permettant d'avoir $I\\cos(\\omega.t)+Q\\sin(\\omega.t)$\n", "> On doit obtenir une sinusoïde d'amplitude 0.5 avec $\\frac{\\pi}{3}$ d'avance de phase sur le cosinus, car \n", "> $\\mathcal{R}\\!\\!\\left(\\frac{1}{2}.e^{2\\pi.t+\\frac{\\pi}{3}}\\right) = \\frac{1}{2}.\\cos\\left(2\\pi.t+\\frac{\\pi}{3}\\right)$" ] }, { "cell_type": "code", "execution_count": 11, "id": "1aab2f9f-3ec2-4bb4-b5ae-4e1ce743bbd9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w = 0.66600\n", "A = 0.66600\n", "phi = 2 pi / 3\n", "z = 0.66600\n", "a = 0.66600\n", "b = 0.66600\n", "c_n = 0.66600\n", "c_moins_n = 0.66600\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## VOS VALEURS manquantes à la place de \"0.666\"\n", "clear all;\n", "w = 0.666 % pulsation [rad/s]\n", "A = 0.666 % amplitude [V] \n", "phi = 0.666 *pi; % phase [rad]\n", "printf(\"phi = 2 pi / %.0f\\n\",2*pi/phi)\n", "z = 0.666 % phaseur [V] complexe\n", "a = 0.666 % I in phase ou a(n) [V]\n", "b = 0.666 % Q Quadrature ou b(n) [V]\n", "c_n = 0.666 % c(n) [V] complexe\n", "c_moins_n = 0.666 % c(-n) [V] complexe \n", "\n", "f=w/2/pi; T = 1/f; t=-T/2:T/20:T/2;\n", "plot(t,real(1/2*exp(i*(2*pi*t+pi/3))),'k.-');hold on;\n", "plot(t,real(z*exp(i*w*t)), \"kd-\"); \n", "plot(t,A*cos(w*t+phi), \"ro\"); \n", "plot(t,a*cos(w*t)+b*sin(w*t), \"b+\");\n", "plot(t,c_n*exp(i*w*t)+c_moins_n*exp(-i*w*t), \"gd\");\n", "plot(t,cos(w*t),'k--');\n", "tm = -phi/2/pi*T;\n", "plot([0,tm,tm],[1,1,A],\"k->\")\n", "text(tm,0.9,[\"Dt=1/\",num2str(T/abs(tm)),\".T\"])\n", "grid on;\n", "legend([\"formule exo\"; \"phaseur\";\"ampli., phase\";\"a(n),b(n)\";\"c(n),c(-n)\";\"cos\"])\n" ] }, { "cell_type": "markdown", "id": "bb0e9172-e0ab-4ee7-942b-568e05e859b1", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Corrigé\n", "\n", "Déroulez la cellule cachée ici." ] }, { "cell_type": "code", "execution_count": 13, "id": "f36f6af1-e3b6-42d4-929e-f99d3caf167e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w = 6.2832\n", "A = 0.50000\n", "phi = 2 pi / 6\n", "z = 0.25000 + 0.43301i\n", "a = 0.25000\n", "b = -0.43301\n", "c_n = 0.12500 + 0.21651i\n", "c_moins_n = 0.12500 - 0.21651i\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## VOS VALEURS manquantes à la place de \"0.666\"\n", "w = 2*pi % pulsation [rad/s]\n", "A = 0.5 % amplitude [V] \n", "phi = pi/3 ; % phase [rad]\n", "printf(\"phi = 2 pi / %.0f\\n\",2*pi/phi)\n", "z = 0.25+i*sqrt(3)/4 % phaseur [V] complexe\n", "a = 0.25 % I in phase ou a(n) [V]\n", "b = -sqrt(3)/4 % Q Quadrature ou b(n) [V]\n", "c_n = 0.125 + j*sqrt(3)/8 % c(n) [V] complexe\n", "c_moins_n = 0.125 - j*sqrt(3)/8 % c(-n) [V] complexe \n", "\n", "f=w/2/pi; T = 1/f; t=-T/2:T/20:T;\n", "plot(t,real(1/2*exp(i*(2*pi*t+pi/3))),'k.