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@pierre-haessig
Created May 7, 2014 11:14
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Study of 2nd order autoregressive process (AR(2))
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{
"metadata": {
"name": "second order process"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Study of 2nd order process\n",
"==========================\n",
"\n",
"that is, the AR(2) process : $X_k = \\phi_1 X_{k-1} + \\phi_2 X_{k-2} + Z_k$\n",
"\n",
"with the 2 degrees of freedom : $(\\phi_1, \\phi_2) \\in \\mathbb{R}^2$\n",
"\n",
"*Pierre Haessig - June 2012*"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"from scipy.signal import lfilter\n",
"import scipy.stats as stats\n",
"import matplotlib\n",
"from IPython.core.display import display, HTML, Image"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 100
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Choose the filter\n",
"c1, c2 = (1.5,-0.90)\n",
"# Plot\n",
"c_range = np.linspace(-2,2,101)\n",
"fig = plt.figure('coeff', figsize=(9,5))\n",
"ax = fig.add_subplot(111, aspect='equal', title='AR(2) coefficient space',\n",
" xlabel='coeff $\\phi_1$', ylabel='coeff $\\phi_2$')\n",
"# Plot the coeff point:\n",
"ax.plot(c1, c2, 'r*', ms = 10)\n",
"\n",
"ax.plot(c_range, -c_range**2/4, 'r--', label='$\\Delta=0$', color='#FF0000')\n",
"ax.plot(c_range, -np.ones_like(c_range), 'b-', label='stability')\n",
"ax.plot(c_range, 1-np.abs(c_range), 'b-', label='stability')\n",
"ax.fill_between(c_range, -np.ones_like(c_range), 1-np.abs(c_range), color='#0077FF', alpha=0.05)\n",
"ax.legend(loc='upper right')\n",
"ax.set_xlim(-2.5,2.5); ax.set_ylim(-1.5,1.5)\n",
"ax.grid(True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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nnpDmDVUTexiIiEgW5P79HR0djblz5+LChQvF4oyIiECTJk2wZMmSap9z5MiREAQBX3zx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\n"
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## Second order statistics of AR(2)\n",
"\n",
"compute the *autocovariance* function $\\gamma(h)$ to find :\n",
"\n",
"* Variance $V = \\gamma(0)$\n",
"* *autocorrelation* function $\\rho(h) = \\gamma(h)/\\gamma(0)$\n",
"\n",
"Reference : http://www.dynare.org/stepan/oldies/note04.pdf + own calculus\n",
"\n",
"### Computation of $\\gamma(h)$ :\n",
"\n",
"Taking the variance of the AR(2) process equation :\n",
"$$\\gamma(0) = (\\phi_1^2 + \\phi_2^2) \\gamma(0) + 2 \\phi_1 \\phi_2 \\gamma(1) + \\sigma^2$$\n",
"and the correlation at lag one is : \n",
"$$\\rho(1) = \\frac{\\phi_1}{1 - \\phi_2}$$\n",
"\n",
"Therefore :\n",
"$$\\gamma(0) = (\\phi_1^2 + \\phi_2^2 + 2 \\frac{\\phi_1^2 \\phi_2 }{1 - \\phi_2}) \\gamma(0) + \\sigma^2$$\n",
"\n",
"Grouping the variance terms on the left-hand side :\n",
"$$(1 - \\phi_1^2 - \\phi_2^2 - 2 \\frac{\\phi_1^2 \\phi_2 }{1 - \\phi_2}) \\gamma(0) = \\sigma^2$$\n",
"\n",
"\n",
"Factored expression :\n",
"$$\\gamma(0) = \\frac{1 - \\phi_2}{(1 + \\phi_2) (1 - \\phi_2 + \\phi_1) (1 - \\phi_2 - \\phi_1)} \\sigma^2$$\n",
"\n",
"Compressed expression :\n",
"$$\\gamma(0) = \\frac{1}{1 - \\phi_2^2 - \\phi_1^2 \\frac{1 + \\phi_2}{1 - \\phi_2} } \\sigma^2$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def Var_AR2(c1,c2):\n",
" '''Variance of an AR(2) process\n",
" X_k = c1 X_{k-1} + c2 X_{k-2} + Z_k\n",
" with Z_k of unit variance\n",
" '''\n",
" return 1/(1-c2**2 - c1**2 * (1+c2)/(1-c2))\n",
"\n",
"def std_AR2(c1,c2):\n",
" '''standard deviation of an AR(2) process'''\n",
" return np.sqrt(Var_AR2(c1,c2))\n",
"\n",
"# Apply the computation to the current coefficients\n",
"Vx = Var_AR2(c1,c2)\n",
"\n",
"print('Variance for c1,c2 = (%.2f,%.2f) : Vx = %.2f' % (c1,c2, Vx))\n",
"display(HTML('<strong>Standard deviation</strong> sqrt(Vx) = <strong>%.2f</strong> * sigma_eps' % std_AR2(c1,c2)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Variance for c1,c2 = (1.50,-0.90) : Vx = 13.97\n"
]
},
{
"html": [
"<strong>Standard deviation</strong> sqrt(Vx) = <strong>3.74</strong> * sigma_eps"
],
"output_type": "display_data",
"text": [
"<IPython.core.display.HTML at 0x3c7d250>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"Impulse Response\n",
"----------------"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = 100\n",
"# Dirac Impulse:\n",
"imp = np.zeros(N)\n",
"imp[0] = 1\n",
"# Impulse response:\n",
"imp_res = lfilter(b=[1], a=[1,-c1, -c2], x = imp)\n",
"# Plot\n",
"plt.figure('coeff', figsize=(10,5))\n",
"plt.plot(np.arange(N), imp_res, '-o')\n",
"plt.title('AR(2) Impulse Response\\n$(\\phi_1, \\phi_2) = (%.2f, %.2f)$' % (c1,c2))\n",
"plt.xlabel('instant k')\n",
"plt.xlim(0,30)\n",
"plt.grid(True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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IRCZX7G1xpKZNwc8P1qzROxJRFMuWqb68p5/WOxLniI2NzVZsASQm\nFr01QJhLXisWmzd7kJCgPjzu3g1796pl6G7d7l5s2UsKLgPQYx6XrPnnLbO3pWXLSMqWdY3eFkcz\nS/O8K+XckW7eVFv2TJli376g+TFKzt2pNcAoOTeivK7G7dAhnW+/VVu1+flpE4ssCBhA69aweLHe\nUYjbhYYGsnFjIMHBMFFWEXPo3RveeAOOHIHatfWORhTWV1/Bvfeq+VWuylljL4S5jBgRzG+/jeHk\nyduXlkcTHt5Z81ikh8sAjh6FFi3g9GnHf9oU9nvgAfWLqVUrvSMxpogIdep9kn1Dl4VOrl6FunVV\nY/mDD+odjfPk1ixdo8Zovvii6GerhXl8/z0MHJhAgwZxlCrlgZdXOuHhnYr8HrCnbpGCyyBq1oT1\n66FOHb0jEQCHD6tC69QpNS9N5LRvnzpDcvSo61zh5g7ee09d+OAOZ9Wt1gSiouJISfEgKSmdq1c7\n8ccfgXKxh5v45hu1dL5qFfzrX449tjTNm5jW87hkzT9/Vit06eLYYsvVct6oEdSrBytX6h1J3lwt\n50V14QJ89JFzz0oaKeehoYFER08kPn48u3ZNpHbtQD79VO+oHM9IOTeKDz+ECRMgPt7xxZa9pOAy\nCNlX0VhWrVJXq4j8DR1qjuZ5oUyZoq5KrFtX70i0Z7GoPVEnTYLjx/WORjiLzabOan35JWzcqD4U\nGoUsKRrE9u0waBDs2aN3JOLqVahWTf1QLldO72iMLTVVLYdv2iTL4UZ37Bg0awa//abe3+5q/Hg1\nBuC//9U7EuFo6enwyivwyy9qbE3lys57LXvqFlnJNoimTdUgyUuX1AbBQj8//KAuYpBi6+5KloRH\nH02gU6dYateWad5GNn68OiPpzsUWwDvvqJ+3K1dCjx56RyMc5cYNePZZOH9eDTJ11iytopAlRYMo\nXlxtH/Dzz9q8nqz5581Zy4mumHOrNYFffonh8GG10Xds7CQiImLuuleZVlwx5/bYt09dlfjWW85/\nLaPn3MtLLYOHh6udPlyB0XPubFevQvfuquiyWo1ZbIEUXIaixwBUkZ3Npv7BSv9WwcyYEcvRozLN\n2+jGjFHFlpw9V9q3h6AgGDdO70hEUSUlqe14/Pxg6VJjb5EnBZeBaNk4HxQUpM0LmczOnVCmjHOa\nil0x50af5u2KOS+szZtVT8vw4dq8nllyPm0afPst7NihdyRFZ5acO9qpU2rfw9at1cxEo4/7kILL\nQB55BLZuhbTcByQLDcjViYUj07yNzWZTPUvjxxv7k78e7rkH3n9f9bWly9vVdBIT4dFH4Zln4IMP\nzDE0XAouA/HxgRo1tLlS0d3X/PPizILLFXNu9I2+XTHnhREdDefOwXPPafeaZsr5oEFQqpQaF2Fm\nZsq5I+zeDYGBapl81ChzFFsgVykaTuayYvPmekfifs6cgT/+UJ+aRMFkXo0YFRXJxYse7NiRzrRp\nsnWKEWRkqF9Gkycbf6lFLxaLaqAPDIQnn4Tq1fWOSNzOak1gxoxYUlNvXQFdsWIgTzwBM2ZAnz56\nR1g4MofLYL7+GtauhQUL9I7E/cyerRrmly7VOxLzat8eXn4ZevXSOxIxfz588on6AGeWMwB6iYyE\n33+Xf/tGkttemNWqjeHq1RCWLAkkJETH4JCtfVxCmzYycV4v0r9VdEOGqAnPQl83bqgiYsoUKbYK\nYvRodcGM1ap3JCLTjBmx2YotgFOnJtOwYZzuxZa9pOAymHr11GyYEyec+zrutuZ/NzduqDOLXbo4\n7zXcIedPPqmuiDt8WO9IFHfIeW5mzoQGDdQVXFozY84z+7heeUXNdDIbM+b8bvK6AtrLyxhXQNtD\nCi6DsVhkX0U9bNyofkH5+uodibl5eUH//mppXOgjOVn1bb3/vt6RmEvHjqp/c8IEvSMR4JpXQEsP\nlwFNmaIauD/6SO9I3MfIkVCpEowdq3ck5rdnjzpTePiwNGvr4d//Vhd/zJ+vdyTmc/YsPPCAOtvd\npIne0bg3qzWBl16K4dixW8uKAQGjmT7dGBfl2FO3SMFlQAkJ8Oab2m3zI9RS7uLFcnWoozz8sOoh\nCg3VOxL3cu4cNGyo5vndd5/e0ZjTf/6jhmhu2gTFZA1IN0lJcP/9CdxzTxw+Ph54eaUTHt7JEMUW\nSNO8y2jRAn77Da5dc95ruOKav73+/FP1bTRr5tzXcaecv/CC+sWlN3fKOailxH799C22zJ7z559X\nZ2ZnztQ7koIze87vlJ6u3sd9+waye/dE4uPHEx090TDFlr2k4DKgUqXUae3t2/WOxD1kXp0oV3M5\nTt++sGGD2npDaOPwYZg3T5bFi6pYMVVsvfuuvH/1MmaM2nHlgw/0jsSxZEnRoEaOhCpV1LYcwrke\newwiIqBHD70jcS1DhqgzLaNG6R2Je3juObj3Xmn6dpTRo+Gvv2DRIr0jcS+LF6vfe9u2QeXKekeT\nN12WFKOjo2nQoAF169Zl6tSpuT5mxIgR1K1bl6ZNm7LDFXYK1UCbNvDTT3pH4fouX1b/sB97TO9I\nXM+QIaoXJiND70hc3+7dEBMDr7+udySuY+xY9bMhOlrvSNzHrl1qk/XvvjN2sWWvIhVc6enpDB8+\nnOjoaPbt28fChQvZv39/tsesXr2agwcPcuDAAWbNmsVLL71UpIDdReZoCGed+HO1NX97xcaqS8HL\nlHH+a7lbzlu0gNKlQc9v211yPmaMOpNYrpzekbhOzkuXhk8/VTsnOLOf1hFcIecXLpC1ZY+z+2n1\nUqSLtrdu3UqdOnXw9/cHoG/fvqxYsYKGDRtmPWblypUMHDgQgFatWnHp0iXOnDlDlSpVsh0rLCws\n6zgVKlSgWbNmBAUFAbfeTO5229s7iD//hFOnHH/8nTt36v79GeG21Qr16sUTH+/818tkpO/f2beH\nDIHJk+MpVswY8bjK7S1bdrF+/TlSUz05fTqR06cfYtmyCEPEt3PnTl1f35G3O3eGe++NZ8gQmD9f\n/3jyum32n+fp6fD++0E89RRUq6bNz+PC3s78++EiTHUuUg/XsmXLiImJ4T//XI707bff8vPPPxMV\nFZX1mO7duzNq1Chat24NQMeOHZk6dSoPPvjgrSCkhytX/furpa7Bg/WOxDWlp0O1auoS+n9qfeFg\nSUmqjysxUc05E0WX2x5zvr5j+PrrENNfxWVEp09D48awfr26mEk43htvqGXx1avNM7tP8x4uSwEv\n67ozqII+z93JxHnn2rZNXZggxZbz+PioK0C//VbvSFxHbnvMnT07maioOJ0icm1Vq8LEidCrVwIh\nIWMJChpPSMhYrNYEvUNzCQsWqJ6tRYvMU2zZq0gFl5+fH8eOHcu6fezYMWrUqJHvY44fP46fn19R\nXtZtOLPguv00qbuyWrUdzOmuOc+cyaXHSWxXzHlee8ylpBhjjzlXzLmfXwKHDsUQGzuJDRvGExs7\niYiIGMMUXWbN+a+/qivEv/tOfThzdUUquB566CEOHDjA4cOHuXHjBosXL6bHHdfW9+jRg7lz5wKw\nZcsWKlSokKN/S+SucWM4flwtywjHy5y/JZyrXTtITZWdExzFFfeYM7pPPoklNTX7WcXERDmrWBTn\nzqnN7j/7zH22USpSweXp6cknn3xCSEgIjRo1ok+fPjRs2JCZM2cy858xvV27duW+++6jTp06DB06\nlM8++8whgbsDT09o2RI2b3b8sTMbAt3V8eNw9KjagkYr7ppzi0W/yfOumPMRI4IJCBiT7b6AgNGE\nh3fSKaLsXDHnRj+raLac37wJffqoafK9eukdjXZk8KnBjRunJu5Onnz3x4qCmzVLTUKXDX61cfq0\n2uPvyBFjjC4wu7ffTmDmzDiaNTPeHnOuKCRkLLGxk3K5P5Lo6Ik6RGRur76qNlhftQo8jFGzFprs\npeiCWrd2zgBUs675O4oey4nunPOqVaF9e+2ndrtizjMyYPXqQBYsMOYec66Y89zOKtaqZZyzimbK\n+dy5qn92wQLzFlv2cvFrAszv4YfVnoo3b0Lx4npH4xquX4f4eJg9W+9I3MuQIeqM7Ysv6h2JuX33\nHXh5QZcuekfiPjIL2qioSFJSPDh7Np3U1M489phxCl0z2L5d7YYQHw8VK+odjfZkSdEEmjRRW6S0\naKF3JK5hzRp4/31IMMYFRm4jPV3t9fe//0HTpnpHY04ZGdC8OUyaBN276x2N+7LZVO9R1arwySd6\nR2MOZ86o32Eff6ya5c1OlhRdlMzjciy5OlEfHh5qiO+XX+odiXmtWKEuppH3r74sFvUheM0aWLZM\n72iM7+ZNVaAOHOgaxZa9pOAyAWcUXGZa83ckm02/gstdc367QYNU78b169q8nivl3GaDf/8b3n1X\n/cI3KlfKeX7Kl4fFi9Vei4mJ+sZipJxbrTkHxI4cqfI1YYLe0elLerhMoE0bGD1a/cA18g9aM9i7\nF4oVU1fMCe3Vrq1GnSxfDgMG6B2Nuaxcqf57x6hDoaOHHoKxY9WIg59+gpIl9Y5IX7ltO7VjxxiK\nF4d9+wIp5uaneKSHywRsNtUrsG0b1KqldzTmNmUKnDgBt233KTS2fDnMmKHGcoiCsdngwQchMhKe\neELvaMTtbDZ46imoUUO9r91ZXuMzHn00ko0bXWt8hvRwuSiLRfq4HEX6t/TXvbuawfPnn3pHYh6r\nVqmLDh5/XO9IxJ0sFvj6a/X/6L//1TsafeU1INbD3eY/5EEKLpNo08ax87iMtOavlQsXYM8etdWM\nHtwx57kpUQKee06b5nlXyLnNpnpf3n0XUyzJuELOC6tCBTVjbtgw+Osv7V/fKDmXbafyZ4J/vsJq\nTWDp0rHMni271BdFdLQavunlpXck4oUXYM4cuHFD70iMb/VqtRelLCUaW8uWqte2b1/3fV+PGBHM\nffcZd9spvUkPl8Hl1oQYEDCG6dNDDDVd2gz69YPHHlO/7IX+2rWDESNU/4vInc0GrVrBm2+6155z\nZmWzqcLY31/Nm3I3KSnQqlUC58/HUbeua287ZU/dIgWXwckeXo6Rlga+vvDbb1C9ut7RCIBvv1V7\nWa5Zo3ckxrVmjSq2du82x3KigKQk+Ne/VMHVs6fe0Wjnxg01Y6tsWfXv2tXbtqRp3gU5a5d6o6z5\na2XTJjXlXM9iy91yfjdPPQVbt6oNrZ3FzDnP7N2KjDRXsWXmnDuCj4+az/Xii3D4sDavqXfO09LU\nmBcPD5g3z/WLLXuZ6J+xe5ImRMeQqxONp1QpeOYZ+OYbvSMxpthYuHIFnn5a70hEYbVqBe+8o+Zz\nuXo/V0YGPP88XLqkCk3Z8zdvsqRocLn1cN1772iiojq75Lq4s9x/v/rF3rKl3pGI2+3apcZEHDok\nn4pvZ7OpK5PDw1XvoTAfm02N8ahbFz78UO9onMNmU5P2f/tNXZRUpozeEWnHnrpFJs0b3J271O/Z\nk86AAVJsFcZff8H582oqtDCWpk3VUN/YWOjSRe9ojGPtWrh4EXr31jsSYS+LBWbPVpuNt2vnejsE\n2Gyqv/CXX9T71Z2KLXvJkqIJhIYGEh09kfj48YwaNZHz54tebOm95q8lqxVCQ/Xvg3GnnBfGCy84\nbyaXGXOe2bs1dqw5z/qZMefO4uOj5nMNGeJ6vYoTJkBcnDqzVa6c5i9vSlJwmUznzurKJVmBLbjM\ngksYU79+sG4dnDmjdyTGsG4dnDun5jkJ83vkEXjjDfX/8+ZNvaNxjA8+UIVkXJwqKkXBSA+Xydhs\nULOm+qFcr57e0Rjf339DtWpq/0T5FGZczz8P9evDW2/pHYm+bDa1/DRkCDz7rN7RCEfJyFBLig0b\nqmLFzD79VPWkbdwIfn56R6MfGQvhBiyWW2e5xN2tXQsPPyzFltENGaKWFd39c1d8PJw6JY3yrqZY\nMbWzwuLF6opps5o9G6ZOhR9+cO9iy15ScJlQly5q3bwo3KXPwkjLie6Sc3u0aqX2WExw8K5VZst5\nZu+Wp4kvZzJbzrVSqRIsXAgDBiTQrt1YgoIct1WbFjlfvFhtXRQXp2YaisIz8T9r9/XYYxAWBtev\nq1lGIncZGargevttvSMRd2OxqLNc//mPfpuL623DBjh+HPr31zsS4SyXLiXg4RFDQsKtMT+JiWrv\nQSNfef6//0FEhLqauH59vaMxL+nhMqm2bdUn4ZAQvSMxrl9+Ub+8fv9d70hEQVy4AAEBaiZXxYp6\nR6O9Dh1U39agQXpHIpzFjFu1xcWpn6NWK7RooXc0xiE9XG6kc+eiLyu6OiMtJ4q727IlgVKlxtKy\npeOWWsxi40a1DcyAAXpHIpzJWVu1OcvGjWo3iOXLpdhyBCm4TKqojfPu0GdhtO183CHn9srcUeH0\n6UkcPDie2NhJRETEFLnoMkvOJ0yAMWNcY1sUs+RcD3lt1ZaRUbSt2oqac6s1gZCQ7H1l27ap/U4X\nLFArKqLopIfLpJo3V5OoDx2SBsbbWa0JzJgRS3KyJzt2pHHlSjBg3N4IocyYEZtt+yqAxMTJREVF\nGrq3xRF++gkOHoTnntM7EuFsI0YEk5g4Jtt7vVKl0ezY0ZmRI9VG5VrPtcpt+7j9+8dw5QrMmxdI\np07axuPKpOAyqWLFVP9WTAwMG1b45wcFBTk8Jr3l9oPj9dfH4OlpjIZUV8y5ozhrqcUMOf/3v9XV\nX65wdgvMkXO93LlVm5dXOuHhnWnRIpDx46FBA3Wm86WX1FW7BVWUnOf2YefYsck0bRpJ9+76/9x0\nJbKkaGLSx5Vd3mdJ4nSKSBRUXkstXl5FW2oxui1b1EUdYWF6RyK0cvtWbdHREwkNDcTXFz77DNav\nVx+iH3gAVqzQZi5dXh92KlQwZl+ZmUnBZWLBweof6I0bhX+uK/ZZGL0h1RVz7igjRgQTEDAm232e\nnqMZOrRo6xlGz/mECTBqVOHOZhid0XNuZPffD6tXQ1SUOtPVoQP8+uvdn2dvztPSIDnZPT/s6EGW\nFE2scmV1Cvqnn6B9e72j0Z+7niVxBbkttSQnd2bnzkCeeELn4Jxk61bYuxe+/17vSITRhISoeYtf\nfQVdu6ph15MmOWa6u82mirh589R+iOXLB1O58hjOn7+1OhAQMJrw8M5FfzGRjczhMrlx4yAlRW23\n4O5y6+EKCBjN9OmdDdHDJQrnxAlo1kxNn2/YUO9oii7zgo7UVE9KlkwjKSmYQYMCefllvSMTRnbl\nCrz/PsyaBSNGqI2wy5Qp/HEOHVJXHH77rVoVGTBAzdeqV0+9N6Oi4m7rK+skPzPvwp66RQouk9u8\nWTXN79qldyTGsHx5An36xNGqlQfe3vKDw+w++QSWLFF7DBYzcQNEbh8GPDzGsGxZCD17yvtT3N3h\nwx8aQiIAABr5SURBVGr5eeNGmDxZDcldsyZ7ET9iRHC2n3dJSbB0qSqyfv8devdWhdbDD6vdHYT9\npOByQ+np4OsLu3cX7nRzfHy8S15NtGSJOg0fE6N3JDm5as6dKT0dWreGoUNh8ODCP98oOTfjhHF7\nGSXnrmrzZnjtNTh7NoGUlBhOnpwMxANBBASMYdq0EDIyAvn2W1i3Ti1PDhig/utKvYJ6k0nzbsjD\nAzp1MmaBoYfFi6FPH72jEI7i4QEzZ6pP9mfP6h2N/Yx+QYcwj0cegU2boGzZ2H+KrVsSEyfTq1cc\nn3yihj4fOaJ+JnbvLsWWEUjB5QLsGQ/hip9Ak5Nh7VoM22TtijnXQrNmaijo668X/rlGybk7XdBh\nlJy7MosFKla8vYgPyvrbQw95sG6dOiNcvrzmoYl8SMHlAkJCVKGRlvvPdLexcqXagsIdNz52dePH\nq96VtWv1jsQ+uY29UFeCyRhvYZ+8ivjy5V2viHcVUnC5gGrVoFYtdZl5QbnirByjLye6Ys61UqaM\nGgz50ktw/XrBn2eUnIeGBtKzZwilSkXSps14QkIiXfbqWaPk3NVlL+LjASnijc7uOVxJSUn06dOH\nI0eO4O/vz5IlS6hQoUKOx/n7+1OuXDk8PDwoXrw4WwtTFYgCy9zMunVrvSPRx8WLsGGDuhpHuKau\nXWH2bHWF1qSc/eeGtmcPzJkTyJYtgTRponc0whXcPrvu9OljVK36A+HhrlnEuwq7r1J86623qFy5\nMm+99RZTp07l4sWLTJkyJcfj7r33Xn755Rd88tmRU65SLLoNG9R8lm3b9I5EH998o5YUv/tO70iE\nM508CU2bqjER99+vdzQFc/kyPPSQmpk3YIDe0QghHEHTqxRXrlzJwIEDARg4cCDf5zMuWYop53vk\nEThwwNxXchWF0ZcThWNUr662wxk2DDIy9I7m7jIyYODAW5fmCyHcl91LimfOnKFKlSoAVKlShTNn\nzuT6OIvFQseOHfHw8GDo0KEMGTIk18eFhYXh7+8PQIUKFWjWrFnW1S6ZPQFyO//b7dsHERcHfn53\nf/zOnTt59dVXDRW/vbdXrIhn40ZYtswY8eR1O/M+o8Rj1tsNGsRz4QJ89VUQQ4bk//g7c691vFOn\nwoED8bzyCmReSaZ3/px9++OPP5af3xrfdqWf50a9nfn3w4cPY698lxQ7derE6dOnc9w/efJkBg4c\nyMWLF7Pu8/HxISkpKcdjT506RbVq1Th37hydOnUiKiqKtm3bZg9ClhQdYuZMdSVXQfqY4uPjs95Q\nZjdrFvzwgzrLZWSulHO97d4NHTuq3qh/PvflSs+cr12rxlls3Qo1augSgi7kfa49ybn2NJ0036BB\nA+Lj46latSqnTp2iffv2/P777/k+Z8KECZQtW5bX7xioIwWXYxw5Ai1awOnT5t4GpbAeewxeeQWe\nfFLvSISW3n4bjh+H+fP1jiSno0ehZUtYuFA2lhfCFWnaw9WjRw/mzJkDwJw5c+jZs2eOx1y7do3k\n5GQArl69SmxsLI0bN7b3JcVd1K4NlSurneDdxZkz6vvt0kXvSITW3n1XbXNitF0WUlPh6afV9itS\nbAkhMtldcL3zzjvExcVRr1491q1bxzvvvAPAyZMnCQ0NBeD06dO0bduWZs2a0apVK7p160ZwcLBj\nIhe5KujU+dvXpc1s2TIIDYVSpfSO5O5cJedGUaYMfPopvPwyXLuW+2P0yPmrr6olxDff1PylDUHe\n59qTnJuD3U3zPj4+rM1l7HP16tWxWq0A3HfffezcudP+6EShde6sruIaO1bvSLSxeLH7/mIT6sxm\nixZqLtd77+kdjZoTtm6dGs9isegdjRDCSOzu4XJoENLD5TApKeDrq/q5XH2Lm+PHoUkTOHUKSpbU\nOxqhl1On1Ptg/Xp44AH94ti5U20kHx9vnhlhQgj7aNrDJYzJy0vtJ2jWPecKY+lSePxxKbbcXbVq\nMHEiDB2q32yuixfhqacgKkqKLSFE7qTgckEF6eNyhTV/sw07dYWcG9WLL4LNBv/5T/b7tch5RoYa\natqjB/Tt6/SXMzx5n2tPcm4OUnC5oMyCy5VXaQ8fhsRENRJCiGLF1By6sWPVWBQtTZoEV67A//2f\ntq8rhDAX6eFyQTYb1Kmj9hV01Y1y/+//4OBBNfRUiEyjRsGhQ7BokTavFx0Nzz8P27erpU0hhHuQ\nHi4BqKujunQp2HgIs1q8WJZvRE6RkeoKwTVrnP9ahw6pfRIXLZJiSwhxd1Jwuai79XGZec3/4EE4\ncQLatdM7ksIxc87NonRp+OwzCAtLoGPHsTRrFkZIyFis1gSHvk5Kihpu+s476iIVcYu8z7UnOTcH\nu+dwCWMLCoJ+/SA5Gby99Y7GsRYvVr/sPDz0jkQYUVpaAteuxfDDD5OBeCCIxMQxAISGBjrkNYYP\nV8v2/+wXLIQQdyU9XC6sY0cID1ejE1xJ48bqLIacWRC5CQkZS2zspFzujyQ6emKhjmW1JjBjRiyp\nqZ6ULJnGiBHBnDoVyP/7f2pT6rJlHRW1EMJM7Klb5AyXC8vs43KlgmvfPjXzqE0bvSMRRpWamvuP\ntZSUwp0StVoTiIiIITFxctZ9+/aN4fJl2Lo1UIotIUShSA+XC8tvPIRZ1/wXL4ZevdQYALMxa87N\npmTJtNtuxWf9bcuWdB5+GJ58Up35nTIF5s6FH36A/fvVaIfb/63MmBGbrdgCOH58MgEBcTRo4Nzv\nwczkfa49ybk5yBkuF9aoEaSlwZ9/Qv36ekdTdDabKrhmz9Y7EmFkI0YEk5g4JluxdN99oxk7tjP1\n68PJk+qii5Mn4bffbv39xAn1WD8/qF4d9u3L/cdj+fLSPCiEKDwpuFyYxaLOcq1Zk7PgCgoK0iWm\noti9W10d1qqV3pHYx4w5N6PMxvioqEhSUjzw8vqB8PDOd22Yt9nURSaZBdirr6Zx9mzOx3l5pTsj\nbJch73PtSc7NQZrmXdx//6uGg7rCTK7Ro9UZO5noLbSQWw9XQMBopk+/e/EmhHBtMvhU5PDYY/DT\nT3D9evb7zbbmn7mcaKa9E+9ktpy7gqLkPDQ0kOnTQwgJiaRdu/GEhERKsVUA8j7XnuTcHGRJ0cWV\nLw/Nm8OGDWp50ax++UU1yv/rX3pHItxJaGigFFhCCIeQJUU38N57cPYsfPyx3pHY7403wMtLbRQs\nhBBC6EmWFEWuunTRZm85Z8nIgCVLzL2cKIQQwr1JweUGmjaFy5fhr79u3WemNf8tW9RE7wce0DuS\nojFTzl2F5Fx7knPtSc7NQQouN1CsGISEQEyM3pHYJ7NZ3mLROxIhhBDCPtLD5SYWLoRFi2DFCr0j\nKZz0dKhZE9atQ6Z7CyGEMATp4RJ56tQJ4uMhNVXvSArnxx/hnnuk2BJCCGFuUnC5icqVoWFDNZML\nzLPmb/bZW7czS85dieRce5Jz7UnOzUEKLjeSuZm1WaSlwbJlrlNwCSGEcF/Sw+VGtmyBF19UexKa\nQVwcjBoF27frHYkQQghxi/RwiXy1aKE25j1+XO9ICmbxYujbV+8ohBBCiKKTgsuNeHhAcLAaD2H0\nNf8bN+C776B3b70jcRyj59wVSc61JznXnuTcHKTgcjNm6eNauxbq14datfSORAghhCg66eFyM6dO\nQaNGcO4ceBp46/KBA9VG1RERekcihBBCZGdP3SIFl5uxWhPo1y+WgABPfH3TGDEimNDQQL3DyiYl\nBapVg717oXp1vaMRQgghspOmeZEvqzWBiIgYkpMnsXNnELGxk4iIiMFqTdA7tGxiYqBJE9crtqTP\nQnuSc+1JzrUnOTcHKbjcyIwZsSQmTs52X2LiZKKi4nSKKHeuNOxUCCGEACm43Epq6u1NW0FZf0tJ\n8dA8lrxcuwarV8NTT+kdieMFBQXpHYLbkZxrT3KuPcm5ORi4bVo4WsmSabne7+WVrnEk2VmtCcyY\nEUtqqicXL6ZRu3YwVaoYq69MCCGEKAo5w+VGRowIJiBgzD+34gGoXHk04eGddIsps68sNnYSGzaM\nZ/fuSZw6Zby+MkeQPgvtSc61JznXnuTcHOQMlxvJvBoxKiqS06eP4e39A7t2dcbfX7+zSbn1lZ07\nN5moqEjDXT0phBBC2EvGQri5b76BDz+EbdugVCntXz8oaDwbNozPcX+7duOJj895vxBCCKE3GQsh\nCi0sTI1gGDlSn9c3al+ZEEII4Uh2F1xLly7l/vvvx8PDg19//TXPx0VHR9OgQQPq1q3L1KlT7X05\n4WCZa/4WC3zxBcTFwfLl2scxYkQw9903Jtt9AQH69pU5i/RZaE9yrj3JufYk5+Zgdw9X48aN+e67\n7xg6dGiej0lPT2f48OGsXbsWPz8/WrRoQY8ePWjYsKG9LyucoFw5WLQIQkPhwQfB31+71+7cOZDK\nleH69Ujq1fPAyyud8PDO0r8lhBDCpdhdcDVo0OCuj9m6dSt16tTB/5/f4H379mXFihW5FlxhYWFZ\nj/v/7d1/TJV1/8fx5xFNJUhsBvJr06gEDTmgQQtRXKF5E5ipaeWvRd6su1KX0zvvO+/SyvJWV2i2\nNea6uW+MO62h/JimVoRSplPPHU26125BScXl1CH+SPnx/YNxvhpgnMO5rnMO5/XY2rjOuTjXm9c+\nc++uz+d8rqCgIKxWq31vkbbuXceuPW7Tdrx0aSpPPw0rV5bRu7fx1x83LpWFC6GxsZm8vIdJS/v/\n98vKytyej469/zg1NdWj6vGF47bXPKUeXzlu4yn19LTjtp9rampwVrcXzY8fP55169aRkJDQ7r1P\nP/2Uzz//nNzcXADy8/P57rvv2LBhw81FaNG8R2huhj/8ofUu11tv/f753bVmDfzzn7BvHwwYYPz1\nREREXMHli+bT0tKIjY1t919xcXGXCxLP9Nv/KwLo1Qvy8uAf/4AvvzT2+v/+N6xf37qrvK80Wx1l\nLsZS5uZT5uZT5t7hllOKu3d37xl74eHh1NbW2o9ra2uJiIjo1meKsUJCWpuuOXPg8GEIDnb9NcrL\nYcEC2LMHIiNd//kiIiKexiVTimvXrmXUqFHt3mtsbGTYsGF88cUXhIWFkZiYSEFBQbs1XJpS9DzL\nlsF//gMlJa13vlylqgpSUyE/H9J63hcRRUTEB5i6D1dhYSGRkZHs37+f9PR0Jk2aBMCpU6dIT08H\noHfv3rz//vtMnDiR4cOHM2PGDH1D0UusXAnnz8N777nuM0+fbl0j9ve/q9kSERHfop3mfdSN3yLq\nTHU1JCW1rrMaPbp712togHHjYPJk+NvfuvdZ3qormYtrKXPzKXPzKXPzaad5camhQ2HjRpg5E+rr\nnf+cxkaYMQPi42H5ctfVJyIi4i10h0t+1x//CJcvw7/+1bozvSNaWiA7G06cgOJi6NPHmBpFRETM\nojtcYoj33oMjR1r3zHLUqlWtD8beulXNloiI+C41XD7KkX1b/P1b981avBj++9+uXyM/H3JzobQU\nAgMdr7Gn0V455lPm5lPm5lPm3kENl3RJbCy8+Wbreq5ff/3987/8srVBKy2FsDDj6xMREfFkWsMl\nXdbSAtOnQ3g45OR0fl5lJTz8MGzZ0rrnloiISE+iNVxiKIuldYpw+3YoKur4nJMnIT29dd2Xmi0R\nEZFWarh8lLNz/gMHwubNMGdOOePGvUpq6utMnPgqpaXl1Ne3bmz6pz/B00+7tt6eQOsszKfMzafM\nzafMvcMtn6Uo0pELF8rx8/uc8vK37K/9739/JTAQkpPH8uc/u7E4ERERD6Q1XOKwiRNfZdeuN9u9\nPmjQck6ffoPeauNFRKQH0xouMcWvv3bcUcXE+KnZEhER6YAaLh/VnTn/vn0bO3zd37/J6c/0BVpn\nYT5lbj5lbj5l7h3UcInDFiyYQFTUX296LSrqL7z0UpqbKhIREfFsWsMlTiktLWfDht1cvepHv35N\nvPRSGunpY91dloiIiOGc6VvUcImIiIg4QIvmpcs0528+ZW4+ZW4+ZW4+Ze4d1HCJiIiIGExTiiIi\nIiIO0JSiiIiIiAdSw+WjNOdvPmVuPmVuPmVuPmXuHdRwiYiIiBhMa7hEREREHKA1XCIiIiIeSA2X\nj9Kcv/mUufmUufmUufmUuXdQwyUiIiJiMK3hEhEREXGA1nCJiIiIeCA1XD5Kc/7mU+bmU+bmU+bm\nU+beQQ2XiIiIiMG0hktERETEAVrDJSIiIuKB1HD5KM35m0+Zm0+Zm0+Zm0+Zewc1XCIiIiIG0xou\nEREREQdoDZeIiIiIB1LD5aM0528+ZW4+ZW4+ZW4+Ze4d1HD5KJvN5u4SfI4yN58yN58yN58y9w5O\nN1xbt25lxIgR+Pn5cfjw4U7PGzJkCCNHjiQ+Pp7ExERnLycuduHCBXeX4HOUufmUufmUufmUuXfo\n7ewvxsbGUlhYSHZ29i3Ps1gslJWVceeddzp7KRERERGv5nTDFR0d3eVz9Q1Ez1NTU+PuEnyOMjef\nMjefMjefMvcO3d4WYvz48axbt46EhIQO37/77rsZMGAAfn5+ZGdnM3/+/PZFWCzdKUFERETEVI62\nT7e8w5WWlkZdXV2711etWkVGRkaXLlBRUUFoaCi//PILaWlpREdHk5KSctM5ugMmIiIiPdktG67d\nu3d3+wKhoaEA3HXXXUyZMoUDBw60a7hEREREejKXbAvR2R2qy5cvc/HiRQAuXbrErl27iI2NdcUl\nRURERLyG0w1XYWEhkZGR7N+/n/T0dCZNmgTAqVOnSE9PB6Curo6UlBSsVitJSUk89thjTJgwwTWV\ni4iIiHgJpxuuKVOmUFtby5UrV6irq2PHjh0AhIWFUVpaCrQumLfZbNhsNn744QeWLVvW7nN27txJ\ndHQ09957L6tXr3a2HHGA9kYz3rPPPktISMhNd3TPnTtHWloa9913HxMmTNDeOS7WUeavv/46ERER\nxMfHEx8fz86dO91YYc9TW1vL+PHjGTFiBPfffz/r168HNNaN1FnmGuvGuXr1KklJSVitVoYPH27v\nZRwd5259eHVTUxPDhg1jz549hIeH88ADD1BQUEBMTIy7SvIJQ4cO5dChQ9obzUB79+4lICCAOXPm\nUFlZCcDSpUsZNGgQS5cuZfXq1Zw/f5533nnHzZX2HB1lvmLFCgIDA3n55ZfdXF3PVFdXR11dHVar\nlYaGBkaNGsW2bdv46KOPNNYN0lnmW7Zs0Vg30OXLl/H396exsZExY8awdu1aioqKHBrnbn20z4ED\nB7jnnnsYMmQIffr0YebMmWzfvt2dJfkMfTPUWCkpKQwcOPCm14qKipg7dy4Ac+fOZdu2be4orcfq\nKHPQWDfS4MGDsVqtAAQEBBATE8PJkyc11g3UWeagsW4kf39/AK5du0ZTUxMDBw50eJy7teE6efIk\nkZGR9uOIiAj7wBHjWCwWHnnkEUaPHk1ubq67y/EZZ86cISQkBICQkBDOnDnj5op8w4YNG4iLiyMr\nK0tTWwaqqanhyJEjJCUlaaybpC3zBx98ENBYN1JzczNWq5WQkBD7lK6j49ytDZc2PHWPiooKjhw5\nwo4dO9i4cSN79+51d0k+x2KxaPyb4Pnnn6e6uhqbzUZoaCiLFy92d0k9UkNDA1OnTiUnJ4fAwMCb\n3tNYN0ZDQwPTpk0jJyeHgIAAjXWD9erVC5vNxs8//0x5eTlfffXVTe93ZZy7teEKDw+ntrbWflxb\nW0tERIQbK/INHe2NJsYLCQmxbyR8+vRpgoOD3VxRzxccHGz/h/C5557TWDfA9evXmTp1KrNnz+bx\nxx8HNNaN1pb5rFmz7JlrrJtjwIABpKenc+jQIYfHuVsbrtGjR/PTTz9RU1PDtWvX+OSTT8jMzHRn\nST2e9kZzn8zMTPLy8gDIy8uz/0Mpxjl9+rT958LCQo11F2tpaSErK4vhw4ezaNEi++sa68bpLHON\ndeOcPXvWPkV75coVdu/eTXx8vMPj3K3fUgTYsWMHixYtoqmpiaysrA63jhDXqa6uZsqUKQA0Njby\nzDPPKHMDPPXUU3z99decPXuWkJAQVq5cyeTJk3nyySc5ceIEQ4YMYcuWLQQFBbm71B7jt5mvWLGC\nsrIybDYbFouFoUOH8uGHH9rXXEj37du3j7FjxzJy5Ej7dMrbb79NYmKixrpBOsp81apVFBQUaKwb\npLKykrlz59Lc3ExzczOzZ89myZIlnDt3zqFx7vaGS0RERKSnc+uUooiIiIgvUMMlIiIiYjA1XCIi\nIiIGU8MlIiIiYjA1XCLiEZKTk536ve3bt1NVVeX0dY8fP05BQUGH75WVlZGRkeH0Z4uItFHDJSIe\noaKiwqnfKyws5OjRo05ft7q6mo8//tjp3xcR6Qo1XCLiEQICAoDWu0qpqalMnz6dmJgYZs2aZT/n\nlVdeYcSIEcTFxbFkyRK+/fZbiouLWbJkCQkJCRw7dozc3FwSExOxWq1MmzaNK1euADBv3jwWLlxI\ncnIyUVFRfPbZZ/bP3Lt3L/Hx8eTk5HRa38GDB0lISKC6utrAFESkp+rt7gJERODmZ6vabDaOHj1K\naGgoycnJVFRUEB0dzbZt2/jxxx8BqK+v54477iAzM5OMjAyeeOIJAIKCgpg/fz4Ay5cvZ9OmTbz4\n4osA1NXVUVFRQVVVFZmZmUydOpXVq1ezdu1aiouLO63tm2++YcGCBRQVFenxYyLiFN3hEhGPk5iY\nSFhYGBaLBavVyvHjxwkKCqJfv35kZWVRWFhI//797effuH9zZWUlKSkpjBw5ks2bN9unGy0Wi/3R\nGzExMZw5c6bd73akqqqK7OxsSkpK1GyJiNPUcImIx+nbt6/9Zz8/P65fv46fnx8HDhxg2rRplJSU\n8Oijj9rPufHu2Lx58/jggw/4/vvvee211+xTigC33Xab/eeuPGTDYrEQGhpK//79OXz4cHf/LBHx\nYZpSFBGvcOnSJS5dusSkSZN46KGHiIqKAiAwMJD6+nr7eQ0NDQwePJjr16+Tn59PZGTkLT83MDDQ\n/kD332ppaSEoKIhNmzaRlpbG7bffzrhx41z3R4mIz9AdLhHxCDfepbrx57bjixcvkpGRQVxcHCkp\nKbz77rsAzJw5kzVr1jBq1CiOHTvGG2+8QVJSEmPGjCEmJuZ3rxEXF4efnx9Wq7XdonmLxYLFYiE4\nOJiSkhJeeOEFDh486NK/W0R8gx5eLSIiImIw3eESERERMZgaLhERERGDqeESERERMZgaLhERERGD\nqeESERERMZgaLhERERGD/R95LyPuL8sELAAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"Roots of the characteristic AR polynomial $\\phi(z)$ \n",
"-----\n",
"\n",
"$$P(z) = z^2 - \\phi_1 z - \\phi_2$$\n",
"\n",
"(this is not the delay polynomial $\\phi(z)$, but rather its \"reciprocal\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1) *Numerical* Root Finding\n",
"the *quick and easy* way to analyze the process"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy.polynomial import Polynomial\n",
"p_ar = Polynomial([-c2, -c1, 1])\n",
"roots = p_ar.roots()\n",
"if roots.dtype == np.float:\n",
" print('Real roots: %.2f and %.2f' % tuple(roots) )\n",
"else:\n",
" rho = np.abs(roots[0])\n",
" theta = np.abs(np.angle(roots[0]))\n",
" print('Complex roots: %.2f exp(+/- %.2f)' % (rho, theta))\n",
" print('Pseudo-period: %.1f' %(2*np.pi/theta))\n",
" print('Frequency: %.2f (normalized /pi)' % (theta/np.pi))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Complex roots: 0.95 exp(+/- 0.66)\n",
"Pseudo-period: 9.5\n",
"Frequency: 0.21 (normalized /pi)"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2) *Analytical* Root analysis\n",
"Polynomial $P(z) = z^2 - \\phi_1 z - \\phi_2$ has two possibly complex roots: $z_1$ and $z_2$\n",
"\n",
"Those roots are the basis of the filter impulse response.\n",
"Therefore, the filter is *stable* if and only if $|z_1|$ and $|z_2|$ are *smaller than unity*.\n",
"\n",
"**Discriminant** $\\Delta = \\phi_1^2 + 4 \\phi_2$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"delta = c1**2 + 4*c2\n",
"print('delta = %.2f' % delta)\n",
"if delta > 0:\n",
" display(HTML('Delta is <strong> positive </strong>'))\n",
"elif delta < 0:\n",
" display(HTML('Delta is <strong> negative </strong>'))\n",
"else:\n",
" display(HTML('Delta is <strong> zero </strong>'))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"Delta is <strong> negative </strong>"
],
"output_type": "display_data",
"text": [
"<IPython.core.display.HTML at 0x4846790>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"delta = -1.35"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2a) Case Positive $\\Delta$\n",
"\n",
"$\\Delta > 0 $ : two separate real roots, when $\\phi_2 > -\\phi_1^2 / 4 $\n",
"\n",
"$z_1 = (\\phi_1 - \\sqrt{\\Delta}) /2$ \n",
"\n",
"$z_2 = (\\phi_1 + \\sqrt{\\Delta}) /2$ \n",
"\n",
"Consequence for stability : \n",
"\n",
" * since $\\text{max}(|z_i|) = (|\\phi_1| + \\sqrt{\\Delta} ) /2$\n",
"\n",
" * Therefore, stability implies $|\\phi_1| + \\sqrt{\\Delta} \\leq 2 $ e.g. $|\\phi_1| \\leq 2$\n",
"\n",
"This ends up with **stability conditions** :\n",
"\n",
"$ \\phi_2 \\leq 1- |\\phi_1|$, with $|\\phi_1| \\leq 2$ (iff, once $\\Delta > 0 $ is verified)"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"# Check Stability:\n",
"if delta > 0:\n",
" if np.abs(c1)<= 2 and c2 <= 1 - np.abs(c1):\n",
" display(HTML('system is <strong> stable </strong>'))\n",
" else:\n",
" display(HTML('system is <strong> unstable </strong>'))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2b) Case Negative $\\Delta$\n",
"$-\\Delta > 0 $ : two separate complex conjugate roots, when $-\\phi_2 > \\phi_1^2 / 4 $. E.g. $\\phi_2$ is negative.\n",
"\n",
"Equations to find $z_1 = r.e^{i\\theta}$ and $z_2 = r.e^{-i\\theta}$ :\n",
"\n",
" * $z_1 z_2 = r^2 = -\\phi_2$ and\n",
" * $z_1 + z_2 = 2r \\text{cos} (\\theta) = \\phi_1$\n",
"\n",
"Therefore : \n",
"\n",
"* $ r = \\sqrt{|\\phi_2|}$\n",
"* $ \\text{cos} (\\theta) = \\phi_1/2 \\sqrt{|\\phi_2|}$\n",
"\n",
"Therefore, the **stability condition** : $ - \\phi_2 \\leq 1$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Check Stability:\n",
"if delta < 0:\n",
" if np.abs(c2)<= 1:\n",
" display(HTML('system is <strong> stable </strong>'))\n",
" else:\n",
" display(HTML('system is <strong> unstable </strong>'))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"system is <strong> stable </strong>"
],
"output_type": "display_data",
"text": [
"<IPython.core.display.HTML at 0x4846f90>"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Information about oscillations:\n",
"if delta < 0:\n",
" # Damping factor `r`\n",
