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Phys 411 Assignment 02
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"<figure>\n",
"<IMG SRC=\"../lectures/images/PhysicsLogo.jpg\" WIDTH=100 ALIGN=\"right\">\n",
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"# [Physics 411](http://jklymak.github.io/Phy411/) Time Series Analysis\n",
"*Jody Klymak*\n"
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"source": [
"Assignment 3"
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"source": [
"Q1: Lag correlations of weather time series"
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"hourdata=np.genfromtxt('http://web.uvic.ca/~jklymak/Phy411/Data/AllHourly.txt')[[6,28],2:]\n",
"dc = hourdata[0,:]\n",
"jb = hourdata[1,:]\n",
"\n",
"dc_raw = dc\n",
"jb_raw = jb\n",
"\n",
"print np.shape(dc_raw)"
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"a**1** From the hourly time series at Deep Cove (`dc`), calculate the *lag correlation co-efficient* $\\rho_{xx}(\\tau)$ out to a lag of $\\tau=30\\ \\mathrm{days}$ (Umm, remember this data is hourly!). (also rememebr to remove the mean of $dc$ before trying to to the calculations). \n",
"\n",
"Comment on the resulting plot."
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"import numpy as np\n",
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"\n",
"import numpy.ma as ma\n",
"\n",
"good = np.isfinite(dc_raw)\n",
"dc = dc_raw[good]\n",
"\n",
"dc = dc - np.mean(dc)\n",
"\n",
"lags = arange(0.*24.,31.*24.)\n",
"cxx = 0.*lags\n",
"\n",
"\n",
"for ind,tau in enumerate(lags):\n",
" if tau==0:\n",
" cxx[ind]=np.mean(dc*dc)\n",
" else:\n",
" cxx[ind]=np.mean(dc[:-tau]*dc[tau:])\n",
"\n",
"fig,ax=plt.subplots(1,1)\n",
"ax.plot(lags/24.,cxx/np.var(dc))\n",
"ax.set_xlabel(r'$\\tau [days]$')\n",
"ax.set_ylabel(r'$\\rho_{xx}$')"
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z5qbzDvK9SEvTt6tKhy/XSiTlZJuWam+3m/UkR3TwprpgMeaFISND/3X3L6Vt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\nbCvYXvwiAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7ff8a96f4650>"
]
}
],
"prompt_number": 22
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This shows a steady downward trend as is expected where the corellation coefficient decreases as the data used becomes futher away in time. Note: the sinusoidal waveform within the overall trend corresponds to tau times that vary between integer increments of the day, i.e. if the tau time corresponds to n*day+12 hours it would be checking the correlation between day and night time (or a similar delta time) and therefore the correlation would be reduced when comparing different times of the day."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*2* Now, instead of doing the whole year, look at just the winter months and the summer months and compare the lag correlations (no need to do this for the whole time series, just choose one winter and one summer). Make sure to indicate which lag correlation is which on the plots.\n",
"\n",
"Comment below on the different charcter of these two lag correlations."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# summer start: june 21 = 172 day of year = 4128 hr\n",
"# summer end: sept 21 = 264 day of year = 6336 hr\n",
"\n",
"# winter start: december 21 = 355 day of year = 8520 hr * last day = 365 = 8760 hr\n",
"# winter end: march 21 = 80 day of year = 1920 hr\n",
"\n",
"\n",
"dc_s = dc_raw[4128:6336]\n",
"\n",
"good = np.isfinite(dc_s)\n",
"dc = dc_s[good]\n",
"\n",
"dc = dc - np.mean(dc)\n",
"\n",
"lags = arange(0.*24.,31.*24.)\n",
"cxx = 0.*lags\n",
"\n",
"\n",
"for ind,tau in enumerate(lags):\n",
" if tau==0:\n",
" cxx[ind]=np.mean(dc*dc)\n",
" else:\n",
" cxx[ind]=np.mean(dc[:-tau]*dc[tau:])\n",
"\n",
"fig,ax=plt.subplots(1,1)\n",
"ax.plot(lags/24.,cxx/np.var(dc))\n",
"ax.set_xlabel(r'$\\tau [days]$')\n",
"ax.set_ylabel(r'$\\rho_{xx}$')\n",
"ax.set_title('Summer Correlation')\n",
"\n",
"\n",
"\n",
"dc_w1 = dc_raw[8520:8760]\n",
"dc_w2 = dc_raw[0:1920]\n",
"\n",
"dc_w = np.append(dc_w1,dc_w2)\n",
"\n",
"good = np.isfinite(dc_w)\n",
"dc = dc_w[good]\n",
"\n",
"dc = dc - np.mean(dc)\n",
"\n",
"lags = arange(0.*24.,31.*24.)\n",
"cxx = 0.*lags\n",
"\n",
"\n",
"for ind,tau in enumerate(lags):\n",
" if tau==0:\n",
" cxx[ind]=np.mean(dc*dc)\n",
" else:\n",
" cxx[ind]=np.mean(dc[:-tau]*dc[tau:])\n",
"\n",
"fig,ax=plt.subplots(1,1)\n",
"ax.plot(lags/24.,cxx/np.var(dc))\n",
"ax.set_xlabel(r'$\\tau [days]$')\n",
"ax.set_ylabel(r'$\\rho_{xx}$')\n",
"ax.set_title('Winter Correlation')\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 45,
"text": [