-');hold on;\n", "plot(t,real(z*exp(i*w*t)), \"kd-\"); \n", "plot(t,A*cos(w*t+phi), \"ro\"); \n", "plot(t,a*cos(w*t)+b*sin(w*t), \"b+\");\n", "plot(t,c_n*exp(i*w*t)+c_moins_n*exp(-i*w*t), \"gd\");\n", "plot(t,cos(w*t),'k--');\n", "tm = -phi/2/pi*T;\n", "plot([0,tm,tm],[1,1,A],\"k->\")\n", "text(tm,0.9,[\"Dt=1/\",num2str(T/abs(tm)),\".T\"])\n", "grid on;\n", "legend([\"formule exo\"; \"phaseur\";\"ampli., phase\";\"a(n),b(n)\";\"c(n),c(-n)\";\"cos\"])\n" ] }, { "cell_type": "markdown", "id": "fa89885f-a11c-49a1-9861-d3e6f0e0e4eb", "metadata": { "tags": [] }, "source": [ "### Exercice : IQ vers phaseur vers A$\\varphi$\n", "> Exercice [Ch2-Ex4 c)](https://moodle.insa-toulouse.fr/mod/resource/view.php?id=24741#page=35) : \n", "> * Dans $\\frac{\\sqrt{3}}{2}.\\cos\\left(2\\pi.t\\right)+\\frac{1}{2}.\\sin\\left(2\\pi.t\\right)$ vous avez directement la représentation IQ. Donnez le phaseur $Z_c=a + i.b$ en faisant attention au signe. Quelle doit être la période $T$[s], la fréquence $f$[Hz] et la pulsation $\\omega$[rad/s] de ce signal.\n", "> * Passez ce phaseur à la représentation polaire $Z_c = \\rho.e^{i.\\varphi}= a+I.b$ et trouvez ainsi l'amplitude et le déphasage du cosinus $\\rho .\\cos\\left(\\omega.t+\\varphi\\right)$" ] }, { "cell_type": "code", "execution_count": 14, "id": "571c5adc-1c21-4335-bbc3-e58f2e0528b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w = 0.66600\n", "A = 0.66600\n", "phi = 0.66600\n", "phi = 2 pi / 9.4z = 0.66600\n", "a = 0.86603\n", "b = 0.50000\n", "c_n = 0.66600\n", "c_moins_n = 0.66600\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## VOS VALEURS manquantes à la place de \"0.666\"\n", "w = 0.666 % pulsation [rad/s]\n", "A = 0.666 % amplitude [V] \n", "phi = 0.666 % phase [rad]\n", "printf(\"phi = 2 pi / %.1f\",2*pi/phi)\n", "z = 0.666 % phaseur [V] complexe\n", "a = sqrt(3)/2 % I in phase ou a(n) [V]\n", "b = 1/2 % Q Quadrature ou b(n) [V]\n", "c_n = 0.666 % c(n) [V] complexe\n", "c_moins_n = 0.666 % c(-n) [V] complexe \n", "\n", "\n", "f=w/2/pi; T = 1/f; t=-T/2:T/20:T/2;\n", "plot(t,real(z*exp(i*w*t)), \"k\"); hold on;\n", "plot(t,A*cos(w*t+phi), \"ro\"); \n", "plot(t,a*cos(w*t)+b*sin(w*t), \"b+\");\n", "plot(t,c_n*exp(i*w*t)+c_moins_n*exp(-i*w*t), \"gd\");\n", "plot(t,cos(w*t),'k--');\n", "tm = -phi/2/pi*T;\n", "plot([0,tm,tm],[1,1,A],\"k->\")\n", "text(tm,0.9,[\"Dt=1/\",num2str(T/abs(tm)),\".T\"])\n", "grid on;\n", "legend([\"phaseur\";\"ampli., phase\";\"a(n),b(n)\";\"c(n),c(-n)\";\"cos\"])\n" ] }, { "cell_type": "markdown", "id": "2751f67b-3db1-4e07-995f-4fff31dd5390", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "#### Corrigé\n", "\n", "Déroulez la cellule cachée ici" ] }, { "cell_type": "code", "execution_count": 15, "id": "8c746a8d-f232-4bf4-8887-57b38f60858f", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w = 6.2832\n", "A = 1\n", "phi = 2 pi / -12.0\n", "z = 0.86603 - 0.50000i\n", "a = 0.86603\n", "b = 0.50000\n", "c_n = 0.43301 - 0.25000i\n", "c_moins_n = 0.43301 + 0.25000i\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## VOS VALEURS manquantes à la place de \"0.666\"\n", "w = 2*pi % pulsation [rad/s]\n", "A = 1 % amplitude [V] \n", "phi = -pi/6; % phase [rad]\n", "printf(\"phi = 2 pi / %.1f\\n\",2*pi/phi);\n", "z = sqrt(3)/2 -i/2 % phaseur [V] complexe\n", "a = sqrt(3)/2 % I in phase ou a(n) [V]\n", "b = 1/2 % Q Quadrature ou b(n) [V]\n", "c_n = sqrt(3)/4-i/4 % c(n) [V] complexe\n", "c_moins_n = sqrt(3)/4+i/4 % c(-n) [V] complexe \n", "\n", "\n", "f=w/2/pi; T = 1/f; t=-T/2:T/20:T/2;\n", "plot(t,real(z*exp(i*w*t)), \"k\"); hold on;\n", "plot(t,A*cos(w*t+phi), \"ro\"); \n", "plot(t,a*cos(w*t)+b*sin(w*t), \"b+\");\n", "plot(t,c_n*exp(i*w*t)+c_moins_n*exp(-i*w*t), \"gd\");\n", "plot(t,cos(w*t),'k--');\n", "tm = -phi/2/pi*T;\n", "plot([0,tm,tm],[1,1,A],\"k->\")\n", "text(tm,0.9,[\"Dt=1/\",num2str(T/abs(tm)),\".T\"])\n", "grid on;\n", "legend([\"phaseur\";\"ampli., phase\";\"a(n),b(n)\";\"c(n),c(-n)\";\"cos\"])\n" ] }, { "cell_type": "markdown", "id": "7685b372-f259-4685-8162-b188eb5593dc", "metadata": { "tags": [] }, "source": [ "## G - Somme partielle de Fourier\n", "---\n", "Si l'on ajoute des phaseurs d'ondes qui ont des fréquences multiples d'une fréquence fondamentale $F_0$.\n" ] }, { "cell_type": "markdown", "id": "c1ff5cb9-9154-49b1-bd02-aaff930981df", "metadata": {}, "source": [ "\n", "\n", " - Les **petits cercles colorés** : sont chacun une onde complexe $z(n).e^{i.n.\\omega_0.t}$ phasée par $z(n)$ (amplifiée de $|z(n)|$ et déphasée de $\\angle z(n)$ ) tournant à la fréquence $n.F_0$ \n", " - **les bras articulés** : sont la somme de ces ondes complexes tournant à des fréquences multiples : $\\sum z(n).e^{i.n.\\omega_0.t}$. **Attention axe réel vertical**\n", " - **le signal temporel** : est la partie réelle de cette somme $\\mathcal{R}\\left(\\sum z(n).e^{i.n.\\omega_0.t}\\right)$ et donc la somme des parties réelles $\\sum\\mathcal{R}\\left( z(n).e^{i.n.\\omega_0.t}\\right)$ et donc une somme d'ondes réelles $\\sum A(n).\\cos{(n.\\omega_0.t+\\varphi_n)}$. **Attention ! Axe du temps inversé** dans cette animation...\n", "\n", "L'angle $\\theta$ varie en fonction du temps $t$ et du rang $n$ : $$\\theta = n.\\omega_0.t=2\\pi.n.F_0.t $$\n", "\n", "| rang |  nom | $\\theta$ \n", "|---------|------------------------------------|----------------------------------\n", "| n=0 | composante continue | $\\theta=0$\n", "| n=1 | fondamentale ou harmonique de rang 1| $\\theta=2\\pi.F_0.t=\\omega_0.t$\n", "| n=2 | 1ᵉ harmonique ou harmonique de rang 2| $\\theta=2\\pi.2F_0.t=2.\\omega_0.t$\n", "| n=3 | 2ᵉ harmonique ou harmonique de rang 3| $\\theta=2\\pi.3F_0.t=3.\\omega_0.t$\n", "\n" ] }, { "cell_type": "markdown", "id": "17f38e88-3669-47e3-a912-3c5eaa9c1af1", "metadata": { "tags": [] }, "source": [ "### Exercice global\n", "\n", "Ce code calcule la somme partielle des sinus de l'animation ci-dessus.\n", "\n", "Complétez au fur et à mesure le code pour ajouter les représentations :\n", " 1) Avec $a(n)$ et $b(n)$ : facile on a une somme de sinus...\n", " 2) Avec phaseur $z(n)$ : facile en utilisant les phaseur $z_I$ de cos et $z_Q$ de sinus. Attention au signe !