" r = np.sqrt(-c2)\n",
" display(HTML('<strong>damping factor</strong> : r = %.3f' % r))\n",
" display(HTML('-> damping <strong>time</strong> (at 10 %%) : T_10 = %.1f' % (np.log(0.1)/np.log(r))))\n",
" # complex angle theta\n",
" theta = np.arccos(c1/(2*r))\n",
" display(HTML('<strong>oscillation frequency</strong> : theta = %.2f (rad) = %.2f (normalized /pi)' % (theta, theta/np.pi)))\n",
" display(HTML('-> oscillation <strong>period</strong> : T = %.1f' % (2*np.pi/theta)))\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<strong>damping factor</strong> : r = 0.949"
],
"output_type": "display_data",
"text": [
"<IPython.core.display.HTML at 0x6069cd0>"
]
},
{
"html": [
"-> damping <strong>time</strong> (at 10 %) : T_10 = 43.7"
],
"output_type": "display_data",
"text": [
"<IPython.core.display.HTML at 0x6069cd0>"
]
},
{
"html": [
"<strong>oscillation frequency</strong> : theta = 0.66 (rad) = 0.21 (normalized /pi)"
],
"output_type": "display_data",
"text": [
"<IPython.core.display.HTML at 0x6069cd0>"
]
},
{
"html": [
"-> oscillation <strong>period</strong> : T = 9.5"
],
"output_type": "display_data",
"text": [
"<IPython.core.display.HTML at 0x6069cd0>"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2c) Case Zero $\\Delta$\n",
"$\\phi_2 = - \\phi_1^2 / 4$ and there is one double root: $\\phi_1$\n",
"\n",
"Therefore, the **stability condition** : $ |\\phi_1| \\leq 1$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3) Analyze the damping factor\n",
"\n",
"that is, the magnitude of the greatest absolute root value: $\\text{max}(|z_i|)$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"c1_max = 2.5\n",
"c1_range = np.linspace(-c1_max,c1_max,1001).reshape(1,-1)\n",
"c2_max = 1.5\n",
"c2_range = np.linspace(-c2_max,c2_max,801).reshape(-1,1)\n",
"# Compute delta on a grid:\n",
"delta_grid = c1_range**2 + 4*c2_range\n",
"# Compute the magnitude:\n",
"magnitude = (delta_grid<0) * np.sqrt(np.abs(c2_range)) + \\\n",
" (delta_grid>=0)* (np.abs(c1_range) + np.sqrt(np.abs(delta_grid)))/2\n",
"### Plot:\n",
"fig = plt.figure('delta_img', figsize=(15,5))\n",
"ax = fig.add_subplot(111, title='Damping factor', aspect='equal',\n",
" xlabel='coeff $\\phi_1$', ylabel='coeff $\\phi_2$')\n",
"axim = ax.imshow(magnitude, origin='lower', aspect='equal', interpolation='nearest',\n",
" extent=(-c1_max,c1_max, -c2_max,c2_max), vmax=2)\n",
"ax.plot(c_range, -np.ones_like(c_range), 'b-', label='stability')\n",
"ax.plot(c_range, 1-np.abs(c_range), 'b-', label='stability')\n",
"ax.set_xlim(-c1_max, c1_max)\n",
"fig.colorbar(axim);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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Jv6Lnw7lpXSyC9Npxlr4y/0tpfEk/J5fmmvSrJPX3IXuP28BZfl2+g47qJwXqnZ7AJEE7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\n2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AyMB9+fNSg+g//9uzIY/y1QCb5/a1DcHbQXB+M7gnbwwCm+ik+qqsH3eRCxKgTkrejB\nxDicGzx5/y0Qtr/Nb/I0fsBrNf7z4t+D052E/xx50X87TvDfYkqeZ7v9WwJMTyGM+YqWpQUvueQS\ndu/enej/7//9v3P11Vezf//+sG/BggW8/vrribmvvPIKxx9/PK+99hqXXHIJt912GxdeeGFsTivS\ngjLVp9J9sk+OxVKFjp8O7MgF/8GI9F2xFvyBBqk6Y/pPpvN0sXo39dOCueS5ql2RA7syCg2tFLTU\nnwy8j9ATRqy+OvCnVCvtod3CEL1h6ZoRetjLIrbvWz49v4jDxPhPHqHtggsbT7SYMth73nrMlnu+\nfOF2FrE3WO4yTCdj7L9vIf92w7tCo1GZCuxmWIur6ylD0e+VcWoe2dI47QeJ0oMqxaenC/W03ojW\nX9Pma+nC4itQ6DS8R3BcteyL28dKyfSgelW1bc0wNh2YVWnBXx3Cdb4lM7fSgj/+8Y9TxxYvXszu\n3bs57rjjeOWVVzj22GON844//ngA3vSmN9Hf38+WLVsS5Gq6kWYIakoD6iJ2ZRiacbVJLhQUOdLT\nefVShmnpP71f97fKRUahJmKVVsZG1f4rk2O42sXXB64NU4Fjuc64ISi97GIJw29047jm8P2RhnPR\n+ViZaGth73nrMVvu+a43jmf46B6WsCsQqbsseu+rvJ1/DVcRnrx2G7UgNdjsSsKgA+Xg7uZFgWeI\n593kE9FkDgrJtJ+0YgjmFd5EPI+npQvTjEX1Z4fJ4UGOzfv04Az+WM+ItOAVV1zBXXfdxa233spd\nd93Fe9/73sSc0dFRPM+jp6eHgwcP8i//8i/8zd+0QroehyRMaiu1Via9VZg7d0mvH1hPc2UqaaPX\nCDQRLd3fSrSlUajZDDSNWGUTxMrXWPkWC0P0sodjeeXgkuBntvoqCwuL5jB2sINtrOD4rl0sxsGh\nxrHv3c3bhU2DKpWTprnyxwzfO8F3aGgwKqeklclRUPueNicvtiXDPEnOBFOSxqLVWrw4s87JEGN6\nwWdLro70BaRjRpCrv/qrv+J973sfX/rSl0IrBoBdu3Zx/fXX84Mf/IDdu3fzh3/4hwDUajU+8IEP\n8Lu/+7stvc40ywV9K/+e9KgVYCRUxQNQOFaME40lTupo52nmJd5T2S4oy4WoKhhXCdQAACAASURB\nVL3cRhYM0u9qrNoREqtoVaBvsTAWCNdfLS8OlkHPbNT+7ae47/idI30Z8wr2nrces/Gev1pejJvz\n6GQUF49j37ubCycejNUirFDBJSrm7ATGDHH7GN+qoYZfOrrmOHhuNbJngHjICOIRKdlWc6Wlg2fY\n1nytbKGHiFTp3+XBvHY3Hr1CTJEWDPpWjs9rgjWDf/gZQa4WLFjAAw88kOhfsmQJP/jBDwA4+eST\n+fd///dWX1oMMiqlpwX1qJUkYLLMTUb+gUnio14y0pSW6jPtm9KB+jzHTweWc37UymQCqm9jJWuq\nHXx54EZDKrCbIY4JVwTOBmIFMO6Mz5prnSuw97z1mK33fI+3GMfxWMg+etnPm/r3cAHFMIK1au1v\nAcI0oUS9lKGb9xXnOUT9QY/4ikA9ipVWMkeNS6Imv7tNqcWAWKWVxdFTgjJ6ZUoZzmB+Mf2YwR/r\nGUGuZgPSHNf1eoEJkhX83ce0VgYn9cJC0tOF0mIhzZpBTxnq7VycWKm6gYdPrPzagM+zEgDHmcGf\ndg3OO89hRv91zkHYe956zOZ7vofF7GExK3ne12D1v8r5PGy0aZBII1cuXlh/MCRYalCRpLw4QBZ7\n1msPSvajpQULx4u2jIAhzuNFxqK1wME9raizjFrZmoMCU5QW3LRpE7fccgue53Hddddx6623JuYU\ni0X+4i/+gmq1yqJFiygWi3XPaclVE0iLTOlRKzUXOVdErWJRKp0cqQiTJFKm6FYaiTKRMLlS0PV1\nVtKBvUw2dFfXBexpxOo9G+5jJBeJ1veykO2cMKX328LCwkLieVZSJssisizsf43zeTgs9mwiWCY9\nloNHmSwOXujgXqtp/lcQJ0WKNKnvU8RcOQZJIpUnqdGS84K2W0tGr/R6g3r0Sj+dGpt3mAJy5Xke\nN910Ew888ABLly7l7LPP5oorrmDNmjXhnKGhIf7sz/6MH/3oRyxbtoy9e/c2PK8lV00iTW+VRriM\nZW7Sok4OFN8INFcmwiWJUxqJkinCHAmSpgoyK6PQeisDx+gMidVItZuvDvxpLGLlk6pFDNIXfFnN\nYFVhHVSKj5EtnHekL2Newd7z1mOu3PNdLGEfi+hjkEX9e7mAInevvyYUuXeK9OCYIXKlvqfCqJYy\nGFUFniWhktAjU57WNtQpLO6EwiIi4qWnB0U746YXddaJFNjSODFMwQ++ZcsWVq5cSV9fHwADAwPc\nf//9MXL1zW9+k//wH/4Dy5YtA2DRokUNz2vJVROoF7VKa6uoVbuMWtV7tWFOC5qsGWS/HqXS5+Qa\nEatcgliV6xCrYXrYxRK2szy4N7Mz3QDgMT6rr382wt7z1mMu3XMPh22soEKW5f3bwxShXEUI5rSg\n6ouNSYIlH9QyCgXxWoP6HJNGS2Yo9PMZBPPSmqFeUWeTa7tq28hVCn5RhGeKqcM7d+5k+fLIi3HZ\nsmVs3rw5Nmfr1q1Uq1UuvvhihoeH+fM//3Ouuuqqum9ryVUDpJWxSRApbVxFrUIRe5r1QkCICsdh\nJk4mQqVpqRJ9Wt1AE7FSlnuRWWhErMY0YnXJhh8wnItMQXexpK5gdLags7CO2apFma2w97z1mIv3\nfBdLyFJhUf9ezuERvrX+gwwIglWPTCbGAoLleuMYi6no5Envq5EgToUT8U1DXdGvH5tizaCiV2hv\nARG5StNlzTuC1Qy5OrXgvxS++enYcCbTuIROtVrlySef5MEHH2R0dJTzzz+f8847j1WrVqUeY8lV\nE0j7r0HfxsTtMh3ophyUZqkgx01Rq0Z9YszXWSUtFmpCc6WE7TUcvxBztZO7Bq6nWmkPI1ZjdPpu\n6yyfE8TKwsJidkNFzxf37+F3NJG7X8DZ/6arkMMNLBrKZMlSxtHsZjzXo+aMR/5XkgDJ72U5Jr2s\ndFsH/bgmLBxCcbuIXukpQH0rx+clpiAtuHTpUrZv3x62t2/fHqb/FJYvX86iRYvo6Oigo6ODd7zj\nHTz99NOWXB0qGhmENirOPBnD0OI+KCwhXVPVKFqll8YRflZpRqEqgjVKZxjBGq728L8HPkK5kgsj\nVkP08gpL2E/vrNVXmTBa/HnwX71Fq2Dveesxl+/5Lo5njA6O79/FOTzCN9dfw8DGf2b12l+Hczzt\nMVehkjyRA1npf2WKVKmtPqa+o4Umq7hX01zpaUFD9AoIxe1p0Svd9UGOq+28i14dJtatW8fWrVsZ\nHBxkyZIl3HPPPdx9992xOX/wB3/ATTfdhOd5lMtlNm/ezMc//vG657Xkqg4UWYJkGlAPGsXIloxa\nmQiVyWndJExPI1gy/ZeSPpS2C+o/NkmsFJmqT6yOYohetrEiuB9zK2Kl4nkWrYO9563HXL/nfsmt\nU1jRv42z+QnfWv9B/mTjV3jz2ueM80fpTPQ5eFTyviVnzJ5BRZYUOZJid0WSdLG7f8Louz7N/V2a\nkwZbJW5X0Ss1XU2RwTDd0b1d658XmIIf1nVdbr/9di699FI8z+Paa69lzZo13HHHHQDccMMNrF69\nmssuu4zTTz+dtrY2rr/+ek499dS6521Z4eZWYaoKNysCJQswt6fspxZnNhVRdoAukgRJjz6Zju0y\n9KnjuonprKSf1Wjgnq4Tq2F6YsTqzoGPUqlkuXTD/2FfbhF7OJZXWTwFd9PCwsJi+nEse6jel+eJ\nG84PU4R+EejRsKBzD8OJ4s4dQZ2JnFcmW6qSKwcGo6oo8wjpxZ0PGvpKpBd2lufxksdOlGCs3FxR\nZ31fFXg+HM4xqwo3f+MQrvMDc6xw82yDKQUoI1mmyFWiOHOz9QNNzuumyFaKaF3O14lVpUHEaowO\nhqvdoY/Vuzf8kOFcD8/x5rCshIWFhcVswKssJvveMudM+CnCPwkIlodDJ6NA+kpCF0/4WQURLNNq\nQAmpo5J9MpfXaIWhlh6U0SuIpwfVSy99o6cM5030agarVCy5MsBU4kamA9N0VwnD0GYIVTBe3AOF\nk81jIZkylcRxxVguMgqVOitlCKo8rRTBksRKpQKHcsewiyV4uHNeuD5SfJLuwtojfRnzCvaetx7z\n7Z57uEz0w1k8FmqwVKkcgBzlcF9qSMN9h8hgNBeeNIo0Sb2UySjUheKLgYZW11WZSJeeHvRIGIuq\nQ3QSZfpnX82dFwTLkqvZBaOOigakq1nD0FzKWFbr0zVV0oXdlD5M+FllY8J1ZbUgI1fD1W6+FGis\n3rVhE/tyi3g+0FfNJeF6GtqC1UQWrYO9563HfLznw3RDP5zJFr61/oP80cavs2rtVgCyJkE7caG7\nk6sRMxhNu33KoV3XZOn//OqarLRIl6g7KI1FEXUHdRKltnppHEuujiwsudIg6wWaolbGdKFIBxqj\nVk0YgRb6MBOvFMf1WASrgVGoiVgNVXtDYlXY8GP25I7lFZYwl4WvOo4pnM5c8/+Z6bD3vPWYz/e8\n1t/GaTzJd9ZfxR9t/Bqr1m5NjchnyYb7Dl7SYFS3WVARJ4Oje+HN+IRKFnyWb2tybpdtzVgUIud2\nU31BSbykRcOcJ1iWXM0eqBuiF2WWW1ebB1EIN4xa6RP1/Xp6rLS+OisGPTfys/L9q9xE5ErVEfQj\nVr7Gyo9YLeRVFs/5NKCFhcU8RL/HGTzOd9ZfycDGf+ata59hlI7Q5UrVG1SRK9nnuR6eG/hfpa0U\nlGTLRMBMtguSnMk5Lr64XZlPe/6zpVrznzVjmEmUGpPFnedF9MqSq9kBU9qvkTu7jFq11xOm61Es\nSZjcoBbVmzGnA/X5co6jolbRykDpwC41V8P0MFzt5n8N3ES5kuOiDQ+wK7eEIXrnJbF6o/g0RxfO\nONKXMa9g73nrYe850O9xKv/Ot9ZfzQc33hnaNHg49ARTsoEWS0XvpcDdqVX96JUiQyoiJdN9Yry4\nHQrL432x9GBaWlA9I/yLixzZg3FX018hDjX98z/no1eWXM18mAgUJCNZCeLlYjYMNaX/0uY0SgdK\nQbuhvI00CpXGoCodqFKCw9Vu7hj4GOVKjndv+CHP5E6f8vtoYWFhMRPR0T9KH7/ln9dfl/DB6sQh\nl6LFCg1G85jL45j+L5Xf56bVgopA6WlBPZoFMXG7vnJQnUJGqmQh5zkfvZrBP5wlVwKNCjPrkat2\nMIvYTSRKRqwMq/4Kp2DWZsl5miO7tF2IBOxxYjWqEatSJc87N/yIbbmV8zJaJbGg8FbmqxblSMHe\n89bD3vMIx/bvJks5tGmQBMskdFcLAYwGo3pJGxGlKqzBT+9JN5s0zZaCKa1IXNzeXo6/NcSfTfOu\n5uAM/lhbchUgLRXYqMxNQsSuv0wrA2V6z0TCpIeVKXLlxonVqBORqbK2MnA0sFtQxOqiDQ/wfG7+\nrAi0sLCwkFjY/xor+Q3fXP9hBjbeFZbKyQqLBoj7YTlOJ+RHiflfSZuGNCjLBVOEyrBKMKHFCsaU\nuN11iK0cVG+hkyideM1