"<matplotlib.text.Text at 0x7ff8a91fcc50>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Dc1qakbNwKmygVkXJ541y7DO19D5WEHOkYR3srUlwaaNb3Echjbg4g6TsOoyV\nNAZKnpIPhBOZmf0PItKgSgeNjcYAGMQqYsqqd8B4Pz9fTxqU1fFNTYb2riscoERd1M3wBvL8CIDW\nL4KUp8xafxCyqznHoCIgSltunjeONKIc1kjDmgSXNkEkwgHnWYbbo2Mp4b6ug8rknYrM5DV1RBUO\nGxqzrkrGzYOTna0edJuajBk/ZdCl7sOlS17LAUl1Tam9y80nVf7LtnRrbnQEKq8LqGUzKnbuBObN\nU9vIiQ5loBw61JjNO/lmnoWr2qLk/dzIUzo7aqQknyVVW9REOJPGIIdXeaqry3gIEhOdbSQo+Qo3\nkQal5JaS0zBfUyUxUGaU1FJgN9KBrrRSXlNXwmiWd1RbmFCS3JRrUksr5YAkV+07oakJGDVKfwqj\n7MdB7He1datROq1aaS/7hU6eSkoyym515aiUYhHKBqFuZ/SUtnSTNCqBUnZWYHlqkMOrPCU7idwG\nwy9pUBPh1JyGfAhVA1eQ15RtBTGjlHbDh6vbospm8oCcpCR9ZZcu+W6+ptNA6YYYqdKHjkCl/4mJ\ntAWFOsiDk1TnPlAGSi+beuryeYD/iVVnp/FPF7VTpS55L3TFLkwaMQCv8hR1+3TZpnljQ0qk4fds\nDmp04Da60dnoZpRuB9QgNoKkVLYIYeQYCgrUM3Xz7DoITZ1KoFTSoJQpUyDJQrW2xUsfUxGCrl+b\nnyMKUem243HTX3WSEpVAJbFQcoixgpgnDao8Rd3UsKvLmNFIGUt2GCvMD1cQ26xTH0L5Wf3KU9QH\nOshqGjcJep1dR4eR20lL07elu69UYnRzLyRpqAaacFi/uBIANm6kHxakk+qGDqX1HYA2oAY1yXEb\nAfmRusJh4198vLot6X9cnFGxRVEmYgExRxoUeSox0RhUzA+slVwSEnqSwWZQZawg12l0dRm+JCTQ\ncxpBRRq6ttxIMjo7ilREtQuSgKyf0Wmgd3Mv0tON9QlOpaGUhXaA4cuiRcBzzznbyPbGjFG3RZEt\nqX0sSNKgSEVu+76qrfb2nmec6j/Vt1hAzJEGJdIIhfpuX20ll1DIXsaibkni5oEYNszwRwj77Rva\n2gxfQiG1jOJGI3YTtVAqYHQzt/Z2OlHpEs4UO0pS12xHWTQZH68e6CmkITe5090LcymwKoqQi/+o\nlWQ6qS7I6MDNxMRvNE6paDT7HzQZUNuLBcQ8adhFGoB9REKVscx2Tp2K2vG85EcokhJFYggiqS6T\ngTpiSU6IkLk1AAAgAElEQVTWz9yCzO+4jTSCuBduNrmLi9NHN/KgLBUhmM8pUYFaSaaTp/oz0qAM\n9JQBnPK8BRkBubGLBcQsaUgJwUlPtFZQucl9UCINt/KUtNOt+aDqukFVT6n8km1Ra/t1fgUpKbnZ\nKiUoqY6il5t3PKWsTZAHXDnBvCuwCpTT9oKMDsySUlBRCyUa0bVFOUDN64SP5akoRVycISFImcfp\nYCCr9OSU+xgoeUplZ21LFUEMdE5joNtye02dPEXV8d1EXTpiSUrqacvv2oTaWqP8WEUGnZ3GdXQn\n5A10dNBfSXW/8lR7e0+hS5BSXawg5kgD6C1RUeWp/og0zFuS+HlwrIv2KJ3Yyc68iDGoqMVNZUs0\nJsLdkHFQ98K8zb3Kf3lanUp2kpKYm1yRH3lKiOCrp4KKDrwk1f1cU4iexHqsICZJwzyQU+UpO3Lx\nQxrWEkDKmg9qpEGd0ds9+Obqr6CjA0oYP9CJcDekoRoog5I+gq5Ko5zzYY6mdFFXEAN9e7tR2KHL\n2wSZH3ErmyUmGhGY3UJTark8pV90dBjKR1wMjbQx9FF6YI40qPJU0JGGueP5XV3uJeHmNHDZDeB2\nJaRBSwdB5VrMvlFm/ZTqKWk3UJEGZUByI0/pSMMtGfudTHiZ5AQ50FOiAzlp0hWxUCMNyr2IFbgm\njXXr1iEcDuPQoUP94E4w8CJPBR1pmO1UpOElp0GZxVIioCFDnEtIqQOleXYdxKAbdE4jyKR6EP5T\nv0vqKnTK5o3UqrSgqqfMNkEM9PK+qlZ7WwmIKinp/Kcm8lVVlLGUzwA8kEZ7ezs++ugjVFZWBuZE\nWVkZJk2ahOLiYqxevbrP+//zP/+DGTNmYPr06fjKV76CPXv2KNszD5hOXxq15JZydKxutqKLNHQd\n1OsDoXu4VL5RZ4GUAclrItzP1u7SJjHRGLCcji8NMqfhtjKHUmWlG+jllu3t7c7rR6i5Ii8JZ92g\nq5JBgyxt9TLQq+Q1844Pfr5Lp0lrNMM1aZxxxhk4cuQItm3bFogD4XAYy5cvR1lZGfbt24cNGzbg\nk08+6WVz5pln4p133sGePXtw//3349vf/rayTUqk4We7EbOdU77CqzxFISBKpOHkl53/OnLRhehu\nZ9e6gT4hwfjZzyAo/aLmboLIaVAJlHIv3O7sSln0GYQ8ZR2c/fQxa97PzkZu2yP7hKqtoJLX1GfX\nbVuxAtekMXbsWFx++eXIyMgIxIEdO3agqKgIhYWFSEhIwKJFi7Bp06ZeNvPmzeu+3pw5c7RRjpU0\nqJFGJOQpqqRkJQ3daYFO5OLF/yAGSjeRBuA8wAlBz0O4uWYQOQ235btB5DTcbs/iZGOueKLKU5T+\nqrIz31ddW3LbHtWMnhKNuy08oZIG5zQUeP/99yGEwOWXXx6IA1VVVSgoKOj+OT8/H1VVVY72Tz75\npPbaZlmJKk9FKhFuvi6lrSFD+m6BYtcWdRbolzSkbwkJPbNClf9+yUVWo8THuyMgXRThtypN2rmt\nPtJFjZRIg7IRpPTLyffOTmNgdnNfqaThJxq39ldKNE6teOJIwxvi3f6BzGk0NzejsLDQtwMhOYUg\n4O2338bvfvc7vPvuu0o7c2UUVZ6iRhpWcqHOomR0YP24bmZbEvIhtPprd02VX+a27OzMA+WXX/a1\nMc9OzUnK1FR1W3K/JJVvlBmlXwIKcj2BOQIKIqdB8QvoLU/52TbG7BfVjjpQqvJ+XggoqLwfNZEv\nd5iwPrvUqCvWEuGuSUPmNP7yl7/gggsu8O1AXl4eKkwnw1RUVCA/P7+P3Z49e7B06VKUlZUhKyvL\ntq2VK1cCACorgQ8+KMGFF5a4kqdGjFDbSDtK6G2tUoqP730yoLk9XWe3G+hbW42dUp2uqZrdURL5\nFL/M9fhAz0NoJY0gI40gSUP6L/MefrYD7+ykRUBBkwZFxnJTOCD98iNPuYlmvRCQjlzclMk69Wv5\nnMptz+0W6FkJ1G67l8GYCC8vL0d5ebnnv3dNGmPHjsWkSZNw+PBhzxc1Y/bs2di/fz8OHTqE3Nxc\nbNy4ERs2bOhlc/jwYVxzzTV45plnUFRU5NiWJI0PPgAmTzZ+50aeCjKn4dTZraRBnW1Rk9dB5TQo\nftlJB0EO9HYDl1upCHCehVNyKID7Khk3axOc9oxyI0/pchpmCc4PGVDt+lOeUl1TTlao1VOU6i/z\nNVWkMXSo/Xc5GOWpkpISlJSUdP/84IMPuvp7LWn8/Oc/xxtvvIGTJ0/iqquuwg9/+EPExcXh9ttv\nd+2srQPx8VizZg0uu+wyhMNhLFmyBJMnT8batWsBAMuWLcOPf/xj1NTU4LbbbgMAJCQkYMeOHY5t\nepWnqDmNzEy1jd11pV1aWl87LyE6RdcNKqdBnQWqwv2gEuHUgb611dghVnVNr2RWU9PXxkqy7e1G\njse6EtjtjJiaCKfIU7L8OBw2oiKV/21tznKq2/4apDzlp79a2wsyuqH6HwvQksaZZ56JN954A11d\nXXj55Zfx85//HCtWrAjUiQULFmDBggW9frds2bLu/z/xxBN44oknyO3JhxYwHrikJHuboBLhugfC\nqa3OTuPBjI/vsVFt/SFh19m7unqH0NRIgxq1UKUuHYEOlDxFISq3yX5ATcbSxpzfsZ4N3R85DWoi\n3Fx+bJd3kn7FxTnLqZR74WagdxtpBJm89ktUp2tOQ1s9dfz4cbz88ssAgKuuugqTpe4ziGGOIpwO\ndbfLaXiRpyiDCLUtFQHpSEPqsHJmqCIDL5EG5TNS8ii6B9pN9Zff6inrrFlGBzo7yn0NaosN1UJH\nuWhRbj5Jzcl4nZhY7dxMTIKaqVP660CRBiUnMxhzGn6hjTSWLVuG9evX4/LLL4cQAklJSRg+fDjm\nzp2LBLniZpDBLE85RRrUxX3W5JaXnICTnV2uQqfXyrasHdRvrsUKykBp9xl1D45KOnA7OPuNWsz+\nh0I9xGHtBxQys/suna4p5U2KjCKT606J2GHD9Cc6uo3ggGAlGUr/8TvJofgly8HNkb2dXXt7bxmZ\n5aneIK3TKC0tRVlZGV544QXceeed+OMf/4jvfOc7/e2bZ1jlqf6MNPw8OF5m/YD9A0adKbqJlCiJ\ncGoYT5kFUqMbinbtdaD0U2BAibq8zIj9Jt/N998p6vLSf4KcqVPb8ptUdys7OdmZy7XdtBULcFU9\nlZKSgosvvhgXX3xxf/kTCKzylFNOw1zt4CYR7lbHB+w7u9dObNcWNWpxM1C6TYRTQvQgI40gCIgq\nyVDuhZcZsRvSMxdgWG10ifDhw3u3pbqek//ms1gAek4j6IHeD5kFFY13dvbkfty0FQuI2a3RvchT\nQUcaOjuvUYvdwOXl4VJdkxppBNWW1S7ISCOIqKs/ZrFO17PaBVmVRt3ugpI3U8lObuUpeb+suRuv\nZOwnAqLYuWnrtEuERyNkhxdCHWlY5SmrXdDylC46oD6ETvKU10jD60DvZUbpNIBbZ7FBRhpUAvUT\nabhpSze4We1Ua1Yo8hQlIqEMzm5kJ7fRuNM2/V6u6Ucypl7TS5QdK4hp0ujo6FnRaYW1I7S0eJen\nrJ1F1sLHx/e208lTbsL9oCKNIAdKqtSl+oxuqr9UM3WrJOZXqqPMYvsr6qJISpR1Grq2KBOToORU\na07AqT0/ZGwXtVCeN/OKcCe/vN6LWEBMkoZ8MJzKbQH7xX1eIg1VfsG8MKq/5Sm7Tiz3zNHZeZVk\nvGrXlBkZZXCOjzc+n9MmiUFGB5S23A4ibiINnV9+16xQvks/UbbVf7ntinmRYVAykDxe1WvUErQ8\nxaQRBZAPhlM+A7CXpyiRBmVGaReS+iENyuBmtZFJOsohUpTcgd+Zutu2gshDeJGn7GbElKjFTh70\nKk9ZZ+GUXIubMzx0a1akb7qJCTUyHqhnROcb5zSCQUyThirSCFKe0nUolV2QOQ3rNSmzRbu27MoJ\nvWq/VjsZ4VkX0XkhA5VvVElM15Z5y3Dd9YKKNKjXNPtPlaf8SKBWG1lwYo1mqdG4XX/tT6LqT9Kg\nTBJiBTFNGqpIIyh5KiHByF+YB0G72YXdg+9loFG1Rb2mjvSsu9eqNGK30YF5EZ3OL2oehRIpUQZ6\n6qDlxy8KaXiREN1skkglY91Aad4BVue/3X2lTtJ0bXn1n3r/zdWYbtviRHiUwK08JYT9ilsKaYRC\nfTuVXUehzvq95g6oMzfKw2UnddkNDl7yENJON4gEKWP5kaf85J0osllQbbk5LdBrNOtGwnU7U1fZ\nec2jUAjIri1OhKsRk6QxbJg7eaqtrXf9uZ2NBOXB6e8Hwu8D7ZY0qG25mdFTBucgIw2vBOQn0qDk\nNPy2RZWnKFKjF9mVMoFx+r6pkzSvE5P+JCA3pME5jSiArDahylN2+Qygb0eQWr9150870ggqPyLt\nvOY0dJKYHwIKMtLwmtOw818eOytLrf0M9E7fURCL0BITDT+t+R0v0ofTZ7R+hiClOukb5Z55laco\nExO5w3N/RQeUtswn/KnsYgExSxpuIg27fAbQV3ayav3mtswd2c8sijILdHqggyIqO9Lwk6T0QlRB\naNe6lcteErbmbcN1n1E3IMn8jpeZutV/N6QR1EBJtXMTtej6mF1b1pXqbvyiSHVDh+rzNnFxtNxH\nLCCmSYOa07AbJK02Kjvrg+h1APdT2eKURwkip0G18yN9BBlp9GdbVP/9kJ6X++r0Ga3tUaMuah/z\nSnpBylNecy1+CNSr/7GAmCWN5mb64j6/pGFn5yWnkZhozGApK1kpkQYld+BG6vIyo7STDqgDfVCD\nrh95yum+epkRU+2ClqfMn8HN7FrXX+V1vczo/chT/RkBUe28XjMWEJOkkZoKNDbSIw3q6X5U0vCq\n/YZCtBJGN7PAICMNLwO9rEoLanW8l+iAOlAGGcHZDW6ySs+t9k6JlJw+o/Uz+Ik0/OQ0vA66FAnX\nDQFRSMPLd6Sy40R4FCAtDWhoCEae0p0jbm0LcDfr1z2E1oNjZFt+ooOg5CmvYbzXBL2db0FLXZSH\nnjI42A1udjmxIOUpOxs3K9op0WxQM3pqv6D2VwqZUfyi7onlNQKNBQwK0igrK8OkSZNQXFyM1atX\n29rceeedKC4uxowZM7B7925le3JmW1vrT56KjzfklXBYbedVnqIMzl41dWmnG5ypbVEG1EjkBLxK\ncNRreiW9ICUNijwlJzhWabOjw+jHco8nCgEF7T9VTqVGGhS/KJM0u7bkORlu98Si+h8LiDhphMNh\nLF++HGVlZdi3bx82bNiATz75pJfNli1b8Pnnn2P//v34zW9+g9tuu03bbloacPQokJJi/778goVw\njkis1S1+5SkvGrHTA+El0pDlnbqoJUgCovrvNTqgyiN+JBkvpEchMyffvMhT1L3GVARKkeq85jSC\nknf8TEz6kxjd2EU7Ik4aO3bsQFFREQoLC5GQkIBFixZh06ZNvWw2b96M0tJSAMCcOXNQW1uL6upq\nZbtpacAXXwBZWfbvy50wOzudyQDo3RGc9Enrg+9mdq3reF4HXTu/pP9u8wtOdnYPtNeopb8jDa/y\nlBsZhaK9U2fEbuUpql9Ueaq/IyVqND7QfvUHaXBOI2BUVVWhoKCg++f8/HxUVVVpbSorK5XtpqUB\nhw/3HHNpB/klU0nDyY4SHXgdnIOMNPxIXVRJJqjkqZ9Iw3pNKTNat1Dvz0hjoOUp6X9QUl2QiXDq\nffUj+3nJwcl946T8DPRNglPbcmMX7Yg4aYSse3c4QFjEWt3f6SINoGc9R2trsOs5/MxC7KIDKmlQ\nIw1dW0Enwr3kR6iRBuWaTovogsxpUKIurwONm0jJq1QX1CzcrnAjyJm63Sp6r1GL3b5xfsjAev/t\nDmOLBUT84+Tl5aGioqL754qKCuTn5yttKisrkZeX16etlStXdv+/q6sE4XCJMtIwLwL0E2lYO1Vr\nK5CRobZxas+PPKWzU11PiB7ZymtE4pXM7NoyzwLNSUkvA6W0a2vrnePyquNT8zteydirPOV11k+1\no0wAVIOutY9Ro3GngV5O9PwO9G1tPQUzQcpT0oY4Lx4wlJeXo7y83PPfR5w0Zs+ejf379+PQoUPI\nzc3Fxo0bsWHDhl42CxcuxJo1a7Bo0SJs374dmZmZyMnJ6dOWmTSqq4Ht29WRRnJyT6QRJGm4CeO9\nSEpuBueGBvX1zLkduVeTV0mMql1TZJRQqO8DbS0flddsbFS3pfLfS3RAzUNEQp7yKvsFFWnY2ZjP\n/5bST1tbX+nYrfQkScOJjK27/nr1P8h7MRhQUlKCkpKS7p8ffPBBV38fcdKIj4/HmjVrcNlllyEc\nDmPJkiWYPHky1q5dCwBYtmwZLr/8cmzZsgVFRUVISUnBunXrtO1mZhqvNtzSDblyvD9Iw0vy16kt\na8czlwLLWbjT4Hz8uPp65mtK0mht7VuqPNCRhvma0hdZDhlk9Rdlpm6VLr0mnAdCnqK0FVRSXfqv\ni2alXVtbb9LQ3Qu7NRN2dk42tbU0//uTNGItCQ4MAtIAgAULFmDBggW9frds2bJeP69Zs8ZVm9nZ\nxquK6fsrp+FGY/WS07CbhVM6sSqR39pqrKSXdtZZIGVAosoQw4b1faAp0YHfRL5X0pMTEDfX9BNp\ntLb2jpCDlKec2qLIa35m19IuLc3+ekDf+y/XmFg3CLXaqaIRt/77SYTb+TUYIw2/iHgivL9w113O\nh9JISHkq6JyGm8HBS6Qh7XQDKmXQtbum15m6lCHMVUpBRBpuPiPVzmnNCpWAdBGV10HXzi5oecpq\n09XVWzqSdkFKMl4GejtiodpR5eDTUZ7yi5gljbg4fWho3kKdGml4HcCper+fh1CnvTuFy1TSoD44\n1nuhm5E5XdNrpEGN4IYN652kdCPJ2MkoukHXDQFR5Ck7SUl3TbsyU3k96/qdoBLhsj23g3OQbUk7\nL5M0r6ThNF5EO2KWNCiQOY2mph5pxgpKpEFJXnuVUZw6HnVApUQalLbsZuqhUN9yQoqu64ZA3fql\nsgsimrK7piQM3Z5SXiNQlaSkiyKs99Wu/Jgy4aD6H2Q07jTJofbXoKIDPxO+WMxpnNakIeWpxkb9\ndiOAv0S4We+n2KlsAG+Rhptw36t0YPdA+4k0vJKx7ppuBhoveadIyFNO1/QSwXlNhFMjY2pkGXSk\nwfKUf5zWpCHlKb+RBmXQte4N1Nlpv/DH60NIGdz85jT6U+ryGilRZSA/shmFjKmTBC8Dkht5KihJ\nye740oGWlKh9jBrNUq5plwhPSOi7oNBpksaJ8BhHcnKPPEWJNKhniVNkLDtN3a4tCmnYrV+wXk/l\nFyWKoM4CqRFQJCQlykDT2kqLBnWEbVcU4JVA7T6j3XfuNY9i539cXN+zXQY6p+E3EU4lDV1/dVo5\n7iU/Egs4rUlDnrtBladaWuztvHR2P9ov0PvB7+zsGaSsbekGB2tbTr55nVH6kYG8Skpek+pOA6Uf\n2Y8iY+kGN+sW/YDz2RwUAqVEXXa++Yk0vPYxr9IslTQiQXrRDiaNBro85VRlRY00zHaqB4L6EJoJ\nyOuDaue/0wDuNppy8t/N4BZUpEGV6igRCWWmbue/18HNvC7HjV9O16TKKNTB2Wsf8xrNepVAB4u8\nFu047Umjvp4uTzmdOU6d0VsjDcrsVDW4STs/s36qHTXXEmQewsvslHpN1b3QDVzUGSWVQCn+U3My\n/XkvIjHoBtWWn9XlVDvOaZwGSE93L0/ZkYaX3IFfecr8QFOIRdoFJR34malbByOnnAxV6rKbXfuJ\nNHQTADcRnNuZusrOy72g5jQopOcnpxF0H9N9R9a27HbftbOzS4RLO7Ns6YeAoh2nNWmkpQE1NUYE\nIbc3sGKg5SkvGvFARBrUgcbLjNh6JKnTNf1GGl7kKScy8yJPucnveJE+gpbqzHYDMVP32hZlwuH3\neeOcRg9Oe9I4fNjYxty6v40EVZ6idBZKpOFl5uYm0vAjT3l9CP0MWl5n1zqi8hN1uWkrKHmKEjU6\nyVNeZRRze3ZnZ9v57yeCDnKgdyOnuiWNcLjvFjRu/I92nNakkZ4OHDoEjBjhbEORp8w2cv2F3DHW\nDOtA76cTUyINilRkd02qdEAddCkDuFfS85oTUN0Lt5KS38HNS6ThR6pz0y8o0ayXpLqd/9YtTvwk\nwqmTLy+kIW28lstHO05r