\n", " 3) Avec amplitude $A_n$ et déphasage $\\varphi_n$ : facile d'avoir l'amplitude et la phase d'un phaseur\n", " 4) Avec $c(n)$ et $c(-n)$ : construire du réel par somme de conjugués." ] }, { "cell_type": "markdown", "id": "f32b3728-2362-4d80-9892-970b1b221278", "metadata": { "tags": [] }, "source": [ "#### 1 - Commencez par les a(n) et b(n)\n", "Le corrigé est dans l'exo 2 suivant " ] }, { "cell_type": "code", "execution_count": 15, "id": "6517b30d-d21f-4f74-974e-5d32c20bdbc9", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clear all;\n", "F0=3;T0=1/F0; % Arbitraire ont est T0 périodique\n", "Te = T0/50; % échantillonnage du temps\n", "t=-T0:Te:T0; % on regarde deux périodes\n", "theta = 2*pi*F0*t; % l'angle theta varie dans le temps \n", "\n", "%amplitude des sinus de l'animation \n", "Asin = [-2/pi, 2/2/pi, 2/-3/pi, 2/4/pi] ;\n", "% F0 2F0 3F0 4F0\n", "\n", "%% 1 - VOTRE CODE a= ... b=... \n", "% On peut recopier des tableaux a = Asin\n", "% faire des calculs vectorisés a = Asin/2 + i*Asin\n", "a = Asin*0.666 ;\n", "b = Asin*0.666 ; \n", "\n", "% somme partielles : signaux nuls au départ \n", "s_sin= s_an = t*0; %signaux réels\n", "\n", "style = [\"y\"; \"g\"; \"b\"; \"r\"];\n", "\n", "for n = 1:4\n", " subplot(4,1,n) % 4 rangée de figure, 1colonne, on se met dans la figure n\n", " % somme de sinus de l'animation\n", " s_sin= s_sin + Asin(n) * sin(n*theta); hold on;\n", " plot(t,s_sin, style(n));\n", " \n", " % 1 - CORRIGER 2 ERREURs du calcul du signal à partir de a(n), b(n)\n", " s_an = a(n) * cos(theta) + b(n) * sin(theta);\n", " plot(t,s_an, [style(n),\"o\"]);\n", " \n", " title(sprintf(\"Somme partielle de rang %d\", n))\n", "end\n" ] }, { "cell_type": "markdown", "id": "4838bc5a-a334-4849-8304-171a775fcc0a", "metadata": { "tags": [] }, "source": [ "#### 2 - continuez avec le phaseur z(n)\n", "Le corrigé est dans l'exo 3 suivant " ] }, { "cell_type": "code", "execution_count": 16, "id": "b106f84a-ac13-45ef-95b7-21ea0c7711e3", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PB !Votre signal y_phaseur n'est pas imaginaire !\n", "PB !Votre signal y_phaseur n'est pas imaginaire !\n", "PB !Votre signal y_phaseur n'est pas imaginaire !\n", "PB !Votre signal y_phaseur n'est pas imaginaire !\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "%% 1 - CORRIGÉ\n", "a = Asin*0; % pas de cos\n", "b = Asin ; % que des sin \n", "\n", "%% 2 - VOTRE CODE z=... en phaseur \n", "% idem on peut faire des calculs avec a et b...\n", "% se rappeler du phaseur du coset du sin \n", "z = i*0.666*a + 0.666*b ; \n", "\n", "% somme partielles : signaux nuls au départ \n", "y_phaseurs = t*0 ; % signal complexe à partir des phaseurs\n", "s_sin= s_an = t*0; %signaux réels\n", "\n", "style = [\"y\"; \"g\"; \"b\"; \"r\"];\n", "\n", "for n = 1:4\n", " subplot(4,1,n) \n", " s_sin= s_sin + Asin(n) * sin(n*theta); \n", " plot(t,s_sin, style(n)); hold on; \n", " % 1 - CORRIGÉ\n", " s_an = s_an + a(n) * cos(n*theta) + b(n) * sin(n*theta);\n", " plot(t,s_an, style(n));\n", " \n", " %% 2 - VOTRE CODE y_phaseurs = ... est un signal complexe !\n", " y_phaseurs = 0.666*exp(n*theta) ;\n", "\n", " % vérification que y est complexe\n", " if (sum(abs(imag(y_phaseurs)))<0.01) disp(\"PB !Votre signal y_phaseur n'est pas imaginaire !