ZcjWDH2GWXBEnT6ARKO2lrxB0HS1qJQlTml+Vnv7LBzn6t5IkWyrSpZEt\naRQqiZVyY1fEaqjayz8N3Eypkuf8DUW255Yzn1YE1sPrxV8G/9VbtAr2nrce9p4ncXz/TtrwuHv9\n1bxv49dYvfbZut+LDh6O44UGo3n5UFf7ghQVfwGFFSRXEqp5jjame2BpmqyMGzx/RHrQVBZHPsNU\nilAJ3ecswZqhsOSK+mm/NJd2pbXKmDRVJr2VjFzpq/4c8TJ5WMk6Vbm4gD0SrpuJ1RcH/pyxSgdn\nbtjMvtyb5n0qUKItWC1k0TrYe9562HtuxpL+nTiZce5Z/0H+aOM3OHPtk6lzs1RICNzVoCpdk4sd\n4LfTVg/q3lfySSyjVjI9CDFjUZM7u+57BXO85qCNXM1c1LNZ0HmSmucGVgvtpskQJ05qrEFfYQ1x\nsmVKFzow4fp+VjXHEQWZs8TL3Pi1Av9p4GYqlSy/s+Ff2Zd70+HdqDmIhfa/+ZbD3vPWw97zdCx+\n7ytMTMCG9X9Cz8ZhTln7bFgKx6EW7lfIhu2a41DJe7jeOBlFqrT0X+EMfNKlp/nq2TBIO4YaSULm\n+s+cWi3InHjxQ2QKUN/Xy+XMGVhyNXMh03+mSBWkR61cKTJPqwVoslXQ9VSm1KG+FTorZRQalbXJ\nhdGqMTrZX+3lfw78BaVKnsKGH7Mrt8T+52phYWFhwNL+HbQxzlfX/ykf3Pi/WRNosCSyVOLfoTlw\naiVff1XGnP6DKKqlP2lNES0VzapTq1BVAoFk9Er6XKk+PaI158jVDP6B5jW50kmTSWtlErHHVgia\nXnoqMGfo0whV8UUovM1wnNBbRSsDI2KlSJVOrMYqHVyw4V/ZkzvWCtdTsLf4axYVTj3SlzGvYO95\n62HveWMs638Zh3HuWn89H9j4ZU5b+0xsXBe7A7h5D6iS1+vb16D4BBRWE08VBmPh97ueDkSMKWji\ndr0sjrRm0O2D0srlzGA+MnnM4JjBvCZXOoEyrRLsQItmuU0Yhqb1SWG6HplqJ0GmJDGbyMdXBla0\naJUiVrcPfJyxSgdv3fAkw7mjsOL1dDiM2/vTYth73nrYe94clve/RBvjfH39tVy58UucKiJYugeW\nE+qvRsmVq3F7hhy+5kq5t5sg+/WC0HIVoh71cuPGorKoc4d2aunWPmd9r2Zw3GDekit9daCJYMmX\njFrFDEPr1Q9sZB4qIliFM4iRKd0odLSrLbYyUBKrYXoSxMrJjU/XrZszeFNhzZG+hHkHe89bD3vP\nm8fS/u0AfH39tfzJxq/y1iCClVbs2XE8nC6PTsZ9ghU87Avn4acEdeKkIlFpeit1DhOxUp5aEBqL\nNirqPOdrDlpyNbOQZhSqtqBFq/AJVUdeMww12SqYCJaMUBnMQBMlbURb6qz01YBq/0C1h9sG/pLR\nSidnbthsiZWFhYXFIeKE/kHaGOeb6z/EH238BqetfTqVXAE4uVqkv5IBQqWjMkFpsUzjOtlS51LP\nhpJID+ZhrESiqLM6PC16BXOEYM3gH2JekitIRqhMfTEC5hoMQxs5sZs0VpoZqOovPguFc0n1s5IF\nmCsierW3upDbBv6Sg5Uuzt7wE0usJoE9xWdZXFh9pC9jXsHe89bD3vPJ48T+F2ljnO+s/wDjG9vo\nXDuGp8JGgFxNWKES6a8CBlPcHPgWmoo1S9sG3Y5BRrYUUgpCK2NRlR5sJnql+mZwwGdymMHZ7nlJ\nrkyEKi1qBcRWaMQMQ+XJ9D7TSsK0fd33Khir5sBzo3RgRWitymQ5UO3m9oGPU6rkOW/Dv1liNUk4\njNtVlC2Gveeth73nh4a+/hdow+N76wc4euMbQQSrHJCqztCmoUzWTw+6HtXcuF/gWX6fqwiVJEka\nUYqRJ72cjpxH1JdRJEukB/VIlXymyb45o72awSyx7UhfQKthKmXTSGuVGrUymYHqKT4TqTJYMRTO\nE/2hgL2N0VxnbGXgMD2M0sH+ai//Y+A/M1bpYO2GxyyxOgQsLpxypC9h3sHe89bD3vNDxwn9L3HO\nPz3KV9bfwDNPnsEQveF3sL/tDLIKWUZznVTybUzkoXAR8e95XSKiZS5izwpdRlLnmaMqhbS7DSqK\nGPpCE9TZDD0X2szLgE2bNrF69WpWrVrF5z73udS3e/zxx3Fdl+9973sNL23eRa7SPmSqL7E6EEIR\ne8YUYTL16UTLpKvS/9hEyjAUsOdktKoj1FopYjVa6eScDY9YYmVhYWExTTipfxttjPOV9Tdw9cY7\nOWPtU+GYgxezaXByNaDiC9w9kmlAiMJHaXqsNKPRfLIvkwe35D+jTEWdlfeV3j9noldT8AN4nsdN\nN93EAw88wNKlSzn77LO54oorWLNmTWLerbfeymWXXcbExETD884rclWvCHNaf0fOIGLXVwumFWFO\ni2oZrBaKz0ChABNdkYA9uSqwm/3VXv5h4JMcrHTx9g0PWWJ1GHiluJXjC6uO9GXMK9h73nrYe374\nWNH/PG7G46711/PHG+9i7donwrGc7oGVg5/8a4lLzsF3cNfrEOYMfXp60LRaUBqMihI6StzekQPK\nyaLOar9Rsef5ii1btrBy5Ur6+voAGBgY4P7770+Qq9tuu43/+B//I48//nhT551X5KqZkGmsX7de\nkCTJlPLTI1R65Mo0T/O5KudgtCtvtFvYW13EFwY+wUilm8KGH+PkrI7icNBmtSgth73nrYe951OD\nk9/7PJmJCb61/mq8jW2cvfZxPNyEBxZAKT9OOVfxDUZ1IgX+akEZkZIw/ap081GtNqG0ZtCLOstK\nI3rkatZHr5r5WL9WhL3F1OGdO3eyfPnysL1s2TI2b96cmHP//ffz0EMP8fjjj5PJZPTTJDBvyJWp\nrI0paqWXuYlFreQnMm1VoMkDSydUsh3sF94ZGYWqVYG6j9X/O3ArQ5VeLtnwQ0uspgBLCiuP9CXM\nO9h73nrYez51OKl/GwDfWX8VIxt7eMfah+lkNDbHocY5hQ4q3kTSYFQRKZNzuyJbuqBdX0moINOD\nQfRKrhyEeORKRamk39Wsj141I2g/puC/FJ79dGy4GaJ0yy238NnPfpZMJsPExIRNC0o0G7VygU60\nqFWaGajB8NMYucqL4/SxLmI6q1En7rquiNVnBz7FG5WjuWzD/7HEysLCwuIIYWX/b2ljnI3r/4C2\njeP87tofxcZDN3wHnK7hSH8loTKJJv1Vva933dpB1h0U0atOD0aJR67U/pyKXk3BasGlS5eyffv2\nsL19+3aWLVsWm/PEE08wMDAAwN69e9m4cSPt7e1cccUVqeedF+RKL8IMcYKlzwEtaqUOMEWo1D7a\nPJMVQ94wFpC0B38G51zmxErblMlxoNrD5wf+C6VKnvdsuM8SqynEzuI2lhZWHOnLmFew97z1sPd8\n6rGq/1na8PjB+n6WbNzJ2rVPBuJ2v8DzE8WDXFTI0uk61Jxxv1yaTojUMyHNikH/qne143Vxuxa9\ngiiAoLuzq/aY1j/rMAUXvW7dOrZu3crg4CBLlizhnnvu4e67747NeeGFF8L9a665hssvv7wusYJ5\nQq7UD5lW4kbuJ6JW6g+gkWeVaemsng6UJqJ5/KhVzvezKnc4jDqdQmvlG4T+/cDfcLDSxcUbfmSJ\nlYWFhcUMwYr+rQDcuf4mPrzxi5y9NhI6l8gxRoacU4HuUaDq+18pyMiVaSVhmh7L0cZdMU/TXqno\nlR6tku12cZpZSa6m4JHoui633347l156KZ7nce2117JmzRruuOMOAG644YZDOm9mopnk4SxCJpPh\nb0RbFV92g+1RRCSqQ4wdpdqBb0hHPijOLFJ3Cb2UPib7ckC31laESryqXTDW3R6mA4c4JhCv+8Rq\npNLNJRt+gGuJlYWFhcWMw/P3vpmHbryMqzf+L85d+xi9DNHLED0M08t+X+DhjdIxUqX9IHAQeAOf\nYB3EF6ar/TIworVLYqv31ZJj1bJfEqdagzEPDuBHqGrBdgyfdNVIjlWBT0NTmqIjjUwmAxcewnU+\nkmnJzzcjIlff+c53+Nu//VueffZZHn/8cdauXWuct2nTJm655RY8z+O6667j1ltvbXhuk8ZK11p1\nyDkBsXL1CJQpEqXrqnRzONmW40JnVcn7DuzxVYE+sXqjcjS/t+FeS6wsLCwsZihO6f8NbYxz1/rr\nKW3Mc9HaYjimbBocx8PJe7heoL+SkSvwIzCyJI5sS5geBVoxaLfmP8Mo+elBJXcZI/48hGRUa9ZF\nr2awQ/uMIFennXYa9957b93wW7NGXxKp3lXamMl6IWEYmlZT0KSr0gmYFLsro9CuQMAeOLD/WzHD\n6oJPrD4z8Le8UTmaP9jwHUusphEvFwc5odB3pC9jXsHe89bD3vPpx+r+X9PGOPesvwpvYxuLD3yb\nCwq9EbnCC8jSqC9wl6QK4iRBF7fXK42jl9QBMhAai7o1cL3oLXTbLXHY7Kw5OIPZ4IwgV6tXNy4q\n2qzRl0I9y/9GZW5ihqEy+mSKZukkSjcVNXle5SKjUBWxKtHG/mqvJVYWFhYWsxBv7n8WgA3rP8Db\n/+63rC68QiejOHihz5iTq+HUSpH/lYlkyTE9eqX8sXRipY4NtlLcLlcO6mTKtHpwVmEGPyJnzb1s\nxuhL4T7gTfiFE48CVgBvxf9hf4X/eT0H/4P1ZNC+NOcz/UfHIeNBISBTxZJ/zsKxQB6KB4AsFI72\nDyy+4p+o8OagvT1orw3azwbz3w50QfEpqBwF6y7LM0wPDxfbGKWNj1ysViMUgVH+R/6/iDZAwbZt\n27Zt+xDaF82w65nr7Z/zLzf8A0vXfZGlB77B0WS4qNADwGPFCh2Mc/npFTIeFDcDJSgEMYLiU0H7\nxKC9DRiDwhLAg+I+oAqFY4LxfUAFCp2AGzyfqv7zy63BTzNQaYO14z6J+pk/ndP86TwH/BZf5lUD\n9jDLMINDbS0TtF9yySXs3r070f+Zz3yGyy+/HICLL76Yf/iHfzBqrr773e+yadMm7rzzTgC+/vWv\ns3nzZm677bbYPCVo7xCvdrGvBO1yvBO/dEBMxC4jUkqQbkr3dWlzZP/RhjldcGChL2Afpid8PfbT\n8/nW/3Mll919v41YWVhYWMxiPHvvqWz9/1Zzw5duZzGvspB94tt+mN6Db5BX4nYlaldi9TdICtf1\nOSVtq4vjg221DAdGfO3VKJGgXYnYD4h2Ndj+ObNI0L7mEK7zN3NM0P7jH//4sI5vxuhLoV6tQGOK\n0DGI2NOc1vVxUzpQvqTtQheUughXBqrK6kP0squyld/77vdowizWYorwUvElTlT/Ilq0BPaetx72\nnrceHcds5Pf/96/ZxRI83CgtSA2HGtkunwHFnBbU/9SmkjkqPahWCBp8rkx6LCVuHytFZXFkNrKd\nZM1Bi6nBjEsLpjHKZoy+FIx6KuIES9daGUXsJjKlR7Ck67ruwK6RrWpQNzAiVccwRC+D9HGAAyxI\n2PhaTCccxnFnctJ+DsLe89bD3vPWw2Gc9uD7fB8L8XDoYzAcz1GBLnBqJd//SjIepauCuNeVSYOl\njhOrBSXhyuSTZXGktkr3vZpxhKARrKC9Pu69915uvvlm9u7dy+/93u9x5plnsnHjRnbt2sX111/P\nD37wg1SjLxNSawUSpQT1FYIJEbsehZIidSlmF/UBTYRK97NSdgtDHMM+FvI8K6iQY0WhhxmtzpuD\nWFFYir3nrYW9562Hveeth37Ph+nhOd7MSvzahKrYs9vtAdVYdZBY5EonWR5xAqUbkOooiVXwWlFn\nkzv7rItczeCP9Zw0Ef1HkpoqRaqOQtNiKa1VM7oqfT+Hr6uSmiuprzra3050wfDRkc5qD8eyj0U8\nw2nTfj8sLCwsLGYOTuXXLGd7aDTa6Y3S80aVjDQY1TVWqq3MR02moml6rIORsehYOdJWjRE3EVWa\nrKuYRZqr5YdwndvnmOaqlWgUuQr9rnJCa9WMrkpaMsiCzHp6UEStQj8rpzPUV73KYp7jlDAPD/BC\ncQcnF8waMovpgb3nrYe9562HveetR717/hyn0MNw1CELPINPimSBZmnPIFOE6tmjkKbHciPtlZqn\n0oOmUjizCjP4guckuTLprTq0dsIwNM30UxEndUKdVOnCdZEKJOcTq+FctE5kiF6eZwWO9qlow0v0\nWUwv7D1vPew9bz3sPW89Gt3z7fi2QuE/2DmAYbpq4/6zQ6FGPDWoXnlt3KTHEufQjUVVelD3vZrB\nEiYzZvAFz0lypUetZH+qYahCPVf2vKFfJ1qC2VUDo9AyWSpkQ3Jlgp+jt2gl7D1vPew9bz3sPW89\nGt3zvSykh2GyVMhRpkyWbC5LNleiXUYHpKFoHj86JVcE5omzJN25XcGJG4sqcXu7OL16Ns4qzGDN\n1ZwkV6ZVgjE7BhG1Mkak9BShXA2opwlTLBfoguGj84zRyQg97KeXVzmW7Sy3K3csLCws5jmi6JXP\nglw8OBoWlEvxiZIo6WJ3GcVSxEs6t+fj891aPHolH3Mwo7NsZszgC56TumSnMQAAE8NJREFU5Eon\nVYlagnrUql6kSi9jY0oDGlYIlrpgjE6G6GU/vbzCEnaxJKazkni+uIuVhSVTfi8s0mHveeth73nr\nYe9569HsPd9Fck6pK/C/qmkviFYMQpxYyLSgqe6gsmbQoldSZ6UKO88qWHLVWsioldRcdZAStTJF\npPRIlZ76k/O64q9SFwx3dTMcRKwUsbKwsLCwsJCQzwYHj2xXBRghbyIOSrSuk6m8GMunHBOQLBm9\n6hD/69vCzVOLOWnFcD9xKwZpydDT5a8SzOhEylS+Ru0fbZinyFRgt0A3cJTvZzV8tF83cDvL2c5y\n9rGoNT+8hYWFhcWsxEL2Bk+M7f7ypzdKtB/E90sYIW7ToFs0qLI5pjI4ukVDGSYCW4bhg8myOBcy\ni6wYModwnRPWiuGQoUet5ApBYzrQpK/SReymlKAiW92ERqGKWA3Ry3aWM0SvXaljYWFhYVEXarFT\naNNwNPRQol0qSZR7u54a9Ij0VbqxqG7NINKDrmMuizNrMIM5YNuRvoDpQJgCFC9Z5iaRDlQeVSYf\nKzkmCZVm1zAROLBLL6u0lYEm/LaYLGptMb2w97z1sPe89bD3vPU41Hsunx3D9DDW3c6EnlWRmRXZ\nJ3XCerk2+awLnn8q2KAv+rKYGszJeymF7ErMnihzozuxp/lY6aJ2rawNXTBxtO/APuz0MEIPr7KY\nQfomtSrQ1v9qPew9bz3sPW897D1vPQ7nng/SB/irB13Hg6OH6aEaGYwqyHCTelapft1sVNdhBdEr\nuXLQYmoxJzVXj5DUWhnL3HST/E9A/peg9pWuSs5ReqsFUDraF7AP0csejuW3nNKyn9fCwsLCYu7h\nzTzHYl71y+QcHCH/BvA6cd1VSeybNFcHtXYZX78V7FcPRmVxlPbqLcwizdUh5QWTmqtNmzZxyy23\n4Hke1113Hbfeemts/Bvf+Aaf//znmZiYoKenhy9+8Yucfvrpdd9lTkauUomV7kulm4HmtH1dX2VY\nGVjtiojVPhZaYmVhYWFhcdj4LadE0a8ucGojtKuVfxJKg1UO2lKHJU1IdV8soF2eq8y8hOd5/397\n9x4Txd3uAfy7LgjtclxZjqjAekDQF+ihgEU3tkV924KtVmKxF9toKfWCGGv8pyFpzx9NU2x6SauN\ntSVpsYeQGENPgF7MppVKraRAD7WXl16EKnWBIB4RlfUKeP5YBmaHXViXYWZn+H6SDTvs7OxvnxLn\n6W+eeX7YsWMHjhw5gujoaCxevBg5OTlISkoa3mf+/Pk4duwYzGYz7HY7tm7divr6+jGPq8vkSlrE\nPqr1grSAXZpUCc89NQuVXBZ0FbCH4TwiRq0XeDv+qO1G4opIP78x+YMxVx5jrjzGXHlyxfxP/AP/\nwJ8woh9Gc7+rwai0/5W0NYOQbAnb10XPhSRLVOQubSyqLRPvxdDY2IiEhATExsYCANavX4/q6mq3\n5Grp0qXDz202G9rb28c9ri6TK2kRu9sdguKiP/FyNdKCQE/bwozV0N2B10wYmrH6d/zJGSsiIpKZ\n+H/a7zR1ufpfiZMg8fI44kWeIdkWJ1zCax6WxdEWX+5vPAbgO6+vdnR0wGq1Dm/HxMSgoaHB6/4f\nf/wxVq1aNe6n6jK58jprJcxGeVr2xlOndXHPq7ChbSGxGqqzEhIrf2esBHetiEBAL5SkQ4y58hhz\n5THmypM75q4ZLODfTH0A+hAqHFrclkF8WU+cXF2H54WeQ0feL5690tafii8zV0uHHoJit1ddtVu+\nOXr0KEpLS1FXVzfuvrpMroRZqztCJQ1DpUmV+C5A8U9pfZU4yTIBN2cIiVUEWhHPPlZERDSpWhHv\n6oEl1F8B7pcFTUM7CgmSMFMlviQovTw4dOe8Aa4aZQCuAnjNmPi5Nzo6Gg6HY3jb4XAgJiZm1H6/\n/PILtmzZArvdjvDw8HGPq8s+V0IRu8eGof7UWInbLgzVWQlNQuXyW+3/yXYs8g1jrjzGXHmMufIm\nK+ZCY+rL5lBX/yvxw9O5SziveWozJC6LES4Pam665aYfD3cZGRloaWlBW1sbbty4gUOHDiEnJ8dt\nnzNnziA3Nxfl5eVISEjwaWSaC6Uvxlw/0NO2MKsl9L8S7ye5ZHjFNG14QeZezJStfwx70SiPMVce\nY648xlx5kxVz4bxzJ64gxHQDpmuDI7VWwvqC4vNav+S5MFsl7touWXdQWyZe0B4UFIR9+/Zh5cqV\nGBgYwKZNm5CUlISSkhIAQEFBAV599VVcuHABhYWFAIDg4GA0NjaOeVxd9rm6KG294GlNQOkaguJe\nVtLHbAAzXHVW500WdCJK1lkrIiIiX1nhQBQ6EeHscfW/ugTgLEb6WokfQl8s6TqDXtYoNHRrqc/V\naT/eGce1Bf01qohdPBslnSL1od2CUMDeazLjLGYzsSIiItU4YIURAzCaBjATF10F7uKaK2mLBnHv\nK2EfYaZLfBeh5iY4Jz5zNVl0mVwFB3koY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}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4) Analyze the oscillation period/frequency\n",
