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    "---\n",
    "# FILT préparation à la méthode bilinéaire : différentiateurs\n",
    "---\n",
    "\n",
    "Si vous naviguez ici avec Github, cliquez ici [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/balaise31/Signal/master?labpath=discret%2Ftp%2FFILT_prepa_bilineaire.ipynb) pour pouvoir **exécuter en ligne** le code octave ou python.\n",
    "\n",
    "|   [Readme du TP](./README.ipynb)        | Sujet | Corrigé |\n",
    "|--------|-------|---------|\n",
    "|Python  | [sujet python](./FILT_prepa_bilineaire_python.ipynb) | [corrigé python](./FILT_prepa_bilineaire_python_corr.ipynb) |\n",
    "|Octave  | [sujet octave](./FILT_prepa_bilineaire.ipynb) | [corrigé octave](./FILT_prepa_bilineaire_octave_corr.ipynb) |\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75175de9-d658-451a-a6a2-5a0bdec2def1",
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    "## I - Etude des différentiateurs\n",
    "---\n",
    "\n",
    "\n",
    "L'exercice 2.1 du polycopié a permi de proposer trois différentiateurs dérivés de 3 intégrateurs permettant d'approcher le comportement de l'opérateur dérivé $D$ et de la variable associée $p$ :\n",
    "\n",
    "$D =\\frac{d}{dt} \\leftrightarrow p \\leftrightarrow \\underbrace{\\frac{1}{T_e}(1-z^{-1})}_{\\text{Backward Euler}}\\leftrightarrow \\underbrace{\\frac{1}{T_e}(z-1)}_{\\text{Forward Euler}} \\leftrightarrow \\underbrace{\\frac{2}{T_e}\\frac{1-z^{-1}}{1+z^{-1}}}_{\\text{Bilinéaire ou Tustin}} \n",
    "$\n",
    "\n",
    "Dans la suite nous notons $H_f$, $H_b$ et $H_t$ les fonctions de trasnfert des systmes respectifs \"forward\", \"backward\" et \"trapezoidal\"\n",
    "\n",
    "### I1 - Récurrences\n",
    "Voici 4 récurrences qui sont à associer à ces 3 différentiateurs :\n",
    "- $ y[k] = \\frac{x[k+1]-x[k]}{T_e} $\n",
    "- $ \\frac{y[k+1] + y[k]}{2} = \\frac{x[k+1]-x[k]}{T_e}$\n",
    "- $ y[k] = \\frac{x[k]-x[k-1]}{T_e} $\n",
    "- $ y[k+1] = \\frac{x[k+1]-x[k]}{T_e} $\n",
    "\n",
    "Lequel de ces différentiateurs n'est pas causal ?\n",
    "\n",
    "Voici trois phrases à associer à chacun des différentiateur :\n",
    "- Te fois la sortie à l'instant k vaut l'incrément de l'entrée entre les instants k et k-1\n",
    "- la pente entre l'instant k et k+1 vaut la moyenne de la sortie aux instants k et k+1  \n",
    "- Te fois la sortie à l'instant k-1 vaut l'incrément de l'entrée entre les instants k et k-1\n",
    "\n",
    "\n"
   ]
  },
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   "id": "16a74d2e-5d8e-4d76-a632-c3cd4b4e57ac",
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    "## II - Réponses harmoniques\n",
    "---\n",
    "\n",
    "Nous allons justifier et retrouver :\n",
    " - pourquoi il faut remplacer $G(p)$ par $G(j\\omega)$ en continu pour obtenir la réponse harmonique (le Bode)\n",
    " - et par quoi il faut remplacer $G(z)$ pour obtenir $G(\\omega)$ et le bode en discret\n",
    " \n",
    "Nous l'utilisons ensuite pour trouver les réponses harmoniques des différentiateurs backward et forward.\n",
    "\n",
    "Le différentiateur bilinéaire est finalement traité.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ee555e5-8d51-471e-8ca8-8f98f79efdf2",
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   "source": [
    "### II-1 - passage de TF à la réponse harmonique\n",
    "\n",
    "On va considérer le passage d'ondes pures continues $e^{i\\omega\\,t}$ et discrètes $e^{i\\omega\\,k\\,T_e}$. Il est fréquent et pratique de considérer les fréquences ou bien pulsations normalisées par rapport à $F_e$ soit avec :\n",