\")\n", " end\n", "\n", " % le signal s_phaseurs est sa partie réelle\n", " s_phaseur = real(y_phaseurs);\n", " plot(t,s_phaseur, [style(n),\"+\"]); \n", " \n", " title(sprintf(\"Somme partielle de rang %d\", n))\n", "end\n" ] }, { "cell_type": "markdown", "id": "e5f12e62-4de1-41d7-9233-cbc3dc084bb5", "metadata": { "tags": [] }, "source": [ "#### 3 - Continuez avec amplitude et phase\n", "Le corrigé est dans l'exo 4 suivant " ] }, { "cell_type": "code", "execution_count": 18, "id": "d4aef65f-0ccc-4ccd-8cb9-a90c23605c84", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "%% 2 - CORRIGÉ\n", "zI =1 ; %phaseur du cos\n", "zQ = -i ; % phaseur du sin \n", "z = a*zI + b*zQ ; % a.cos + b.sin\n", "z = a - i * b ; %\n", "\n", "%% 3 - VOTRE CODE Amp=... phi=...\n", "% facile quand on connait le phaseur z !\n", "% voir : real , imag, abs, angle, conj\n", "% pour manipuler les complexes\n", "Amp = real(z)*0.666;\n", "phi = conj(z)*0.666;\n", "\n", "% somme partielles : signaux nuls au départ \n", "y_phaseurs = t*0 ; % signal complexe à partir des phaseurs\n", "s_sin= s_an=s_amp_phi = t*0; %signaux réels\n", "\n", "style = [\"y\"; \"g\"; \"b\"; \"r\"];\n", "\n", "for n = 1:4\n", " subplot(4,1,n) \n", " s_sin= s_sin + Asin(n) * sin(n*theta); \n", " plot(t,s_sin, style(n)); hold on; \n", " s_an = s_an + a(n) * cos(n*theta) + b(n) * sin(n*theta);\n", " plot(t,s_an, style(n)); \n", "\n", " %% 2 - CORRIGÉ\n", " y_phaseurs = y_phaseurs + z(n)*exp(i*n*theta) ;\n", " s_phaseur = real(y_phaseurs);\n", " plot(t,s_phaseur, style(n));\n", "\n", " %% 3 - VOTRE code avec amplitude et phase\n", " s_amp_phi = s_amp_phi + 0.666*cos(n*theta);\n", " plot(t,s_amp_phi, [style(n),\"+\"]);\n", " \n", " title(sprintf(\"Somme partielle de rang %d\", n))\n", "end\n" ] }, { "cell_type": "markdown", "id": "80ee4164-2670-4060-b3db-b09649c5ab04", "metadata": { "tags": [] }, "source": [ "#### 4 - Continuez avec les c(n) et c(-n)\n", "Le corrigé est dans la suite " ] }, { "cell_type": "code", "execution_count": 19, "id": "deca8ece-a2d6-4859-8fdc-469aa9b7adb5", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "c =\n", "\n", " Columns 1 through 3:\n", "\n", " 0.00000 + 0.84798i 0.00000 - 0.42399i 0.00000 + 0.28266i\n", "\n", " Column 4:\n", "\n", " 0.00000 - 0.21199i\n", "\n", "c_moins =\n", "\n", " Columns 1 through 3:\n", "\n", " 0.00000 + 0.84798i -0.00000 - 0.42399i 0.00000 + 0.28266i\n", "\n", " Column 4:\n", "\n", " -0.00000 - 0.21199i\n", "\n", "Votre signal s_cn n'est pas réel ! conjuguez !\n", "Votre signal s_cn n'est pas réel ! conjuguez !\n", "Votre signal s_cn n'est pas réel ! conjuguez !\n", "Votre signal s_cn n'est pas réel ! conjuguez !\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%% 3 - CORRIGÉ\n", "Amp = abs(z); % amplitude = module de z \n", "phi = angle(z); % phase = argument de z \n", "%% phi = atan(-b./a) ne fonctionne pas car a=0 \n", "%phi = atan(-b*Inf); %marche\n", "\n", "%% 4 - VOTRE CODE c=... et c_moins=... \n", "% facile quand on a le phaseur z\n", "% on veut c(n).exp.. + c(-n).exp = partie réelle de z\n", "% pensez somme de conjugués !