0hgxwiACKmlQ5Cn5ANodvELNabjNQzi1JWvL5boDP4MzRUe2fkYnO+pn\npEQkiYmGvGU9yc2PPBVUpEEloMEgT+kmHW4mJrpB10nqsm5x4tTHKJFSkLKT1Y5KjEwaMYjcXOM1\nPd3ZRm41AtDkKVVISrGjhriUSCMurmdlL0CTDjo7jYdaF3r7jTS85hesdnZ7KVEHet01VTp+UP4H\nLU8FmQg3f04/spPVTq4rspOErRMr6kDvdF/lhIkaKakS4TrS4EjjNIAcGFXHMcpV43IA0T04Tg8X\n1c6rPKW6phtJzG+uhfJAW6MDvzkZqozlNvnrtCmjV9mPMiOmJpypSfWgCJT6fVO+I+oz4uaaVjvz\niZSqtrz0az9+xQJOa9IAjChjyRLn9yVptLb23clUgjIjk3a6WZSbRLiuLTs7rw+0n9m1Tobwkwi3\ns3PS8d0SkBt9Pih5ippwpnxGJ9/cJMKDymlQBl3rNamThCAH+qDbisVE+KA4uS+SqKtTvy9Jw0ma\nAugDuJecBlU6UF3TjcTg1NHN0UFcHH0Q0V0zKYmuXVMlJWry3Xo6odXOzXfkNTpzQ8Y6orLLaVBz\nSl4T4fHxxiSgs9P4v1/SsNpZT0202uj8b2szdnsIkjSo0izLU6cp5JkbKtIw7w3kJvQOSp5yquqS\ndrI9SvWXk/9eowOK/0FEGmZJibIPFyU6oJKBG+1dR2Z+ZCA38hQ10nAruwYhpwbVx7zmR/o7aol2\nRJQ0Tp06hfnz52PChAm49NJLUWs9OBpARUUFLrroIpx11lmYOnUqHn/88QH1UUYaLS3Op/uZB9Qg\n8wvSTjfzVPlmvqZT9Vd/DQ6q9qh5FLeRhpsEPUWqs2uLWpVGmdF7GbSkHVWe0pGLagKjizSsvlG/\nb2pbfmQgL5M0ToTrEVHSWLVqFebPn4/PPvsMl1xyCVatWtXHJiEhAb/4xS/w8ccfY/v27fjVr36F\nTz75ZMB8pMhTQE+HUQ261lk/ZXU5ZXDWSWe6iMSN1DXYIw03iXxK8tfOxlqV5leecjtJkHYUeYqS\n06Dk19xISroBVTXJoUyGzDZO1X5e/KLaUQlINRZEMyJKGps3b0ZpaSkAoLS0FC+99FIfm9GjR2Pm\nzJkAgNTUVEyePBlHjhwZMB+DJA1zp3Jqz00inBppmK+pIyrqA+030nCboFfZeckV+Yk0rO35kT7k\ngjZZSTYQkQY1J0MhY6ud05kzXvorZWLlNzIOUp6SxKWr2Ip2RJQ0qqurkZOTAwDIyclBdXW10v7Q\noUPYvXs35syZMxDuAaDJU0Bv0qDMyFQPBHUWSHkIqZGGjsysdpTZVleX8QA5hftBRRpeKm6oyV9K\n1EgZdKWd9bu0HvATdE6DQi6USEPXx9wM9FTSaG3135ZukhMkaQD0SUc0o9+rp+bPn49jx471+f1P\nfvKTXj+HQiGEFAsmGhsbcd111+Gxxx5DqtPhF/2ApCTjy29sDCbSOHHC+D9lAJd2uhC9uRkYNUrt\nV1eX//wINXdgfrgSE+3XwfRXpEGVilTXPHlS/RnlNXWDw7BhwKlTdP9lX6Pei6wstY3Tmg83yXe3\n0UEQA73Ozkt/pXxGnV1Tk/F/SnSTmup8L6Id/U4ab775puN7OTk5OHbsGEaPHo2jR48iOzvb1q6j\nowPXXnstbrzxRlx99dWO7a1cubL7/yUlJSgpKfHqdjfi4ozB/fhxNWnIjqxLhOukInOIO2SI+sFx\nIynJjq7b3kQXaVCiA2rylDLoBhVpuJGnKPfCS07Gzyx26FBjG39zW06ykxDG92x3up/ZToJyLwZq\noKcQVZDylB2BOkXGcgLg915EGuXl5SgvL/f89xFdp7Fw4UKsX78e99xzD9avX29LCEIILFmyBFOm\nTMHdd9+tbM9MGkEiIwM4dkxNGuZFgJROTOl4CQnGw6/b/JAy2wqio1PIxU1+JKg8BGUQoUoy1Nk1\nVZIxJ2wBfwlbGaU6+W8+lzwhgSZt6q7ZHwN9JKQuN7JfUEQ1WEnDOqF+8MEHXf19RHMaK1aswJtv\nvokJEybgD3/4A1asWAEAOHLkCK644goAwLvvvotnnnkGb7/9NmbNmoVZs2ahrKxsQP3MyAAqK52P\nhAV65z4oOQ3KLNZNKa0uOqAuTgyysoXqv195iprTcBu1+L3/bqqP+uNeqKQ6SiLciwwU5EA/0G0B\n/uU16z2LxeqpiEYaw4cPx1tvvdXn97m5uXj11VcBABdccAG6zFuYRgAZGcDBg8Dcuc425iorp1MA\n3VaQdHT4G8ClHSXSoBKQm4eQSlTNzfY7DVMT4ZRZoHltRSgUjOzn5l7okqdeqnxU0VlamjsC9ZMI\n9yJP+Zmpe6nEam2135jUbOO0mwDVL7trDsZIwy94RTgB6ekGadhtOyEhScPveeNmO1WnsybCVXYt\nLf7JgOp/kNq1dUZMKed0eujl2go3AxI1vxOJ0lCK9ESV/SjVX5R+Qd3UM1KRhs6v9nb7EySD9j/a\nwaRBgIw0rNUqZlDWc7jteH5Lac1++SUDu2sGFcZT8iOy+svP4ExJcnvJaVAIVFeJFVQlGbXCjZLf\ncRtptLaqN/WkzMDd9jEqGVP7jpNf5gmHyk62Jw+TsstHRjuYNAjIzDSSi34jjf5IXguhtktJMXzy\nSwbma6rsqNVHlLase3oNHWo/IFGS6vKa/ZGTiUTClhId+M3vuCFQmYNTEbbbqEUVHbS3G33Db6Rh\nXlzpJsGts5M2qmMXohVMGgSMHWu8UiINFWlQDnQCeh5W1QMRF2d0+PZ2dVspKe4ijSCkAzcDDeDs\nv4CybnAAABgdSURBVHlPL6pURCFHFdFaSS+onAZldgoEK09RE+HU/A5loFR9xvZ2/SRHttXebshE\ndtVmckFke7v//IJ5caXfXAvQu8Q9FqUpgEmDBEkakyc721DkKWkD+JenAFpEkpysjzTi4w0S0hGQ\nW0kpCKIyz2KpSXWdXVubWrumyH7U6ikvCdsg5SlKTsPvBICSg5NnhHR0+G/LbOcmGtRFoFRiD+LZ\njWYwaRAwaZLx6leeMpMGRbqhkIYuIqFEGmbf/EpibhL01OjATaRBGeh1BOQmUursVG+VMtDyFLX8\n2EukEcQkp6WFPkmgkoafnIa8JqUt87HJTBoMJWbP7tkG2wmUGb0cmOVhRk5JMoo8BfQ8YDp5SueX\ntKMeNtXRYcwc7aQDqRGHw/TogDJbpOZHKETlt5TWbCc/o26lPXVG7FeesuY07GwSEw2i6+oyvkvV\nLrEUAk1K0pMB0CPP6u4rpS2KDORWXnOT06CQRiyu0QCYNAJDejpQX0+LNFQDjbSjzrZaWpxnnbKt\npibaA62zowzg5jxEEGtDKJGG26glqDUrFALysjjOrzylizTMOr4cdJ32B6P4T93UU05ggoiMqX3M\nbfWXn6Q6wDkNhgtkZBhHx9bXGwur7JCUFJxUBBgdtLbWucwRoEUQ1GtSQ29z8trvjN5MVEEMDjrS\n648KN4pfZjvKRpYqecosdekGN0oEofOf2l8pdm52ldb577Y0l5L3ADinwaQRECRp1NY6V1nJzePq\n6vzP+gGjg586pZedZFsUO9WASpUhrNKNHdxWPFHzEH63Z3FDGi0twS+apFRiATR5qqXFeW2Im3yY\nruIp6EiD0veTktyRBjXSUEXs5gjOr1QXzWDSCAgZGQZh1Ncb/3dCcrKx8ZzfWT9gdPCaGrVNWpqx\nO6pqpk69JiVvA9ClGzcPtJvB2Y88JQejri71PaPcLy/VU5RKLIBWcuv3XgwZ0rPxYRADvfmeqQZn\ntwRETYRTchq67xugy2uc02AokZEBVFQYncsuqSiRnGyc16B7ICgPTlKSsWW7Uw5F+lVba0Q3dnvv\nWK/pd82H9IsyoLa0GIOzSkaRMzc3OQ0/UldcnNGeOfdkB0pkRlmoZrYDaJFGR4fxalex5Vb20w1u\ncqJAGVB1bbmNNChtBV0mq+qHbqIuzmkwtMjIMMhAtQAQoJ3NQZ1tZWYChw6pr5mRYUQ/p07pFycG\nJR1QBlTzQ++00pvaFmWmDtCkLvM1/d4LuTahszNYeSrIkmHd4EaZKARZ1h2k1OUl0nCyiY83/skF\nhX4LT6IZTBoBITPTeHVKgkukpwNHj+pJg9LxMjONPbHkte0QH2+0UVFBIw2dJKOzAdwNupRSYLfb\noPjZh4vqv5u8k1vt3c7/+HhjltvZSYumAP+VZIBxLxobjcHS70BJiQ7cSF1U0pC71/qteAqS9KIZ\nTBoBQUoFUjpwQkYG8MUX6oGe2vGysoxIQ9WWvKbOLj3dkLE6OpwfLvOMciBm6gAtj2Ku8lENqNRr\npqbSIyVKfodSzqmT16hbqriNNCgD/cmTxrVVJeIUSUZ+l42N+rJ0Vem69Ev3jMh+odq91mxHlepU\ncirnNBiuMXKk+n1JGpR9rIKINKSdTp7KzDT8yshwHhyClqcopcBuCAjQX7OxMdhrUvI7umoaLyuv\ng1o0SSHt48dpEpYuAk1LM4pA4uKcq7qSkgz/a2rUBSWU3AdVNpN2qmgEMO5FTY26xJ2SA4p2MGkE\niLffBp55Rm0j8xCqgZ6aDMzMNPIVujyK3P5EdU3q9u9U0qBWYlHbosz6geByMnV16lX71IHSzfoX\n6b8uiqDKU0FFGseOqWXX1FSjH9bVqQd688TECaGQca3KShppNDeroxY5gOvIgBIpyajL7/cd7WDS\nCBAlJcC4cWobijwly2QbG9VHzEoy0JGGfOB1DzSFzCgD5UDnNOTgIITaTspOlIHyyy/Vq/bdrH+h\nyCjU6i9KpOEmp6EbUFNTgaoqdd+Ra5SopKGq4gOM/qyzk/dfVeLuZdGhjlxOnqQREJMGIzBkZBgP\nq04qqq01/qkGcbmRomr3XaCnk6v29qdUYkl5p6GB9kDrVoR3dBjt+ZW6EhIMvVqXO6D4Je2qqmjR\noE57p0RUspwToK9Z8St1mcuKdRKoLjoYNsyQa44dU98zSltmO10fa2w0SMPJzpx4p5YV6+x0lY9m\nMtORY7QioqRx6tQpzJ8/HxMmTMCll16K2tpaR9twOIxZs2bhyiuvHEAPg0d2tvGq2jHXPHOjkMbU\nqepr/vrXwO7dapvMTKOz6xL0nZ3Gg0ORDlTkEgrR9XJqRHLqVM+qe1VbuuggIwM4fFj9GdPTje+n\npoYWnVEqbrq61FVKblfHB1EmK4stdAM95Z7JCEL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"text": [