    "$\\tilde{f} = \\frac{f}{F_e} = \\tilde{\\omega} = \\frac{\\omega}{\\omega_e}$\n",
    "\n",
    " 1) Retrouvez la relation entre l'opérateur $p$ et $\\omega$ puis $\\tilde{f}$ en regardant ce que donne la dérivée de l'onde pure continue $e^{i\\omega\\,t}$. Dessinez dans le plan complexe le lieu de $p$ lorsque $\\tilde{f}$ va de $-\\infty$ à $+\\infty$\n",
    "\n",
    " 2) De même, retrouvez la relation entre l'opérateur $z$ et $\\omega$ puis $\\tilde{f}$ en regardant ce que donne **l'avance d'un échantillon** sur l'onde pure discrète $e^{i\\omega\\,k\\,T_e}$. Dessinez dans le plan complexe le lieu de $z$ lorsque $\\tilde{f}$ va de $0$ à $1$ puis de $-\\infty$ à $+\\infty$\n",
    " \n",
    " "
   ]
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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clear all; close all; clc;\n",
    "Fe=48000;N=100;Df=Fe/N;Te=1/Fe;\n",
    "f=-2*Fe:Df:2*Fe;         % vecteur des fréquences\n",
    "w=2*pi*f;            % vecteur des pulsations\n",
    "\n",
    "%% VOTRE CODE:  f_tilde =\n",
    "% Calculant la fréquence normalisée à partir de f et/ou de w\n",
    "f_tilde = f;\n",
    "\n",
    "%% VOTRE CODE:  p = \n",
    "% définissez le vecteur p à partir de f_tilde\n",
    "% par défaut i = sqrt(-1)  permet de faire des complexes\n",
    "p=i*f;\n",
    "\n",
    "%% VOTRE CODE:  z = \n",
    "% définissez le vecteur z à partir de f_tilde\n",
    "% la fonction 'exp' de matlab est vectorisée et complexe.\n",
    "z=exp(i*f);       \n",
    "\n",
    "\n",
    "%% Le code suivant  affiche dans le plan complexe\n",
    "% en noir le lieu de p (avec l'axe imaginaire tel que 1 <-> Fe)\n",
    "% en rouge le lieu de z\n",
    "% \n",
    "plot(real(z),imag(z),'r.-');hold on;\n",
    "plot(real(p),imag(p)/2/pi/Fe,'k.-');\n",
    "sel = (2*N)+1:1:N*2.6;\n",
    "plot([real(p(sel)) ; real(z(sel))], [imag(p(sel))/2/pi/Fe ; imag(z(sel))],'-.>'); \n",
    "grid on;\n",
    "xlabel('Reel');\n",
    "ylabel('imaginaire (pour p  1 <-> Fe)');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3ac7603-c308-42b8-9433-140893f0a4b4",
   "metadata": {},
   "source": [
    "### II-2 - Réponse harmonique du Forward et Backward : géométrique\n",
    "Ecrivez les fonctions de transfert en fonction de $z$ et non pas $z^{-1}$ pour obtenir plus facilement l'expression des réponses harmoniques.\n",
    "\n",
    " 1) Dessinez, sous forme de vecteur dans le plan complexe, le vecteur $1-z$ (pôle en $1$) et le vecteur $z-1$ (pôle en $-1$). On prendra pour $z$ un point quelconque du cercle unité. La tradition veut que les pôles soient dessinés par \"des petits plus\" + et les zéros par \"des petits ronds\".\n",
    " 2) Donnez et dessinez le module et l'argument de ces vecteurs pour $\\tilde{f}$ proche de $0$ de $0.25$ et $0.5$.  \n",
    " Déduisez-en géométriquement un équivalent de la réponse harmonique du dérivateur Forward $H_f(\\tilde{f})$ autour de ces fréquences. \n",
    " 3) Faites de même pour un zéro en $0$. Comparez avec l'effet d'un retard de $T_e$ et concluez que c'est bête en fait !\n",
    " 4) Déduisez alors géométriquement un équivalent de la réponse harmonique du dérivateur Backward $H_B(\\tilde{f})$ pour $\\tilde{f}$ proche de $0$ de $0.25$ et $0.5$.  \n",
    "\n",
    "Modifiez le code suivant pour vérifier les valeurs 0, 0.25, 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "6aad727d-3ae8-4ce9-b02e-cf6449088b40",