\n", "c=0.666*(z-conj(z))\n", "c_moins=0.666*imag(z)*2*i\n", "\n", "\n", "y_phaseurs = t*0 ; % signal complexe à partir des phaseurs\n", "s_sin= s_an=s_amp_phi= s_cn = t*0; %signaux réels\n", "style = [\"y\"; \"g\"; \"b\"; \"r\"];\n", "\n", "for n = 1:4\n", " subplot(4,1,n) \n", " s_sin= s_sin + Asin(n) * sin(n*theta); \n", " plot(t,s_sin, style(n)); hold on; \n", " s_an = s_an + a(n) * cos(n*theta) + b(n) * sin(n*theta);\n", " plot(t,s_an, style(n)); \n", " y_phaseurs = y_phaseurs + z(n)*exp(i*n*theta) ;\n", " s_phaseur = real(y_phaseurs);\n", " plot(t,s_phaseur, style(n));\n", "\n", " %% 3 - CORRIGÉ\n", " s_amp_phi = s_amp_phi + Amp(n)*cos(n*theta+phi(n));\n", " plot(t,s_amp_phi, style(n));\n", " \n", " %% 4 - VOTRE CODE s_cn à partir des c(n) c(-n) \n", " s_cn = s_cn + (c(n) + c_moins(n))*0.666 * exp(i*n*theta);\n", " plot(t,s_cn, [style(n),\"+\"]);\n", " if (sum(abs(imag(s_cn)))>0.01) disp(\"Votre signal s_cn n'est pas réel ! conjuguez !\")\n", " end\n", " \n", " \n", " title(sprintf(\"Somme partielle de rang %d\", n))\n", "end\n" ] }, { "cell_type": "markdown", "id": "e0be9f50-0616-400d-b484-ac7945144f4a", "metadata": { "tags": [] }, "source": [ "#### Corrigé 4\n" ] }, { "cell_type": "code", "execution_count": 20, "id": "081f12db-ac7d-4a70-bf02-2da17ec3a932", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%% 4 - CORRIGÉ\n", "c=z/2 ;\n", "c_moins=conj(z/2) ;\n", "% On a bien c(n).exp(i...) + c(-n).exp(-i...) conjuguées et donc\n", "% = 2.Reel(c(n).exp(i...))\n", "% avec c(n) = z/2 => = Reel(z.exp(i...)) = onde réelle voulue\n", "\n", "y_phaseurs = t*0 ; % signal complexe à partir des phaseurs\n", "s_sin= s_an=s_amp_phi= s_cn = t*0; %signaux réels\n", "style = [\"y\"; \"g\"; \"b\"; \"r\"];\n", "\n", "for n = 1:4\n", " subplot(4,1,n) \n", " s_sin= s_sin + Asin(n) * sin(n*theta); \n", " plot(t,s_sin, style(n)); hold on; \n", " s_an = s_an + a(n) * cos(n*theta) + b(n) * sin(n*theta);\n", " plot(t,s_an, style(n)); \n", " y_phaseurs = y_phaseurs + z(n)*exp(i*n*theta) ;\n", " s_phaseur = real(y_phaseurs);\n", " plot(t,s_phaseur, style(n));\n", " s_amp_phi = s_amp_phi + Amp(n)*cos(n*theta+phi(n));\n", " plot(t,s_amp_phi, style(n));\n", " \n", " %% 4 - CORRIGÉ \n", " s_cn = s_cn + c(n) * exp(i*n*theta);\n", " s_cn = s_cn + c_moins(n) * exp(-i*n*theta); \n", " plot(t,s_cn, [style(n),\"+\"]);\n", " if (sum(abs(imag(s_cn)))>0.01) disp(\"Votre signal s_cn n'est pas réel ! conjuguez !\")\n", " end\n", " \n", " \n", " title(sprintf(\"Somme partielle de rang %d\", n))\n", "end\n" ] }, { "cell_type": "markdown", "id": "89cb1f89-af8f-4e57-b12d-f564d892f8de", "metadata": { "tags": [] }, "source": [ "### Bonus spectre ou réponse fréquentielle\n", "\n", "On peut maintenant visualiser les amplitudes des composantes pour chaque fréquence plutôt que de visualiser le signal dans le temps.\n", "\n", "> Visualiser l'amplitude et la phase en fonction de la fréquence (rang n), c'est visualiser un spectre.