"\n",
"One can see that slow oscillations corresponds to $\\phi_1$ in the $[1.0, 2.0]$ range.\n",
"\n",
"For $\\phi_1=0$, oscillations have a fixed period of 4 (freq=0.25)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Compute the cos(theta):\n",
"cos_theta_grid = np.where(delta_grid<0, c1_range/(2*np.sqrt(-c2_range)) , np.nan)\n",
"theta_grid = np.arccos(cos_theta_grid)\n",
"freq_grid = theta_grid/np.pi\n",
"### Plot:\n",
"fig = plt.figure('delta_img', figsize=(15,5))\n",
"ax = fig.add_subplot(111, title='normalized frequency map', aspect='equal',\n",
" xlabel='coeff $\\phi_1$', ylabel='coeff $\\phi_2$')\n",
"axim = ax.imshow(freq_grid, origin='lower', aspect='equal', interpolation='nearest',\n",
" extent=(-c1_max,c1_max, -c2_max,c2_max))\n",
"ax.plot(c_range, -np.ones_like(c_range), 'b-', label='stability')\n",
"ax.plot(c_range, 1-np.abs(c_range), 'b-', label='stability')\n",
"ax.set_xlim(-c1_max, c1_max)\n",
"fig.colorbar(axim);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"-c:2: RuntimeWarning: invalid value encountered in sqrt\n",
"-c:2: RuntimeWarning: divide by zero encountered in true_divide\n",
"-c:2: RuntimeWarning: invalid value encountered in true_divide"
]
},
{
"output_type": "display_data",
"png": 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KS5bURx99lGXLlhEOhykpKeGRRx7p5lELQtcjwipYzJoFpimrCAWhu4kFRsGk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\nSi1X0zU4XZBO65UlsKzr9mgod4FlCx9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6GrFSP7THr3kBy4oV/wXgz8BxoAYr+ejPgH2Y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}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"--- \n",
"\n",
"Stochastic trajectory\n",
"-------------------\n",
"\n",
"Stochastic trajectory of the AR(2) process : \n",
"it is the output of the filter when the input is a **white noise**.\n",
"\n",
"This answers the question : *how does an AR(2) process looks like ?*"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N0 = 0 # Burn-in instants\n",
"N = 2000\n",
"# White noise input\n",
"noise = np.random.randn(N0+N)\n",
"X_traj = lfilter(b=[1], a=[1,-c1, -c2], x = noise)[N0:]\n",
"# Normalize with the theoretical standard deviation\n",
"X_traj = X_traj/np.sqrt(Vx)\n",
"# Plot\n",
"fig = plt.figure('stochastic trajectory', figsize=(10,8))\n",
"fig.add_subplot(211, title='AR(2) Stochastic Trajectory\\n$(\\phi_1, \\phi_2) = (%.2f, %.2f)$' % (c1,c2),\n",
" xlabel='')\n",
"plt.plot(np.arange(N), X_traj, '-')\n",
"fig.add_subplot(212, title='Stochastic Trajectory : zoom',\n",
" xlabel='instant k')\n",
"plt.plot(np.arange(N), X_traj, '-o')\n",
"plt.xlim(N-100,N)\n",
"plt.grid(True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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BAIqLizF8+PDozIJ85V7fgRAWLABycoKdH+S72oS0FK2tzuOKZIUQCrmvD4dL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\nFVaGGm3o/HkRhV6t9qOGy8iBA+L/4GCPq3AbtfyLlVad5+YmIT1dvRRKr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nb9N2o0AnPm\nbMPUqRN1k7ei7cuXrdiyBSgutqBatYrLiw+JODi+/w4ciMPzz/9fibGg9/W4st2vXxOHkVPxe40a\nR1BQADjqEwAuXSr//DrTf3b2OeTlDS93f/z9ZyuWz8/39fh67H9nZ2dDFSqaS7ztttsoIiKi3L/l\ny5eXlLFYLFJ9snx9p9Hnn5efY+3Zkygjw5UZUMYbSq8YXFfhisFvviGKji6d0JgxBnr5ZNkZMoTo\nww89O5ZDg8jVn5Hvp7NI4r6++idA94TWrYk++WRdpeWup5XZZVfVupO8Xkn/zZpNo/r1JynWAQxT\nvV1UZre4S4UjWWvWrFHHsvsbpRVVwACsXRuLYcOulTt1SkTD1XEGpMrg6opBIuD554F//5unCZny\nDB4s/LJGjXL/WCNEIr+eMEKOQmc4W1U7Y8ZabN5cvrwRZK6Izp2B336rvNz1tDK77KpaMRXq2vPr\nTP8LF2YiM7P8ucLD6yE/31x9g5TpQmH8eUZZBZ0/D4SHA1lZ15bqpqcDcXHmW95qRkq/4CwAgLp1\nn8Pjj5duxOnpIrL34MHay8hUjkXnL5IaNWxYtiwTsbHVUafONafVso6szhZUHD0KjBuXgogIXzRt\nWvUWVMjUn9Ff6EqhLxYuVHjDwjgyO6NzZ+DSJUul5a7nDwl3w9E4C32idH9eeskY6cTcwYc8tJCW\nLl2KCRMm4K+//kKDBg0QHR2NVatWla7cx8cjA+ybb4AnnrAhPDwTBQXVsXdvIe6/Px6vvWbcG3k9\nkZ5uw+uvrylxnD13Lg41awJ162bi6lXxgjx4MB4vvhiLu+/WW1rGaCg59TZv/jCABjhx4rWSfcHB\nSViwIAFAaePr4YdF/stJk4BHH9Va+usPJX2I/JfGfTmZUWZApMZZuBCKozBlSU+34YEH1qBFC1+0\nbFmE8ePjDH1tWuP4HhLGlDb3x1O7xWl9nhpZLlXuobDp6TYMG7YaeXnXHrCgoCS88UYCN0INsTsp\nLl1qw/33r8bly6VzFC5ZkoBBg1gfRsTRwVRrEhKSkZn5Qpm9yQDK7gM6d34E5883LfUyrVs3CX37\nJmDlyqrbtmTrT68XljeYUebjx4GQECvOnbNU6kZx4QLQqpUIyOnvr418TOXINrJ0j/iuxMKFmaUM\nLADIzjb2Ms3rmf/8J7OUgQUABQWz8OabKWxkMeVQ9gFS7moOHryIs2ffLbXv0qVZKCxMgdliBhkZ\nI0SjdxezyWwPOXHpUg4slm/xzDMVRy5fswbo2ZMNrOsdQxpZRnbUrErYv6RZH+ZDT58sZR8gZb+g\nCxeUHS2vXq3abUtvnzrGPcpOb9pswNGjzuMLimOAxETNRGR0opreAihhdEfNqgbrg3GHCRPiERyc\nVGpf8+bH0Lz5U6X2BQU9h+Bg5c94bluMmXAeuV55hX5xMbByJRtZVQFDjmRdzysvzITdL4T1YT70\n9MlSXl00WmGfaD+uLveuSuipP8Z9So/2W2Ffme1stP/nn4FGjYCbblJbMkZvDGlkubsElFEX1gfj\nLs78aZy1GW5bjJlxd7SfpwqrDoZcXcgwDMMwZkEp5ERAwHNYvFj5g6FrV+CVVzjAthGpEiEcGIZh\nGMZMOIacAIrw009x+O23WLRoUbrc8eNAWBjw559AjRq6iMpUgGy7xZCO74wxcEygyZgL1p25Yf2Z\nj8TEWGRkzERqqgVW60yMHRuLF8qHhsOqVUB8PBtYVQU2shiGYRhGMlOnAl98AfzxR+n97I9VteDp\nQoZhGIZRgeefB37/Hfj4Y7F95QrQtKnY16SJvrIxyvB0IcMwDMOYgMmTRR7DXbvE9vr1QGgoG1hV\nCTayGKewX4h5Yd2ZG9afeXHUXf36wKBBNtx6azIsllSMGZOMdu1s+gnHaI4h42QxDMMwjNlJT7dh\n3brVOHVqFrKyxL6ioqS//bI4FlxVgH2yGIZhGEYFEhKSkZlZfolhQkIKMjJm6iARUxnsk8UwDMMw\nJqB0up1rOEu3w1x/sJHFOIX9QswL687csP7Mi6Pu3E23w1x/sJHFMAzDMCowYUI8goOTSu0TCdDj\ndJKI0Rr2yWIYhmEYlXBMtyMSoMex07uB4dyFDMMwDMMwKsCO74xmsF+IeWHdmRvWn3lh3TGOeGxk\nTZkyBaGhoejUqROGDBmC8+fPy5SLYRiGYRjG1Hg8XbhmzRr0798f1apVw9SpUwEAc+bMKV05Txcy\nDMMwDGMSDDNdGBcXh2rVxOHdu3dHTk6ONKEYhmEYhmHMjpS0Ou+//z6GDx+u+Nvo0aMRFBQEAAgI\nCEBUVBQsFguAa3PXvG3M7fnz57O+TLrt6BdiBHl4m/VXVbbt+4wiD29XvG3/Ozs7G2pQ4XRhXFwc\nTpw4UW7/iy++iEGDBgEAZs2aha1bt2LJkiXlK+fpQlNjtVpLGiRjLlh35ob1Z15Yd+bGUCEcPvzw\nQ7z77rv47rvvULt27fKVs5HFMAzDMIxJkG23eDxdmJGRgVdeeQVZWVmKBhbDMAzDMExVppqnB44f\nPx65ubmIi4tDdHQ0nnjiCZlyMQbAcc6aMResO3PD+jMvrDvGEY9Hsvbv3y9TDoZhGIZhmOsKTqvD\nMAzDMAwDA8XJYhiGYRiGYZzDRhbjFPYtMC+sO3PD+jMvrDvGETayGIZhGIZhVIB9shiGYRiGYcA+\nWQzDMAzDMKaAjSzGKexbYF5Yd+aG9WdeWHeMI2xkMQzDMAzDqAD7ZDEMwzAMw4B9shiGYRiGYUwB\nG1mMU9i3wLyw7swN68+8sO4YR9jIYhiGYRiGUQH2yWIYhmEYhgH7ZDEMwzAMw5gCNrIYp7BvgXlh\n3Zkb1p95Yd0xjrCRxTAMwzAMowLsk8UwDMMwDAP2yWIYhmEYhjEFbGQxTmHfAvPCujM3rD/zwrpj\nHGEji3HK9u3b9RaB8RDWnblh/ZkX1h3jiMdGVkpKCjp16oSoqCj0798fR44ckSkXYwDOnTuntwiM\nh7DuzA3rz7yw7hhHPDaynnnmGfzyyy/Yvn077rzzTjz//PMy5WIYhmEYhjE1HhtZ9erVK/k7NzcX\nN9xwgxSBGOOQnZ2ttwiMh7DuzA3rz7yw7hhHvArhkJSUhI8//hh169bFjz/+iICAgNKV+/h4LSDD\nMAzDMIxWyAzhUKGRFRcXhxMnTpTb/+KLL2LQoEEl23PmzMG+ffvwwQcfSBOMYRiGYRjGzEgJRnr4\n8GHcfvvt2LVrlwyZGIZhGIZhTI/HPln79+8v+XvZsmWIjo6WIhDDMAzDMMz1gMcjWXfffTf27dsH\nX19fBAcH4+2330bTpk1ly8cwDMMwDGNK3B7Jeuihh9CsWTPs27cPO3fuxPbt2/Hvf/8bd9xxByIj\nIzF48GBcvHixpPzs2bPRrl07hISEIDMzs2T/zz//jI4dO6Jdu3aYOHGinKthKsSuu44dO5bs++WX\nX9CjR49yuluzZg26dOmCyMhIdOnSBevWrSs5hnWnD+7oz87hw4fh7++PV199tWQf60973NXdjh07\n0KNHD0RERCAyMhJXr14FwLrTC3f0l5+fj+HDhyMyMhJhYWGYM2dOyTGsP+05cuQI+vXrh/DwcERE\nRGDhwoUAgDNnziAuLg7t27dHfHx8qfhmUu0WchObzUZbt26liIiIkn1dunQhm81GRETvv/8+paSk\nEBHR7t27qVOnTnT16lU6ePAgBQcHU3FxMRERde3alTZt2kRERAMHDqRVq1a5KwrjJu7obtu2bXT8\n+HEiItq1axe1bNmy5BjWnT64oz87Q4cOpXvuuYfmzp1bso/1pz3u6K6goIAiIyNpx44dRER05swZ\nKioqIiLWnV64o78PPviA7r33XiIiunTpEgUFBdGhQ4eIiPWnB8ePH6dt27YREdHFixepffv2tGfP\nHpoyZQq99NJLREQ0Z84cevbZZ4lIvt3i9khWnz590LBhw1L79u/fjz59+gAAbrvtNixZsgSA8NUa\nPnw4atSogaCgINx8883YtGkTjh8/josXL6Jbt24AgAceeADffPONu6IwbuKO7qKiotC8eXMAQFhY\nGC5fvoyCggLWnY64oz8A+Oabb3DTTTchLCysZB/rTx/c0V1mZiYiIyNLRk0aNmyIatWqse50xB39\nBQYGIi8vD0VFRcjLy0PNmjVRv3591p9ONG/eHFFRUQAAf39/hIaG4ujRo1i+fDlGjRoFABg1alSJ\nLmTbLVJyF4aHh2PZsmUAgK+++qokxc6xY8fQqlWrknKtWrXC0aNHy+1v2bIljh49KkMUxk2c6c6R\nJUuWICYmBjVq1MDRo0dZdwbCmf5yc3Px8ssvIzU1tVR51p9xcKa73377DT4+PhgwYABiYmLwyiuv\nAGDdGQ1n+ktISED9+vURGBiIoKAgTJkyBQEBAaw/A5CdnY1t27ahe/fuOHnyJJo1awYAaNasGU6e\nPAlAvt0ixch6//338dZbb6FLly7Izc1FzZo1ZVTLaEBlutu9ezemTp2Kd955RycJmYpwpr/U1FRM\nnjwZdevWlRpYj5GHM90VFhZiw4YN+PTTT7FhwwYsXboUa9eu5eDOBsOZ/hYvXozLly/j+PHjOHjw\nIObOnYuDBw/qLC2Tm5uLoUOHYsGCBaUy1gAicLpaz1d1GZV06NABq1evBiC+wtLT0wEIS89xZCQn\nJwetWrVCy5YtkZOTU2p/y5YtZYjCuIkz3QFCL0OGDMHHH3+Mtm3bAgDrzmCU1d/KlSsBAJs3b8aS\nJUvwzDPP4Ny5c6hWrRrq1KmDIUOGsP4MgrNnr3Xr1oiNjUWjRo0AALfffju2bt2KESNGsO4MhLNn\n7/vvv8ddd90FX19fNGnSBL169cLPP/+M3r17s/50oqCgAEOHDsXIkSNx5513AhCjVydOnEDz5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}