   "metadata": {
    "vscode": {
     "languageId": "json"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f normalisée = 0, Hf module = 48000.000000, Hf argument = 180.000000 degrés\n",
      "f normalisée = 0.25, Hf module = 48000.000000, Hf argument = 180.000000 degrés\n",
      "f normalisée = 0.5, Hf module = 48000.000000, Hf argument = 180.000000 degrés\n"
     ]
    }
   ],
   "source": [
    "% fonctions de transfert (fonctions inline de la variable z VECTORISEE \"./\")\n",
    "Hf = @(z) ((z-1)/Te);  %Forward\n",
    "Hb = @(z) ((z-1)./z/Te);  %Backward\n",
    "\n",
    "%% VOTRE CODE : z_0 =\n",
    "% calculez l'équivalent harmonique de z pour w=0 \n",
    "z_0 = 0;\n",
    "\n",
    "%% VOTRE CODE : z_quart =\n",
    "% calculez l'équivalent harmonique de z pour w=we/4\n",
    "% soit f normalisée de 1/4\n",
    "z_quart = 0;\n",
    "\n",
    "%% VOTRE CODE : z_nyquist =\n",
    "% calculez l'équivalent harmonique de z pour w=we/2\n",
    "% la fréquence la plus haute possible\n",
    "z_nyquist = 0;\n",
    "\n",
    "%% On affiche ici les modules et arguments de Hf(w) et Hb(w)\n",
    "le_w = 0; le_z = z_0;\n",
    "printf(\"f normalisée = %d, Hf module = %f, Hf argument = %f degrés\\n\",le_w,abs(Hf(le_z)),arg(Hf(le_z))/pi*180)\n",
    "le_w = 1/4; le_z = z_quart;\n",
    "printf(\"f normalisée = %d, Hf module = %f, Hf argument = %f degrés\\n\",le_w,abs(Hf(le_z)),arg(Hf(le_z))/pi*180)\n",
    "le_w = 1/2; le_z = z_nyquist;\n",
    "printf(\"f normalisée = %d, Hf module = %f, Hf argument = %f degrés\\n\",le_w,abs(Hf(le_z)),arg(Hf(le_z))/pi*180)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c3c66a6-76bd-4e09-9bb8-08398d43ad01",
   "metadata": {},
   "source": [
    "### II-2 - Réponse harmonique du Forward et Backward : analytique\n",
    "\n",
    " 5) Calculez analytiquement (remplacez $z$ par $e^{i2\\pi\\tilde{f}}$, et calculez module et argument) ces deux réponses harmoniques que vous exprimerez aussi bien en fonction de $\\omega$ que de $\\tilde{f}$.  \n",
    " Faites apparaître des cosinus et sinus avec **ASTUCE !**  \n",
    " Factoriser les $e^{i\\,\\omega\\,T_e} \\pm 1$ en $e^{\\frac{-i\\,\\omega\\,T_e}{2}}(e^{\\frac{i\\,\\omega\\,T_e}{2}} \\pm e^{\\frac{-i\\,\\omega\\,T_e}{2}})$ et avec la vision d'Euler obtenez des $e^{i.\\ldots.\\omega}\\cos(\\ldots\\omega)$ ou avec des $\\sin$.  \n",
    " 6) Vérifiez géométriquement ces résultats avec les équivalents des questions précédentes.\n",
    " 7) Esquissez un grahique de la réponse harmonique (module et argument) en échelle linéaire ($\\tilde{f}\\in[-2\\,,\\, 2]$) puis logarithmique (Diagramme de Bode avec $\\tilde{f}\\in]\\frac{1}{10}\\,,\\, 2]$).\n",
    "\n",
    "Modifiez le code suivant pour vérifier vos calculs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c1de3c75-6c86-404d-a226-fa127ae0585a",
   "metadata": {
    "tags": [],
    "vscode": {
     "languageId": "json"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% fonctions de transfert (fonctions inline de la variable z VECTORISEE \"./\")\n",
    "Hf = @(z) ((z-1)/Te);  %Forward\n",
    "Hb = @(z) ((z-1)./z/Te);  %Backward\n",
    "\n",
    "%% VOTRE MODIF :\n",
    "% Passez l'axe des fréquences en unités normalisées (1<-> Fe)\n",
    "% Passez la phase en degrés\n",
    "subplot(211)\n",
    "plot(f,abs(Hf(z)),'g+-'); hold on;\n",
    "plot(f,abs(Hb(z)),'bo-'); \n",
    "plot(f,abs(p),'k'); grid on;\n",
    "xlabel(\"frequence [Hz]\");\n",
    "ylabel(\"module en echelle lineaire\")\n",