\n", "\n", "On peut passer du temporel d'une fonction $f$ au spectre fréquentiel $\\hat{f}$ par la décomposition de $f$ :\n", "\n", "\n", "\n", "\n", "\n", "De ces 4 représentations des composantes nous tirons 4 visions fréquentielles (en fonction du rang $n$) associé à la fréquence de l'onde :\n", "\n", "$n \\leftrightarrow n.F_0$ fréquence de la composante de rang $n$ " ] }, { "cell_type": "markdown", "id": "2374467e-3235-4425-af65-d2ab33763e2a", "metadata": {}, "source": [ "On peut représenter les coefficients réels a(n) et b(n) pour les fréquences positives :\n" ] }, { "cell_type": "code", "execution_count": 22, "id": "5206f601-a49a-4553-b615-1d3f4c51ea9e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "F0 = 3\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n=1:4;\n", "F0\n", "f = n*F0;\n", "subplot(211);\n", "stem(f,a,'b');\n", "ylabel(\"a(n) [V]\");\n", "xlabel(\"frequence [Hz]\");\n", "subplot(212);\n", "stem(f,b,'r');\n", "ylabel(\"b(n) [V]\");\n", "xlabel(\"frequence [Hz]\");\n", "grid on;\n" ] }, { "cell_type": "markdown", "id": "5df8fdb1-dc4f-4389-a6a4-4d7f97e5d35a", "metadata": {}, "source": [ "On peut représenter le coefficient complexe c(n) pour les fréquences positives **et négatives** :\n", " - en module\n", " - en argument\n", "\n", "**Attention** on a bien \n", " - 0 de module 1 et d'argument $\\pi$,\n", " - -1 de module 1 et d'argument $\\pi$," ] }, { "cell_type": "code", "execution_count": 23, "id": "3d60e016-52b9-4966-888c-df3c0afa0528", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot(211);\n", "stem(f,abs(c),'b');hold on;\n", "stem(-f,abs(c_moins),'r');\n", "ylabel(\"|c(n)| [V]\");\n", "xlabel(\"frequence [Hz]\");\n", "subplot(212);\n", "stem(f,angle(c)*180/pi,'b'); hold on;\n", "stem(-f,angle(c_moins)*180/pi,'r'); \n", "ylabel(\"argument c(n) [deg.]\");\n", "xlabel(\"frequence [Hz]\");\n", "grid on;\n" ] }, { "cell_type": "markdown", "id": "d4abf3c5-0176-4d11-9ea4-2beebc510f03", "metadata": {}, "source": [ "Remarquez la symétrie de Hilbert $c(f)=\\overline{c(-f)}$, car **le signal est réel** :\n", " - en module rouge est le pair de bleu\n", " - en phase rouge est l'impair de bleu\n", " \n", " > Souvent on omet de représenter les fréquences négatives qui se déduisent des positives dans le **cas des signaux réels**" ] }, { "cell_type": "markdown", "id": "3bc47c49-a72a-44d4-b8c3-ba8ce0819dd3", "metadata": {}, "source": [ "On peut représenter le module et l'argument du phaseur $z$ pour **les fréquences positives seules** (le phaseur tourne dans le sens positif uniquement et on prend sa partie réelle) :\n", " - Amplitude : $|z_n| = 2.|c_n| = A_n$\n", " - Phase : $\\angle{z_n} = \\angle{c_n} = \\varphi_n$\n" ] }, { "cell_type": "code", "execution_count": 24, "id": "b25da23d-d6d3-4b11-8e81-8187a4ecb162", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot(211);\n", "stem(f,abs(z),'b');\n", "ylabel(\"|z(n)| [V]\");\n", "xlabel(\"frequence [Hz]\");\n", "grid on;\n", "subplot(212);\n", "stem(f,angle(z)*180/pi,'b'); \n", "ylabel(\"argument c(n) [deg.]