],
"prompt_number": 127
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Histogram : how is $X_k$ distributed ?\n",
"It should be normally distributed, with unit variance\n",
"\n",
"(this checks that the variance formula is correct)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Histogram plot\n",
"fig = plt.figure('histogram', figsize=(15,5))\n",
"fig.add_subplot(122, title='Histogram\\n$(\\phi_1, \\phi_2) = (%.2f, %.2f)$' % (c1,c2),\n",
" xlabel='$x_k$')\n",
"plt.hist(h, bins=50, normed=True)\n",
"print('Observed standard deviation, with %d instants : %.2f (1.0 expected)' % (N, h.std()))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Observed standard deviation, with 2000 instants : 1.08 (1.0 expected)"
]
},
{
"output_type": "display_data",
"png": 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gNq0DqCLyti9ydl/IHjGFhoZi9erVyMnJgcPhwOzZs5GUlITi4mIAQGFhIX7z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\nRKQBjjEFQPDuS6dmXdHa1WM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}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"## Spectral Density of an AR process\n",
"\n",
"ARMA process have so-called rational spectra. For an AR(2) it reduces to :\n",
"\n",
"$$f_x(w) = \\frac{1}{|1 - \\phi_1 e^{iw} - \\phi_2 e^{i2w}|^2} , \\quad w \\in [-\\pi, \\pi]$$\n",
"\n",
"It happens to be a rational function of $\\cos(w)$ :\n",
"\n",
"$$f_x(w) = \\frac{1}{(1 + \\phi_2)^2 + \\phi_1^2 + 2 \\phi_1 (\\phi_2-1) \\cos(w) - 4 \\phi_2 \\cos^2(w)} , \\quad w \\in [-\\pi, \\pi]$$\n",
"\n",
"But is this special dependance on $\\cos(w)$ *only* a general rule ?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Appendix : Get this result with sympy\n",
"from sympy import symbols, simplify, factor, expand, I \n",
"from sympy import exp, cos, sin\n",
"c1sym, c2sym, wsym, x = symbols('phi1 phi2 omega C', real=True)\n",
"fsym = 1-c1sym*exp(I*wsym) - c2sym*exp(2*I*wsym)\n",
"f2sym = fsym *fsym.conjugate() # f2 = |f|^2\n",
"f2sym = simplify(expand(f2sym, complex=True,trig=True))\n",
"f2sym = f2sym.subs({cos(wsym):x, sin(wsym)**2:1-x**2})\n",
"1/factor(f2sym, x)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 47,
"text": [
"1/(-4*C**2*phi2 - C*(-2*phi1*phi2 + 2*phi1) + phi1**2 + phi2**2 + 2*phi2 + 1)"
]
}
],
"prompt_number": 47
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"def spectrum_ar2(c1,c2,w, normed=True):\n",
" '''spectrum of an AR(2) process with unit variance input\n",
" http://en.wikipedia.org/wiki/Autoregressive_model#AR.282.29\n",
" '''\n",
" cosw = np.cos(w)\n",
" f = 1/(1 + 2*c2 + c1**2 + c2**2 + 2*c1*(c2-1)*cosw - 4*c2*cosw**2)\n",
" if normed:\n",
" return f/Var_AR2(c1, c2)\n",
" else:\n",
" return f"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 32
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Peak frequency** : obtained by taking the derivative of $fx(w)$\n",
"\n",
"$$ cos(w_{max}) = \\frac{\\phi_1 (\\phi_2 - 1) }{4 \\phi_2}$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Peak frequency\n",
"def peak_ar2(c1,c2):\n",
" '''peak frequency of an AR2 spectrum\n",
" (when there is indeed a peak... )'''\n",
" return np.arccos(c1*(c2-1)/(4*c2))\n",
"omega_max = peak_ar2(c1,c2)\n",
"display(HTML('<strong>Peak frequency</strong> : %.2f (normalized /pi)' % (omega_max/np.pi)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<strong>Peak frequency</strong> : 0.21 (normalized /pi)"
],
"output_type": "display_data",
"text": [
"<IPython.core.display.HTML at 0x4c494d0>"
]
}
],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N_omega = 4000\n",
"omega_list = np.linspace(0, np.pi, N_omega)\n",
"# Spectral Density\n",
"\n",
"c1a, c2a = (1.5,-0.90)\n",
"poly_a = Polynomial([1, -c1a, -c2a])\n",
"f_ar2a = 1/np.abs(poly_a(np.exp(1j * omega_list)))**2 /Var_AR2(c1a, c2a)\n",
"omega_max_a = peak_ar2(c1a,c2a)\n",
"# another set of parameters\n",
"c1b, c2b = (1.8,-0.90)\n",
"poly_b = Polynomial([1, -c1b, -c2b])\n",
"f_ar2b = 1/np.abs(poly_b(np.exp(1j * omega_list)))**2 /Var_AR2(c1b, c2b)\n",
"omega_max_b = peak_ar2(c1b,c2b)\n",
"# another set of parameters\n",
"c1c, c2c = (1.4,-0.80)\n",
"poly_c = Polynomial([1, -c1c, -c2c])\n",
"f_ar2c = 1/np.abs(poly_c(np.exp(1j * omega_list)))**2 /Var_AR2(c1c, c2c)\n",
"omega_max_c = peak_ar2(c1c,c2c)\n",
"\n",
"# Plot\n",
"fig = plt.figure('spectrum', figsize=(10,5))\n",
"fig.add_subplot(111, title='Spectral density of an AR(2) process (normalized)',\n",
" xlabel='normalized frequency $\\omega/\\pi$' )\n",
"plt.plot(omega_list/np.pi, f_ar2a, 'b-', label='$(\\phi_1, \\phi_2) = (%.2f, %.2f)$' % (c1a,c2a))\n",
"plt.plot(omega_max_a/np.pi, spectrum_ar2(c1a,c2a,omega_max_a), 'b*')\n",
"\n",
"plt.plot(omega_list/np.pi, f_ar2b, 'r-', label='$(\\phi_1, \\phi_2) = (%.2f, %.2f)$' % (c1b,c2b))\n",
"plt.plot(omega_max_b/np.pi, spectrum_ar2(c1b,c2b,omega_max_b), 'r*')\n",
"\n",
"plt.plot(omega_list/np.pi, f_ar2c, 'g-', label='$(\\phi_1, \\phi_2) = (%.2f, %.2f)$' % (c1c,c2c))\n",
"plt.plot(omega_max_c/np.pi, spectrum_ar2(c1c,c2c,omega_max_c), 'g*')\n",
"\n",
"plt.legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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v3r0a74U62o5X1ENh5cqVTCKRMDc3NzZt2jR269YtzmVxuZeavq/GfI8pkNJH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\nCCGEEMJGkkgJIYQQQtjo/wGhZ+gd20mXaQAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 127
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Check that the intergral is one\n",
"print f_ar2a.sum()/N_omega \n",
"print f_ar2b.sum()/N_omega\n",
"print f_ar2c.sum()/N_omega"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0.999806695046\n",
"0.999993598862\n",
"0.999862847222"
]
}
],
"prompt_number": 128
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"# Approximating the Bretschneider spectrum \n",
"\n",
"... for *ocean waveforms* synthesis\n",
"\n",
"**Extract from Chapman 1990 :**\n",
"\n",
"As shown in SARPKAYA and ISAACSON 1981, the Bretschneider spectrum has the\n",
"form:\n",
"\n",
"$$S(f) = (A/f^5) exp(-B/f^4 )$$\n",
"\n",
"in which f is frequency, S(f) is the spectral density of the sea surface elevation, and A and B are :\n",
"\n",
"* $ A = 5 z_{rms}^2 f_0^4 =5 H_s^2 f_0^4 /16 $ (because $ z_{rms} \\approx H_s/4$)\n",
"* $ B = 5 f_0^4 /4 $"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Hs = 4. # (m)\n",
"Tp = 10. # (s)\n",
"fs = 10. # (Hz) sampling freq\n",
"A = 5/16 * Hs**2 /Tp**4\n",
"B = 5/4 / Tp**4\n",
"f_list = omega_list/(2*pi)*fs\n",
"f_Bret = A/f_list**5 * np.exp(-B/f_list**4)\n",
"f_Bret[0] = 0\n",
"print('frequency resolution : %.3f Hz' % (f_list[1]-f_list[0]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"frequency resolution : 0.001 Hz"
]
}
],
"prompt_number": 176
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Convert 1/Tp in normalized radians:\n",
"omega_p_Bret = 1/Tp/fs*2*np.pi\n",
"# Manual correction\n",
"omega_p_Bret *= 1.00\n",
"print omega_p_Bret\n",
"c2_Bret = -0.971\n",
"c1_Bret = -4*c2_Bret * np.cos(omega_p_Bret) / (1-c2_Bret)\n",
"print(c1_Bret)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0.0628318530718\n",
"1.96668483674"
]
}
],
"prompt_number": 205
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Plot\n",
"fig = plt.figure('Wave spectrum', figsize=(10,5))\n",
"fig.add_subplot(111, title='Bretschneider Spectral density (Hs= %.1f, Tp=%.1f)' % (Hs, Tp),\n",
" xlabel='frequency (Hz)' )\n",
"plt.plot(f_list, f_Bret * fs/2, 'b-', label='Bretschneider')\n",
"plt.plot(f_list, spectrum_ar2(c1_Bret,c2_Bret,omega_list), 'r--',\n",
" label='AR(2) with (%.3f, %.3f)$' % (c1_Bret,c2_Bret))\n",
"plt.xlim(0,0.5)\n",
"plt.legend(loc='upper right')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 206,
"text": [
"<matplotlib.legend.Legend at 0xf614290>"
]
},
{
"output_type": "display_data",
"png": 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kJER17tzZuD89PV3VqlVL3bhxw/jeW2+9pc6dO6eUUuq3335T7u7u6pdffjHu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\n/fqZ419/hZUrzTZ9upnU3ratGQ7M3bx8Hr+IiMs0Z8pmf/2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nsnHjRiIjI7nhhhvyFgwd\nN24cq1atokWLFixYsIBrrrkGMAsuP//887Rv357u3bvTvHnzvHPNmTOHmTNn0rp1a1q0aMGiRYsK\nvWbufo8ePYiLiyM6OpqoqCgmT56c95oBAwYQGBhI9+7dC/2aOnXqxMaNG136uidPnsxPP/2UNwn9\nrbfeAmDDhg106dKl2HOIiO/TQsci4hENGzZk06ZNhIeHe+R6kyZN4tSpU3l3ChaUlpZG165dC51P\n5ar777+fJ598kqioqFKfQ0ScT3OmRMQjPDm36O677+bAgQN88803Rb6mSpUqdO3alZUrV9K1a9cS\nX+P48eOcPHlSiZSIqGdKRERExB2aMyUiIiLiBiVTIiIiIm5QMiUiIiLiBiVTIiIiIm5QMiUiIiLi\nBiVTIiIiIm74f8ohE2Y4t58QAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 206