    "legend([\"Forward\";\"Backward\";\"derivateur continu\"],\"location\",\"north\")\n",
    "subplot(212)\n",
    "plot(f,arg(Hf(z)),'g+-'); hold on;\n",
    "plot(f,arg(Hb(z)),'bo-'); \n",
    "plot(f,arg(p),'k');\n",
    "xlabel(\"frequence normalisee [1 <-> Fe]\");\n",
    "ylabel(\"phase [degres]\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "killing-delaware",
   "metadata": {},
   "source": [
    "Remarquez bien la périodicité des réponses harmoniques des systèmes discrets. \n",
    "\n",
    " 1) Quelle est la plage de fréquence la plus petite nécessaire à l'observation de la réponse harmonique : **l'intervale fondamental**  \n",
    " Comment déduire de l'intervalle fondamental le reste de la réponse harmonique ?  \n",
    " 2) Esquissez l'allure d'un filtre passe-haut, passe-bas, passe bande dans le cas discret. Ces filtres approchant la dérivée sont-ils bien passe-haut ?\n",
    " 4) Les 3 systèmes sont-ils à phase linéaire ? Comparez ces phases à celles d'un retard.\n",
    " \n",
    " \n",
    "On peut utiliser l'échelle log en fréquence et en gain pour mieux observer cette zone :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "functional-clearing",
   "metadata": {
    "vscode": {
     "languageId": "json"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% fonction pratique pour faire des dB et \n",
    "%% éviter les -infini à afficher etc.\n",
    "dBbrut = @(gain) 20*log10(abs(gain));\n",
    "sat = @(x, xmin, xmax) x.*(x>xmin).*(x<xmax)+xmin*(x<xmin)+xmax*(x>xmax);\n",
    "dBde = @(gain) sat(dBbrut(gain),60, 120); % dB compris entre 60 et 120\n",
    "\n",
    "%% VOTRE CORRECTION de ftilde=\n",
    "% On veut un vecteur en échelle log allant de 0.01 à 2\n",
    "% pour la fréquence normalisée. On garde le 1/100 de résolution\n",
    "% Attention log est en base népérienne et log10 celui en base 10\n",
    "ftilde = 10.^(-2:1/100:2); % de 10^-2 à 2\n",
    "\n",
    "%% on redéfinit z et p pour ces fréquences\n",
    "z = exp(i*2*pi*ftilde);\n",
    "p = i*2*pi*ftilde*Fe;\n",
    "\n",
    "%% VOTRE MODIFICATION\n",
    "% Passer l'axe des fréquences en fréquences réelles [Hz]\n",
    "subplot(211)\n",
    "semilogx(ftilde,dBde(Hf(z)),'g+-'); hold on;\n",
    "semilogx(ftilde,dBde(Hb(z)),'bo-'); \n",
    "semilogx(ftilde,dBde(p),'k'); grid on;\n",
    "xlabel(\"frequence normalisee [1 <-> Fe]\");\n",
    "ylabel(\"module dB\");\n",
    "legend([\"forwar\";\"backward\";\"derivateur continu\"],\"location\",\"northeast\")\n",
    "\n",
    "%% VOTRE CODE\n",
    "% affichant les 3 phases en degrés et fréquences réelles\n",
    "subplot(212)\n",
    "xlabel(\"frequence normalisee [1 <-> Fe]\");\n",
    "ylabel(\"module dB\");\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "color-entity",
   "metadata": {},
   "source": [
    "Les approximations de la dérivée ne sont valables que pour certaines fréquences !\n",
    "\n",
    " 1) Identifiez, à la décade près, la plage de fréquence normalisée où le gain des approximations ne s'écartent pas plus de 3dB de la dérivée continue.\n",
    " 2) Pour dériver un signal de parole entre 0 Hz et 8KHz quelle fréquence d'échantillonnage conviendrait 192kHz, 96kHz, 48 kHz, 24 kHz, 12 kHz, 8 kHz\n",
    "\n",
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f8f7a14-29f1-4f5a-81f3-23f2579fec82",
   "metadata": {},
   "source": [
    "## I3 - Transformée bilinéaire\n",
    "---\n",
    "\n",
    "Faites la même étude pour le dérivateur $h_t$ bilinéaire :\n",
    "\n",
    " 1) fonction de transfert en z ;\n",