"<matplotlib.figure.Figure at 0x7ff8a9396250>"
]
},
{
"metadata": {},
"output_type": "display_data",
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71QTg5ptZuZqeIi+PXdf5+fI2Ku4pY1KJyEVlvN9kVkRzMxt0AwLM3cH8nvTx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\niQZBEAShzP8HR/YxNq5KazoAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7ff8a91d9a50>"
]
}
],
"prompt_number": 45
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see a more constant [average] correlation in the summer months versus the winter months, this is likely because in the winter months the weather changes more drastically causeing greating fluctuations in the temperature. Over the period of a single day however the variation is greater in the summer months when the sun would have a more significant effect on the temperature over the course of 24hours."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Q2 Emperically show that the expected value of a finite spectrum approaches the true spectrum as T goes to infinity."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**1** Consider the process $x(t) = \\int_{t-b}^t y(t) \\ \\mathrm{dt}$ where $y(t)$ is uncorrelated white noise so that $R_{yy}(\\tau)=\\delta(\\tau)$. Compute $R_{xx}(\\tau)$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$R_{XX} = E\\left[ \\int_{t-b}^{t} y(t) \\int_{t+\\tau-b}^{t+\\tau} y(t+\\tau)\\right] = \\int_{t-b}^{t} \\int_{t+\\tau-b}^{t+\\tau} E\\left[ y(t)y(t+\\tau)\\right] = \\int_{t-b}^{t} \\int_{t+\\tau-b}^{t+\\tau}R_{yy} = \\int_{t-b}^{t} \\int_{t+\\tau-b}^{t+\\tau}\\delta(\\tau) $ \n",
"\n",
"By the sifting property we get $R_{xx} = \\int_{t+\\tau - b}^{t+\\tau} (\\tau - (\\tau+\\tau -b) )\\delta(\\tau) = (b - \\tau)$\n",
"\n",
"Therefore $R_{xx} = (b - \\tau)$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**2** Show emperically that you have the right *lag auto correlation* by computing the lag correlation of a random discrete timeseries $x(t)$. Hint: have a look at `np.convolve` to do the integration. Hint 2: Make sure your time series is long enough to get a nice representation of $R_{xx}(\\tau)$. Show what happens if N is too small and what happens if it gets larger.\n",
"(Hint to do this well, I needed N to get pretty large, like 5e6, I used `N in [500, 5000, 50000, 5e6]`, but my machine has a good amount of memory. Don't *test* on the bigger values, just add them for the final product)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.stats as stats\n",
"\n",
"N1 = 500\n",
"N2 = 5000\n",
"N3 = 50000\n",
"N4 = 5000000\n",
"\n",
"b = 10\n",
"\n",
"\n",
"bArray = np.ones(b)\n",
"\n",
"y1 = np.random.randn(N1)\n",
"x1 = convolve(y1, bArray, mode = 'same')\n",
"lags1 = arange(0.,2*b)\n",
"Rxx1 = np.zeros(2*b) \n",
"for ind,tau in enumerate(lags1):\n",
" if tau==0:\n",
" Rxx1[ind]=np.mean(x1*x1)\n",
" else:\n",
" Rxx1[ind]=np.mean(x1[:-tau]*x1[tau:])\n",
" \n",
"y2 = np.random.randn(N2)\n",
"x2 = convolve(y2, bArray, mode = 'same')\n",
"lags2 = arange(0.,2*b)\n",
"Rxx2 = np.zeros(2*b) \n",
"for ind,tau in enumerate(lags2):\n",
" if tau==0:\n",
" Rxx2[ind]=np.mean(x2*x2)\n",
" else:\n",
" Rxx2[ind]=np.mean(x2[:-tau]*x2[tau:])\n",
" \n",
"y3 = np.random.randn(N3)\n",
"x3 = convolve(y3, bArray, mode = 'same')\n",
"lags3 = arange(0.,2*b)\n",
"Rxx3 = np.zeros(2*b) \n",
"for ind,tau in enumerate(lags3):\n",
" if tau==0:\n",
" Rxx3[ind]=np.mean(x3*x3)\n",
" else:\n",
" Rxx3[ind]=np.mean(x3[:-tau]*x3[tau:])\n",
" \n",
"y4 = np.random.randn(N4)\n",
"x4 = convolve(y4, bArray, mode = 'same')\n",
"lags4 = arange(0.,2*b)\n",
"Rxx4 = np.zeros(2*b) \n",
"for ind,tau in enumerate(lags4):\n",
" if tau==0:\n",
" Rxx4[ind]=np.mean(x4*x4)\n",
" else:\n",
" Rxx4[ind]=np.mean(x4[:-tau]*x4[tau:])\n",
"\n",
"fig,ax=plt.subplots(1,1)\n",
"ax.plot(lags1,Rxx1,label='N=500')\n",
"ax.plot(lags2,Rxx2,label='N=5000')\n",
"ax.plot(lags3,Rxx3,label='N=50000')\n",
"ax.plot(lags4,Rxx4,label='N=5000000')\n",
"ax.legend()\n",
"ax.set_xlabel(r'$\\tau$')\n",
"ax.set_ylabel(r'$R_{xx}$')\n",
"ax.set_title(r'Empirical Solution for $R_{xx}$')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 35,
"text": [