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Difference between the two spectra :\n",
"\n",
"* Bretschneider spectrum is zero at $w=0$ \n",
"* AR(2) spectrum is not zero !!"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Going back to the autocorrelation\n",
"\n",
"def f2acf(f):\n",
" '''spectrum to acf, using ifft on a symetrized spectrum\n",
" TODO : check that it is the right formula !!!\n",
" '''\n",
" N = len(f)\n",
" # Create the symetric :\n",
" f_symetric = np.concatenate((f, f[::-1]))\n",
" acf = np.fft.ifft(f_symetric)\n",
" # Take the real part\n",
" acf = np.real(acf)\n",
" # return only one half\n",
" return acf[:N]\n",
"\n",
"# Time vector\n",
"t = np.arange(N_omega, dtype=float)/fs\n",
"\n",
"fig = plt.figure('Wave acf', figsize=(10,5))\n",
"fig.add_subplot(111, title='Theoretical Wave autocorrelation (Hs= %.1f, Tp=%.1f)' % (Hs, Tp),\n",
" xlabel='time (s)')\n",
"plt.plot(t, f2acf(spectrum_ar2(c1_Bret,c2_Bret,omega_list) ), 'b-', label='Bretschneider')\n",
"plt.plot(t, f2acf(f_Bret*5), 'r--',\n",
" label='AR(2) with (%.3f, %.3f)$' % (c1_Bret,c2_Bret))\n",
"plt.xlim(0,50)\n",
"plt.ylim(-1,1)\n",
"plt.legend(loc='upper right');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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VZ1qNsLAwLly4wIQJE4y6inr06MHJkydZtGgRGRkZZGRksHfvXqNB6DnS09NJT0/H3d0d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\nAABJRU5ErkJggg==\n"
}
],
"prompt_number": 207
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## See also :\n",
"\n",
"interactive study of an AR(2) process"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image(filename='interactive_AR2_response.png')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"png": 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h7wBQLfQdACJB3wEgEnbrM1gFMoqCV0TIy8tTWlpajDM6+rz8snT7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\nI5rH44k8UkFx8Wz9939fr/z88ZIyJHklZSg/f7xmzPiBoyZ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zHAItQYYC1qDLBOqNUVDbAm4vP57E4BaBSmaWr3K39R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"prompt_number": 16,
"text": [
"<IPython.core.display.Image at 0x3dd5f50>"
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"Predicting an AR(2) process\n",
"----------------------------\n",
"equation taken from *Brockwell & Davis*, \u00a7 5.5\n",
"\n",
"### Prediction error at step $h$\n",
"\n",
"as given by equation 5.5.5, page 182 :\n",
"\n",
"$$\\lVert X_{n+h}^{pred} - X_{n+h} \\rVert^2 = \\sigma_Z^2 \\sum_{j=0}^{h-1} \\psi_j^2$$\n",
"\n",
"where $(\\psi_j)$ is the impulse response of the ARMA filter."
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"# Numerical computation of the prediction error\n",
"pred_std = np.sqrt((imp_res**2).cumsum())\n",
"# add zero for h=0\n",
"pred_std = np.concatenate(([0], pred_std))\n",
"h_range = np.arange(len(pred_std))\n",
"# Normalization\n",
"pred_std /= std_AR2(c1,c2)\n",
"\n",
"### Plot the prediction error\n",
"fig = plt.figure('pred error', figsize=(10,5))\n",
"fig.add_subplot(111, title='standard deviation of the prediction error',\n",
" xlabel='prediction step h', ylabel='normalized std.')\n",
"plt.plot(h_range, pred_std, '-d')\n",
"plt.hlines(1, 0, h_range[-1], colors='b', linestyles='dashed')\n",
"plt.xlim(0,20)\n",
"plt.ylim(0,1.05);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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SRlUGj9gTRkav5ISNRJVhvpCmmCukbyzCiIiIiCTAIoyMXmBgoNQhkBFhvpCmmCukbwZ7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\niIiIOEBJmIiIiIgDfgKL0dCpp+y+XwAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 68
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Recursive prediction of an AR(p) process\n",
"\n",
"prediction of an AR(2) is given by a simplification of eq (5.5.3) for AR(p) processes :\n",
"\n",
"$$\\hat{X}_{n+h} = \\phi_1 \\hat{X}_{n+h-1} + \\phi_2 \\hat{X}_{n+h-2}$$\n",
"\n",
"The recursion is initialized with the *last two* observations : $X_{n-1}$ and $X_n$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Compute the prediction\n",
"H = 30 # Prediction maximum horizon\n",
"X_pred = np.zeros(H+2)\n",
"# Initialize the recursion using the last two observations:\n",
"X_pred[0:2] = X_traj[[-2,-1]]\n",
"for h in range(2,H+2):\n",
" X_pred[h] = c1*X_pred[h-1] + c2*X_pred[h-2]\n",
"# trash the first elements (that is : keep only the last observation)\n",
"X_pred = X_pred[1:]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 128
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"### Plot the prediction ###\n",
"fig = plt.figure('AR prediction', figsize=(12,7))\n",
"ax = fig.add_subplot(111, title='Stochastic trajectory : Prediction of %d instants' % H,\n",
" xlabel='prediction horizon h = k-N')\n",
"plt.plot(np.arange(N)-N+1, X_traj, 'b-o', label='observations')\n",
"plt.plot(np.arange(H+1), X_pred, 'b-o', label='predictions', mfc='#BBBBFF')\n",
"\n",
"# Add some confidence intervals\n",
"level1 = 0.95 # 95 % confidence level\n",
"color1 = '#FFFF88'\n",
"a1 = stats.norm.interval(level1)[1] # = 1.96\n",
"plt.fill_between(np.arange(H+1), X_pred-a1*pred_std[:H+1], X_pred + a1*pred_std[:H+1],\n",
" color=color1, lw=0)\n",
"level2 = 0.70 # a tighter interval\n",
"color2 = '#FFDD66'\n",
"a2 = stats.norm.interval(level2)[1] \n",
"plt.fill_between(np.arange(H+1), X_pred-a2*pred_std[:H+1], X_pred + a2*pred_std[:H+1],\n",
" color=color2, lw=0)\n",
"# Legend\n",
"conf_rect1 = matplotlib.patches.Rectangle((0, 0), 1, 1, fc=color1)\n",
"conf_rect2 = matplotlib.patches.Rectangle((0, 0), 1, 1, fc=color2)\n",
"handles, labels = ax.get_legend_handles_labels()\n",
"ax.legend(handles + [conf_rect1, conf_rect2],\n",
" labels + [\"%.0f %% conf. interval\" % (level1*100), \"%.0f %% conf. interval\" % (level2*100)],\n",
" loc='upper left')\n",
"\n",
"plt.xlim(-30,H)\n",
"plt.ylim(-3.5,3.5)\n",
"plt.grid(True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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q82uvvUa9evVo2LAhy5YtM51z27ZttGrVCn9/fxo1asSiRYusvk7CvUmem2eT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\nTkSuQmCC\n"
}
],
"prompt_number": 227
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Create *scenarios* of trajectories\n",
"Answer the question *\"how the future would look like ?\"*"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N_scenar = 100 # Number of sceniaros to generate\n",
"X_scenar_list = []\n",
"for i in range(N_scenar):\n",
" noise_scenar = np.concatenate((noise, np.random.randn(H)))\n",
" X_scenar = lfilter(b=[1], a=[1,-c1, -c2], x = noise_scenar)[-H-1:]\n",
" X_scenar /= std_AR2(c1,c2)\n",
" X_scenar_list.append(X_scenar)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 208
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"### Plot the scenarios ###\n",
"fig = plt.figure('AR scenarios', figsize=(12,7))\n",
"ax = fig.add_subplot(111, title='Stochastic trajectories : %d scenarios along %d instants ' % (N_scenar, H),\n",
" xlabel='prediction horizon h = k-N')\n",
"plt.plot(np.arange(N)-N+1, X_traj, 'b-o', label='observations')\n",
"# 95 % confidence interval\n",
"plt.fill_between(np.arange(H+1), X_pred-a1*pred_std[:H+1], X_pred + a1*pred_std[:H+1],\n",
" color='#FFFFAA')\n",
"for i,X_scenar in enumerate(X_scenar_list):\n",
" if i==0:\n",
" zorder=2\n",
" lineformat='^-'\n",
" alpha=1\n",
" else:\n",
" zorder=1\n",
" lineformat = '-'\n",
" alpha=0.3\n",
" plt.plot(np.arange(H+1), X_scenar, lineformat, label='scenario %d/%d' % (i+1,N_scenar), \n",
" color=(0,i/N_scenar,1), alpha=alpha, zorder = zorder)\n",
"\n",
"# Legend\n",
"conf_rect1 = matplotlib.patches.Rectangle((0, 0), 1, 1, fc='#FFFFAA', lw=1)\n",
"handles, labels = ax.get_legend_handles_labels()\n",
"plt.legend(handles[0:3]+[conf_rect1], \n",
" labels[0:3] + ['%.0f %% conf. interval' % (level1*100)],\n",
" loc='upper left')\n",
"plt.xlim(-30,H)\n",
"plt.ylim(-3.5,3.5)\n",
"plt.grid(True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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lb+vN2mUFwqDMPAbgcDhwu92EhoZWWD9p0iQSExMBMJlMdO/e/XIPKUn1UvZN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p96aJI7KnWkIOHJXpk3/nCN25M6m6pOterzic9O4ZRFZnY5jGRcfvvkPj699zDTWZf3f/0A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\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KeMrrkCYCt1uT/5+99w627DrLvH877332yeHm29333s45yJZkW8myJTlQlAMGf1CUYQgz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\n1S5XE7VNrxDxwGJWUyQOX+bCudGsCE9G0iMshBBiQp0OQE0QrjNDqgZ/b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}
],
"prompt_number": 226
}
],
"metadata": {}
}
]
}
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