\");\n", "xlabel(\"frequence [Hz]\");\n" ] }, { "cell_type": "markdown", "id": "cb260a50-ae5a-4117-9c3f-7f5373ef192d", "metadata": {}, "source": [ "On peut faire le même affichage avec une échelle logarithmique en fréquence et en amplitude : **c'est la représentation de Bode**\n" ] }, { "cell_type": "code", "execution_count": 25, "id": "4db3d528-a164-4f14-b665-811e5f9b7a1a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot(211);\n", "semilogx(f,20*log(abs(z)),'b-o');\n", "ylabel(\"amplitude [V dB] \");\n", "xlabel(\"frequence [Hz] \");\n", "title(\"Diagramme de bode\")\n", "grid on;\n", "subplot(212);\n", "semilogx(f,angle(z)*180/pi,'b-o'); \n", "ylabel(\"phase [deg.]\");\n", "xlabel(\"frequence [Hz]\");\n", "grid on;\n" ] }, { "cell_type": "markdown", "id": "2e628066-45ea-4d2e-84d1-c31d514f38a1", "metadata": { "tags": [] }, "source": [ "### Bonus affichage phaseur\n", "\n", "Recalculons notre somme complexe de phaseurs $y$ et regardons :\n", " - $y(t)$ dans le plan complexe paramétré par $t$\n", " - $s(t)=\\mathcal{R}(y(t))$ en fonction temporelle" ] }, { "cell_type": "code", "execution_count": 26, "id": "bc4addc3-ea9e-40a1-9999-9dbb256aecac", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clear all;\n", "F0=1;T0=1/F0; \n", "Te = T0/100; t=-T0:Te:T0; \n", "\n", "z = [-2/pi, 2/2/pi, 2/-3/pi, 2/4/pi] * -i ;\n", "% F0 2F0 3F0 4F0\n", "y = t*0 ; \n", "\n", "for n = 1:4\n", " y = y + z(n)*exp(i*n*2*pi*F0*t) ;\n", "end\n", "plot(t,real(y))" ] }, { "cell_type": "markdown", "id": "ae1d896e-3634-478d-8008-3a9181919f84", "metadata": {}, "source": [ "Regardons certains instants en particulier.\n", "\n", "**Attention le plan complexe est \"tourné\"** :\n", " - abscisses imaginaires\n", " - ordonnées réelles\n", " \n", "pour faciliter le passage au temporel" ] }, { "cell_type": "code", "execution_count": 27, "id": "fe027670-5af7-4335-928c-a3f0a43b246e", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "indices = (0:18:100) +101;\n", "styles = [\"o\", \"+\" ,\"d\", \"s\"];\n", "instants = t(indices);\n", "\n", "subplot(121)\n", "plot(imag(y),real(y),'.');hold on;\n", "for k = 1:4\n", " plot(imag(y(indices(k))),real(y(indices(k))),styles(k));hold on;\n", " text(imag(y(indices(k)))-0.4,real(y(indices(k))),sprintf(\" t=%.2f\",instants(k)))\n", "end\n", "axis(\"square\");\n", "xlabel(\"Imag(y)\");\n", "ylabel(\"Real(y)\");\n", "\n", "subplot(122)\n", "plot(t,real(y),'-');hold on;\n", "for k = 1:4\n", " plot(instants(k),real(y(indices(k))),styles(k));hold on;\n", " text(instants(k)+0.1,real(y(indices(k))),sprintf(\" t=%.2f\",instants(k)))\n", "end\n", "axis(\"square\");\n", "xlabel(\"Temps\");\n", "ylabel(\"signal\");\n" ] }, { "cell_type": "code", "execution_count": null, "id": "72a58ddd-633f-4b49-8109-9dc8ddd5b5d8", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Octave", "language": "octave", "name": "octave" }, "language_info": { "file_extension": ".m", "help_links": [ { "text": "GNU Octave", "url": "https://www.gnu.org/software/octave/support.html" }, { "text": "Octave Kernel", "url": "https://github.com/Calysto/octave_kernel" }, { "text": "MetaKernel Magics", "url": "https://metakernel.readthedocs.io/en/latest/source/README.html" } ], "mimetype": "text/x-octave", "name": "octave", "version": "4.2.2" } }, "nbformat": 4, "nbformat_minor": 5 }