"<matplotlib.text.Text at 0x7fd892c5c6d0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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iI9EjLg5b//0XZpMn8ylI9+0D6tevpOgJKZ6oDLOKFcQ+YIKu/GlC27Rpg/Hj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\nn2qRHC5evIh69erB3t4eYrEY/v7+2Lt3r6rDUnt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"text": [
"<matplotlib.figure.Figure at 0x7fd892c9d290>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**3** Derive (or look up) the power spectral density, $S_{xx}(f)$ of this process:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$S_{xx}(\\omega) = \\int_{-\\infty}^{\\infty}R_{xx}(\\tau)e^{-j\\omega \\tau}d\\tau$\n",
"\n",
"This function is defines as being 0 for $\\tau<0$ and $\\tau>b$, therefore:\n",
"\n",
" $S_{xx}(\\omega) = \\int_{0}^{b}\\left(b - \\tau\\right)e^{-j\\omega\\tau}d\\tau = -\\left( jb\\omega + e^{-jb\\omega} - 1\\right)/\\omega^{2}$\n",
" \n",
" \n",
" *** Note: $\\omega = 2\\pi f \\rightarrow f = \\omega/2\\pi$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"def dft(x,dt,f): \n",
" # where x is your time series, dt is the sample rate in seconds, \n",
" # and f are the frequencies in Hz you want the Fourier Series calculated on\n",
" N = x.size\n",
" K = f.size\n",
" X = np.zeros(K)\n",
" T = N*dt\n",
" \n",
" #*** make sure that f = k/T \n",
" \n",
" for k in range(K):\n",
" for n in range(N):\n",
" X[k] = X[k] + x[n]*np.exp(-2j*pi*f[k]*n*T/N)\n",
" \n",
" \n",
" \n",
" return X # where X is your Fourier tranform\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 46
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**4** Demonstrate with finite values of $T$ that $\\lim_{T->\\infty}S_{xx}(f,T) = S_{xx}(f)$ does *not* converge to $S_{xx}(f)$. Do this by taking longer values of $T$, fitting to the same set of $f$, and graphically showing that the spectral estimate does not improve. (Do **not** use canned `fft` routines, unless you prove they work first.)\n",
"\n",
"Hints: \n",
" - When you choose your discrete values of $f$, make sure you don't choose them to be too high (i.e. if you define $\\Delta t=1 \\ \\mathrm{s}$ in your time series above, then there is no need to have frequencies greater than 1 Hz; actually no need to have them greater than 0.5 Hz, as we will see in the next lecture).\n",
" - I would recommend writing a small funtion to do the integration for the Fourier Transform so that you are not rewriting the same code. To do this, you would do something like:\n",
"\n",
"```python\n",
"def dft(x,dt,f): \n",
" # where x is your time series, dt is the sample rate in seconds, \n",
" # and f are the frequencies in Hz you want the Fourier Series calculated on\n",
" \n",
" # Your code in here\n",
" return X # where X is your Fourier tranform\n",
"```\n",
"\n",
" - Choose the length of your spectra to go up by decades (i.e. 500,5000,...)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$S_{xx}(f,T) = \\frac{1}{T}X^*(f,T)X(f,T)$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"dt = 0.0000001 #1e-7\n",
"f = np.linspace(0., 1/(2*dt),1000)\n",
"\n",
"N1 = x1.size\n",
"T1 = N1*dt\n",
"X1 = dft(x1,dt,f)\n",
"Sxx1 = X1*X1/T1\n",
"\n",
"N2 = x2.size\n",
"T2 = N2*dt\n",
"X2 = dft(x2,dt,f)\n",
"Sxx2 = X2*X2/T2\n",
"\n",
"#N3 = x3.size\n",
"#T3 = N3*dt\n",
"#X3 = dft(x3,dt,f)\n",
"#Sxx3 = X3*X3/T3\n",
"\n",
"\n",
"#print np.shape(Sxx1)\n",
"#print np.shape(f)\n",
"\n",
"\n",
"fig,ax=plt.subplots(1,1)\n",
"ax.loglog(f,Sxx1,label='N=500')\n",
"ax.loglog(f,Sxx2,label='N=5000')\n",
"#ax.loglog(f,Sxx3,label='N=50000')\n",
"ax.legend()\n",
"ax.set_xlabel(r'$f$ [Hz]')\n",
"ax.set_ylabel(r'$S_{xx}$')\n",
"ax.set_title(r'$S_{xx} for various periods')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 52,
"text": [
"<matplotlib.text.Text at 0x7fd891f80890>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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KQ6ohTTqBioYy+p5Yh+SUyc6k95NKVX0Vcfo49MSRmFaHXV7zIyoVpyeYwOav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\nhU0tTeQsDQAAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7fd89288ce10>"
]
}
],
"prompt_number": 52
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is no obvious convergence of $S_{xx}(f,T)$ to $S_{xx}(f)$ as the length increases (i.e. increase in period T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**5** Now demonstrate that the *expected value* of $E\\left[\\lim_{T->\\infty}S_{xx}(f,T)\\right]$ approaches $S_{xx}(f)$ by *averaging* a number of your moderate lengthed spectral estimates together. Comment on the form of the spectrum relative to how you made the timeseries.\n",
"\n",
"Hints:\n",
" \n",
" - Just do what you did above, but average the results of `navg` non-overlapping segments of data. \n",