    " 2) schéma géométrique des pôles et zéros ;\n",
    " 3) équivalents géométriques en 0 et 0.5 et esquisse de réponse harmonique asymptotique ;\n",
    " 4) calcul analytique (elle doit être purement imaginaire et un peu tangente !) ;\n",
    " 5) tracé de la réponse harmonique en linéaire puis en diagramme de Bode ;\n",
    " 6) vérifications avec octave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "3d5c7d86-5e97-425f-835b-8491a233297c",
   "metadata": {
    "vscode": {
     "languageId": "json"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% fonctions de transfert \n",
    "\n",
    "%%VOTRE MODIF de Ht = \n",
    "% attention à bien demander les opérations élément par élément !\n",
    "% genre x.*y ou x.^2 \n",
    "Ht = @(z) ((z-1)*2/Te); % bilineaire ou Tustin ou trapezoidale\n",
    "\n",
    "%%VOTRE BODE de Ht et de p continu\n",
    "% Inspirez-vous du code précédent\n",
    "dBde = @(gain) sat(dBbrut(gain), 60, 120); % dB compris entre 60 et 120\n",
    "subplot(211);\n",
    "% gain en dB avec semilogx et fréquences normalisées\n",
    "hold on;\n",
    "% gain en dB de p en noir\n",
    "subplot(212);\n",
    "% phase en degré avec semilogx et fréquences normalisées\n",
    "hold on;\n",
    "% phase en degré de p en noir\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6156e5a7-4b9b-4896-8139-398325c3674a",
   "metadata": {},
   "source": [
    "Donnez l'expression analytique de $H_t(\\omega)$ que vous avez calculé et superposez l'affichage de la version numérique pour vérifier l'exactitude de vos calculs.\n",
    "\n",
    "> **Cette fonction de transfert est très importante, car elle permet de   \n",
    "> faire des synthèses de filtre à partir du continu**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8599d698-a5ab-4db8-aae2-d28bd7b7ffe7",
   "metadata": {
    "vscode": {
     "languageId": "json"
    }
   },
   "outputs": [],
   "source": [
    "%%VOTRE MODIF de Ht_analytique = \n",
    "% f est la fréquence normalisée !\n",
    "Ht_analytique = @(f) cos(2*pi*f)/Te; \n",
    "\n",
    "\n",
    "%%VOTRE BODE de Ht, Ht analytique et p continu\n",
    "% superposées avec hold on;\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "543332db-ed4e-463e-95f9-84d0601662b3",
   "metadata": {},
   "source": [
    "### I4 - Avec la boite à outils \"control\" \n",
    "---\n",
    "\n",
    "Il est possible d'utiliser la boîte à outils \"control\" pour obtenir ces affichages en quelques lignes de code.\n",
    "Remarquons que ces fonctions n'ont rien d'indispensable puisque nous avons pu tout faire avec des fonctions basiques et quelques conaissances théoriques. \n",
    "\n",
    "Donc on peut utiliser les mêmes fonctions qu'en continu :\n",
    " - tf(num, den, Te) : pour definir un système par sa fonction de transfert\n",
    " - bode\n",
    " - impulse \n",
    " - pzmap\n",
    " \n",
    "Définissons les fonctions de transfert avec `tf`\n",
    "\n",
    "> La différence entre le continu et le discret se fait  \n",
    "> **seulement en précisant un Te** lors de la définition de la fonction de transfert.  \n",
    "> Les fonctions bode, impulse, step s'adaptent alors à un système discret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "charming-exhaust",
   "metadata": {
    "vscode": {
     "languageId": "json"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Transfer function 'backward' from input 'u1' to output ...\n",
      "\n",
      " y1:  4.8e+04 z - 4.8e+04\n",
      "\n",
      "Sampling time: 2.08333e-05 s\n",
      "Discrete-time model.\n",
      "\n",
      "Transfer function 'forward' from input 'u1' to output ...\n",
      "\n",
      "      4.8e+04 z - 4.8e+04\n",
      " y1:  -------------------\n",
      "               z         \n",
      "\n",
      "Sampling time: 2.08333e-05 s\n",
      "Discrete-time model.\n",
      "\n",
      "Transfer function 'tustin' from input 'u1' to output ...\n",
      "\n",
      "      9.6e+04 z - 9.6e+04\n",
      " y1:  -------------------\n",
      "             z + 1       \n",
      "\n",
      "Sampling time: 2.08333e-05 s\n",
      "Discrete-time model.\n",
      "\n",
      "Transfer function 'derivateur' from input 'u1' to output ...\n",
      "\n",
      " y1:  s\n",
      "\n",
      "Continuous-time model.\n"
     ]
    }
   ],
   "source": [
    "pkg load control %% pour octave uniquement, inutile avec matlab\n",
    "\n",
    "% si tf reçoit un troisième argument alors c'est Te\n",
    "%    et tf contruit un système discret\n",
    "% coef des polynomes en z ! pas z^-1\n",
    "backward=tf([1 -1]/Te , [1],Te) \n",
    "        %   (z -1)/Te /  1   = (z-1)/Te = Hb\n",
    "\n",
    "forward=tf([1 -1]/Te ,[1 0],Te) \n",
    "        %  (z -1)/Te / z     = (1-z^-1)/Te = Hf\n",
    "\n",
    "tustin= tf(2*[1 -1]/Te , [1 1],Te) \n",
    "        %  2 (z -1)/Te / (z+1)     = Ht\n",
    "\n",
    "% système continu celui là!\n",
    "derivateur = tf([1 0],[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c54312a-cb49-400e-b7b5-3c9225f05c64",
   "metadata": {},
   "source": [
    "#### Traçons le bode des fonctions\n",
    "\n",
    "Utilisons `bode`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "eligible-residence",
   "metadata": {
    "vscode": {
     "languageId": "json"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bode(backward,forward,tustin,derivateur)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3094000f-b197-450e-b82d-6248265f8bd1",
   "metadata": {},
   "source": [
    "**Critiquons l'outil !**\n",
    "- Ne vous faites pas avoir, les Anglais semblent confondre fréquence et pulsation sur ce coup.\n",
    "- Pas moyen d'afficher en fréquences plutôt que pulsation\n",
    "- Pas moyen d'afficher en fréquences normalisées ou de repérer facilement la fréquence $F_e/2$\n",
    "\n",
    "Spécifions les fréquences d'affichage pour voir l'aspect périodique du système :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "d4e5a765-e376-4db9-8faa-5ef90175bb17",
   "metadata": {
    "vscode": {
     "languageId": "json"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w=2*pi*(10.^(3:0.01:6)); %de 1kHz à 1MHz en échelle log\n",
    "w=2*pi*logspace(3,6,300); % pour les faibles ! cela fait la même chose\n",
    "bode(backward,forward,tustin,derivateur,w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a3c0666-adf0-45e0-b649-205511e022f7",
   "metadata": {},
   "source": [
    "**Critiquons l'outil !**\n",
    "- Les modulos $2\\pi$ sur la phase sont gérés de manière surprenante surtout pour la bilinéaire.\n",
    "- La fréquence d'échantillonnage et de Nyquist $Fe/2$ ne sont toujours pas clairement indiqué.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "33f19569-c9c6-467f-bc0d-f49a00072bb2",
   "metadata": {
    "vscode": {
     "languageId": "json"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "43b84bff16fa7216ed338d9940931cd50142a36f0abc305db4b43b5f154f347f"
  },
  "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"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}