" - This gets computationally expensive, I did `navg` of `1, 5, 50, 200` and got nice results. Test you code on just `navg` of `1` and `5`, and when its working add the higher numbers."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"R1 = 1\n",
"Sxx_R1 = np.zeros(R1)\n",
"for r in range(R1):\n",
" N1 = 500\n",
" b = 10\n",
" bArray = np.ones(b)\n",
" y1 = np.random.randn(N1)\n",
" x1 = convolve(y1, bArray, mode = 'same')\n",
" lags1 = arange(0.,2*b)\n",
" Rxx1 = np.zeros(2*b) \n",
" for ind,tau in enumerate(lags1):\n",
" if tau==0:\n",
" Rxx1[ind]=np.mean(x1*x1)\n",
" else:\n",
" Rxx1[ind]=np.mean(x1[:-tau]*x1[tau:])\n",
" dt = 0.0000001 #1e-7\n",
" f = np.linspace(0., 1/(2*dt),1000)\n",
" N1 = x1.size\n",
" T1 = N1*dt\n",
" X1 = dft(x1,dt,f)\n",
" Sxx_R1 = Sxx_R1 + X1*X1/T1\n",
"Sxx_R1 = Sxx_R1/R1\n",
"\n",
"\n",
"R2 = 5\n",
"Sxx_R2 = 0 #np.zeros((R2,1000))\n",
"for r in range(R2):\n",
" N1 = 500\n",
" b = 10\n",
" bArray = np.ones(b)\n",
" y1 = np.random.randn(N1)\n",
" x1 = convolve(y1, bArray, mode = 'same')\n",
" lags1 = arange(0.,2*b)\n",
" Rxx1 = np.zeros(2*b) \n",
" for ind,tau in enumerate(lags1):\n",
" if tau==0:\n",
" Rxx1[ind]=np.mean(x1*x1)\n",
" else:\n",
" Rxx1[ind]=np.mean(x1[:-tau]*x1[tau:])\n",
" dt = 0.0000001 #1e-7\n",
" f = np.linspace(0., 1/(2*dt),1000)\n",
" N1 = x1.size\n",
" T1 = N1*dt\n",
" X1 = dft(x1,dt,f)\n",
" #print r\n",
" Sxx_R2 = Sxx_R2 + X1*X1/T1\n",
"Sxx_R2 = Sxx_R2/R2\n",
"\n",
"\n",
"fig,ax=plt.subplots(1,1)\n",
"ax.loglog(f,Sxx_R1,label='R=1')\n",
"ax.loglog(f,Sxx_R2,label='R=5')\n",
"#ax.loglog(f,Sxx_R3,label='R=50')\n",
"ax.legend()\n",
"ax.set_xlabel(r'$f$ [Hz]')\n",
"ax.set_ylabel(r'$S_{xx}$')\n",
"ax.set_title(r'Averaged $S_{xx} for various repitions (R)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 68,
"text": [
"<matplotlib.text.Text at 0x7fd891073d50>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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lciQmJmLnzp01DrQMISEh6NevH958801UVVXhwoUL2LJlC6ZNmwYA6NKlC3799VcUFBQg\nOzsb69atY89NSUnBoUOHUFVVBScnJzg7O0MikfBex/Qee/XqBYVCgQ8++AAVFRXQarW4dOkSzpw5\nwx5z9uxZ7NmzBxqNBuvWrYOzszP69Olj1ra/vz9SU1MtPseYmBisXbsWqampKC0txVtvvYUpU6aY\nJXLwsWPHDtYS9/T0hEgk4j0vODgY4eHhOH36tMV7HjZsGMLDw7Fp0yZ225EjRzB69Oga+/FA02SO\nt4eYkSNHksWLF5tt37VrFwkICGBjEuHh4cTHx8ds7kVCQgLp2bMn8fLyIgEBAWTSpEmsj5zre2ZY\ntmwZ8fb2Ji1atCCvvfaakf9Zo9GQV199lfj4+JDWrVuTtWvXEplMxp5bVFREFixYQIKDg4mnpyfp\n2rUr6382PXfjxo1WA/WzZs0ioaGhxMvLi6hUKjJz5kzWN//jjz+S/v37E6VSSTw8PEhUVBTZtm2b\nzc90xYoVZOrUqUbb1q1bR7p06cI+v6ysLOLr60uOHz9OfvrpJxIcHEwKCgoIITSwGh4eTnbu3GnU\nxvTp08l//vOfGq8vFouNgtbJyclk4MCBxNPTk3Ts2JENpBNiHgy3xLFjx4hIJCILFy402r57927S\nsmVLolAoyJgxY8iLL75oFIg2/R2YbsvIyCBjxowh3t7epE2bNkZxscrKSjJ58mTi4eHBxvlCQkII\nITQpoFevXkShUBBvb28yduxYNmhvCt89ZmVlkZiYGOLv70+USiXp27evUfB94sSJZPLkyUShUJBu\n3bqRc+fOsedy/67z8vLIgAEDiFKpJN27dyeEGMdUdDodeeedd0hISAjx9fUl06dPZ+NtfM+He+60\nadOIn58fcXd3J5GRkWTv3r0Wfz8bN240mqfCd8/x8fEkMDCQ/Tvv1KlTs5+n4vCicuvWLTJnzhwy\nceJEdltpaSl59tlnybx588i3337bhL1rfvz666+kZcuWDXqNFStWkLS0NLu2+fnnn5POnTvXmKVV\nG8rLy0n37t2Ngr4CDUNsbKxDTGisDVVVVaRDhw5sJmVN7Nu3r1YTeh9UHN791apVK7MA7I8//ohJ\nkybh888/b5BJgw8TlZWV+PXXX6HRaJCZmYkVK1ZgwoQJDXrN//znPzUG9WvLxIkTERISglatWmH3\n7t31bm/Xrl0ICwuDv78/Jk2aZIceCliDPIAlZORyOZKTk22K1QDA2LFj8d133zVwr5qeJhGV2bNn\nQ6VSoVOnTkbbExIS0K5dO0RERGD16tUWz8/MzGSzWyz5dAVsgxCC2NhYeHt7o1u3bujYsSPeeeed\npu6WEe7u7lAoFGZfJ06cYI9RKpX4+eefkZOTg4kTJ9b7mpMmTUJOTg72798Pb2/vercnYB2RSGRz\nXEjAsbFfTYtaMGvWLLz44ot49tln2W1arRYLFy7EwYMHERQUhJ49e2LcuHFo37692fnBwcFIT09H\nVFRUsyz/0Ji4uLggMTGxqbthFUtJCALNh+XLlzd1FwTsRJNYKtHR0VAqlUbbEhMTER4ejrCwMMhk\nMkyZMgV79+5Ffn4+5s+fj/Pnz7PWy4QJE/DDDz/ghRdewLhx45riFgQEBAQEeGgSS4UPrksLoNbI\n6dOn4e3tjc8++8zoWFdXV2zZssVqe4IpLSAgIFA36hPjcphAfUOIAKHZbQ32tXz58gY/t6bjrO23\ntI9vu+m2mn4WnqdjP8v6XKc259X1eQp/m3U7rjGeZ31xGFEJCgoym9nNLdtQF2JjY80qwNqTQYMG\nNfi5NR1nbb+lfXzbTbfV597qyoP4PB31WdbnurU5r67PU/jbrNtxDfk8Dx8+jNjY2Br7UCOkibh9\n+zaJjIxkf1ar1aR169bk9u3bpKqqinTu3Jlcvny5zu034a01S5YvX97UXWg2CM/SvgjP077Ud+xs\nEkslJiYG/fr1Q0pKCkJCQrB161ZIpVJs2LABI0aMQIcOHTB58mTezC+BpqGp3rabI8KztC/C83Qs\nRHplanaIRCIsX74cgwYNEv7oBAQEBGrg8OHDOHz4MFasWFGv2EqzFpVmemsCAgJ1RMgKNYZvjKzv\n2OkwKcUCAgICjYHwsklpKIF1mOwvAQEBAYEHn2YtKg2dUiwgICDQXLBXSrEQUxEQEHhoEMYFA5ae\nRX2fUbO2VAQEBAQEGhdBVAQEBASamLCwMLi6ukKhUMDf3x/Tp083WtveFv78808MHjwYXl5eaNWq\nVQP1tGYEUREQEBBoYkQiEfbv34+SkhIkJSXh4sWLeO+992rVhru7O+bOnYs1a9Y0UC9tQ0gpFhAQ\nEHAgVCoVhg8fjuTk5Fqd17NnT/Ts2RMHDx5soJ7ZRrO2VITsLwGB2kEIkJXV1L14OGGC4xkZGUhI\nSEDv3r0BAO+//z6USiXvlz1XJRWyv2pAyPIQEKg927cDM2ZQcbEnajVw5AgwbJh9260tNY0L9poP\nWNvnFxYWhry8PIhEIpSWluKJJ57ADz/8ALG49u/9Bw8exLx583D79m2rxwnZX3ouX76MyZMn44UX\nXsAPP/zQ1N0REGhWnDvXMO2eOgU89pj9xcreEGKfr9oiEomwd+9eFBcX4/Dhwzh06BDOnDlj/xts\nBB44UUlISMCLL76ITz/9FNu3b2/q7ggI1Iv164G//27qXlBL4ssvgbS0hmnf1ZV+NlT7zYlHH30U\nL774IpYuXQoAWLlyJRQKBe+Xh4dHE/fWHIcQldmzZ0OlUqFTp05G2xMSEtCuXTtERESw69NPnz4d\n3333HV5//XXk5eU1RXcFBOxGQgLw6adN3Qvg2DFg3jzbBv2KCkCjqV37ajX9LC2tfd8eRl555RUk\nJibi9OnTeOutt1BSUsL7xU07JoSgsrISarUahBBUVVWhurq60fvuEKIya9YsJCQkGG3TarVYuHAh\nEhIScPnyZcTFxeHKlSvw9fXFhg0bsGrVKrRo0aKJeiwgYB9KSoAffwQqKxvvmknZSbhVcMtoG2Mt\n2TLo+/sDc+fW7pqMqOh0tTvvYaVFixaYMWMG+zJtC0eOHIGrqysef/xxpKenw8XFBSNHjmzAXvLj\nECnF0dHRSE1NNdqWmJiI8PBwhIWFAQCmTJmCvXv3wtXVFStXrkRZWRlef/31xu+sgIAVckpzcCL9\nBCa0n2DT8SUlgJMT8NtvwJNPNnDn9HyS+AmCPYIROyiW3ca475m4sEYDSDmjQ2kpIJfTr+Ji4MSJ\n2l2TERWttu79bs7wBdU/raUJO2jQIOgcQLUdQlT4yMzMREhICPtzcHAwTp8+jZYtW2Lz5s02tcFN\njxMW6xJoDD448QF2XtqJJ9s9aVNp8ZISYNYsIC6u9qLyx60/4CZ3Q5/gPrU6L6csB1piPLrn59NP\nxq1VXg5w3fVvvAF06wbMnk1/LiqqXV8FS8VxYRbnshcOKyr2qPVvj5xrAQFbKakqwddJX0NHdEgt\nTEUrpaFUhkYDdO0KLF8OTJzIOacEeOYZYODA2l1LR3R4fOfjcJW54tCMQ+ji38Xmc3NKc1Babezn\nYlzvjBuOEZVr14DOnYHJk41dY3l51Lrp0cO2awqWiuNi+sK9YsWKerXnsKISFBSE9PR09uf09HQE\nBwfXqo3Y2FjBQmkibhfcxkd/fYSdF3dCrVOz20WgLwvclwZmW4AiAB18O6B9i/bs5yMtHoGrzLVx\nO28CIQRn755FB98OVvuy5dwWDG01FAQEJ9JPGIlKVhaQng4sWQJcugQw7zulpUBICB3Ea+JizkWk\nFaVhTNsxyC3LhcJJgcdaP4YLORfQxb8Lhvx3GVY+NQ992oVZbSenLAeSconRNkZMKioAmczQn6Ii\noKoKuHoVYPJo5HIqQj172p4+K1gqjo+9LBaHFZUePXrg+vXrSE1NRWBgIOLj4xEXF1erNgRLpfG5\nmHMRq0+sxm83fsNz3Z5D0vwkeDl7AQAI6AjEnVjFbNMRHTKLM3Hl/hVczr2Mvdf2YtXxVbiRfwMB\n7gFo79sei/suxuBWgxvtXnREh33X9mH1idU4d/cc3op+C/8Z+B/eY7U6LT4+/TG+nfAtTmWcwsn0\nk5gWNY3dn54OtGsHfPstEB1NRUWjoYOzpyf9JMT65Lt91/bh4r2LGNN2DNKL0xHiEYKOvh1x6d4l\nAMCJou/w/fHuVkWFEILs0my2zxIxFReuqHh6AmVlxuclJgJPPEG/9/QEcnON9x89CnToAFjKnRFE\nxfFhXsCbhaUSExODI0eOIC8vDyEhIXjnnXcwa9YsbNiwASNGjIBWq8WcOXPQvn37pu6qQ6HRafD0\n908j0jcSXfy7oLN/Z7RWtoZY1PhJfSfunMCq46tw9u5ZvNL7FWwcvRGezp61asPbxRudVMZp5Rqd\nBrcLbuPYnWN45sdncOmFS/B2sV9pClPK1eU4knoEv9/8HftT9kPposTS/kvRrkU7DN0+FEv6LYGL\nzMXsvH3X9sHPzQ99Q/pCIpbg66Svjfanp1OLJCAAKCig20pLATd3HUQiEaRSETQaaiVYIq0oDffK\n7gEAMoozEOwRjI5+HfHFP1+AEAK1cyauZmVYvb+iqiI4SZzgLndHVkkWQjxp3LKiSg0M+AgVJ95A\nQIDBUuGKAOMiUyjMRWXgQOCll4CPP+a/ruD+enhwCFGxZIGMGjUKo0aNqnO7zd39pSM6TOs0DUk5\nSdiWtA1JB5KQX5GPKFUUOqs6U6FRdUYnVacGcSERQvDbjd+w6vgqZJVkYUm/Jfj+6e95B926IhVL\nEeETgQifCJzPPo9FBxZh6xNba9XHjOIMnL17FmezzuJ6/nXklOUgpzQHOWU5KKosgkwig1wih5PE\nCRWaCnT174oRbUYgfmI8ugV0Y111vYJ6YXvSdjzf43mz6+y6vAvzus0DAHTx74Kb+TdRXFUMDyca\n7U5PB0JDARcXOlDnFBUh9tBKlC74Ejsvrodc/gyqq62LSmphKisq6UUGSyX5XjLyKvJAJFVILUi3\n3ABoPEXlroKnkyeyS7NZUSmV3wKGvQlyZj48PLxQVgYcTj2MVUlfAtgBwCAqEgl/265W/sQES8Xx\nafbuL3vQ3N1fcokcT3V4Ck91eIrdll+Rjws5F5CUnYS/Mv7CZ2c+w9X7VxHqGcqKTGd/KjgB7gF1\nSojQ6DTYlbwL7x9/H2KRGG8MeAMTO0yEVNywf04rh65Ep02d8PuN3zEifITVYy/mXMQbf7yBM1k0\nV7Z7QHf0COyBcY+Mg8pNBZW7Cio3FbycvaDWqVGlqUK1thpucje4y91521zSbwnm7puLed3nmVmD\nZ7PO4t/R/wZAfy/dA7vjVMYpDG8zHABw5w7Qpg11b3l5AR+f/BQX7yWhxdU3sP3Cdjg5PYPyCi2q\nxEVQOit5fy9pRWkorCwEAKQXpyPYIxitla1xr+wert6/CgDIqbBuqeSU5UDlpoKLzAUFlQXs9gon\n/bwVv4vw9IxGeTlwI/s8MspvsMcwomLaNWa7LaIiWCqOS7NyfwnYD28XbwwKG4RBYYPYbWqtGlfv\nX8X57PNIyknC2lNrcT77PACwQsN8tmvRDjIJ/+tyhboCX5//GmtOrkGwRzBWD1uNkeEj7ZKpZwvu\ncndsHrMZz/38HC4uuAiFk4L3uIKKAoyPH4+FPRdi85jNCFIEWe2jTCKzyZKLDo2Gl7MX9l3bh/Ht\nxrPbi6uKkVmSiUdaPMJu6xfcDyfunEBH345YeWwl0jLWYNAgeg2lEjh4+3fEhL6OHdkDcTrjv5B7\n3sOCA4vw6+0f4OnsiYxXM9h4B0Ct0jtFd6DWqqHVaZFRnIEoVRQkYgna+7ZHwo0EoEqBIpKOLp91\nwcjwkVg1dJXRfS9YAETF3IOfmx9kEhnyK/LZfZWuelFRGURl/8mbuJxqOKa6mqYxV/soAXRjt9+9\nSz8LizUI/CgU30741iz2JVgqDw+CqDwEyCQydFJ1QidVJ0zHdADULXS39C4Vmuwk7E/Zj/eOvoc7\nRXfQrkU7as2oDHGanRd34uPTH6NnYE988+Q36B/av0nuZXib4RjcajDe+uMtfDL6E7P9OqLD9D3T\nMbbtWLza91W7XlskEmFxv8X48OSHRqJyPvs8olRRRpZa/9D+WHpwKbac3wKpWAqNuD1CQhYCABQ+\nJbiUfwZhC5mCAAAgAElEQVThbQbCy9UNoyNGY2+/13Ei80/kLsnFIxseQXpxOsK8wtj27pXdg0Ku\ngJZokV+RzwbqAaBPUB/sSv4eyOwFTchfyCx2w/ak7ZjTdQ4ifCLYNj77DOhB8tFltA8kYgluFdxC\nWmEaWnq1hNr9JiSlwdD6XoaHBw3UJ2fdBJwN1kxVFTDy25HQjNAAbq8DB1dDq9XPcRnxKs5X9sfd\n0rs4mnYUoZ6haOPdhj1XsFQeHhyiTEtDIaynYhmRSIRARSBGR4zGm9Fv4ruJ3+HqwqvIXZKLTY9v\nQt/gvkjJS8GyQ8vQdXNXJOcm48C0A9gXs6/JBIXh/4b/H368+iOO3zlutm/lsZUorCzEmscaZvW7\nCe0nILMkE2ezzrLbzmadRfeA7kbH9Q3ui/yKfKwbsQ7xE+OR1WoN/IOon0gXegQRrr2gKXeDQgFM\niZyC8rbb8ErUe3CTuyHCJwLX864btXczLxVhXmHwc/NDbnkuG6gHqIBdz0+BPLcXICtHV+Ug9A7u\njXPZ5iWHzyTnobrYB6jwxtpTa/H2n29DowGI9w243B8AuGfDxYUKSLHkJuBSAOgz9KqrgY6+HWlD\nAz4Agk+hqkqfeNB3Hc67rAMAxB6JRfgn4ew1CREslZqwx3LCsbGxkMlkRsUmTSuVWMNe66k0e1Fp\nrkH6hsJN7obewb3xXPfnsPHxjTgx+wTyXs/DN09+Y5aZ1VQoXZT4ZNQnmLNvDio1hqJZv9/4HZ/+\n/Sl2Pb3LoguvvkjFUsRExmD35d3stn+y/0G3gG5Gx/m4+iDrtSw81eEpdPLuBXI/Agfv7QQAlKoO\noL18OEpKaCbVyPCR8LvwPkYHPQsAaOvdFtfzjUVl+dpUqHOpqGSXZiOrJAtBHkEAgAGhAwAAzhWt\nIatSoaMiGl39u+LcXWNRkckAuORj+2fe+OYLJe6X30dWSRYqKnVA8El43n0CIo+7kEgAjVaLCqdU\nQCcFnEoAUFHJq+AUcfVNRmUlkJenTwvXGLsYX3uNfg4dCixZ+zfgf04QFQvYYzlhkUiEmJgYo2KT\nTJkrWxg0aJAgKg87Oh3w1lvA//7XuAUJHYEJ7ScgShWFFYdpUDGtMA0zfpqBuKfiEKgIbNBrP9nu\nSfx49Ud2vs0/d81FBTBM8MzIAFQpb2Llsfdw4s4J5Ch+R5h2BEpLqajIJXIE3loKjZr+O0b4RCAl\nL8WoreyKNNz8pyVauPji78y/4efmB2epM/77X8C5KhT+rsFw1QTBu2AkunmMRLeAbvgn+x+jNggB\n4JIPlPugPE8JANQFmpkMcbUS7sU9QIJPYpNKhPvqdIgrfYEyP3oOgMpqNXJKcwwNuuahogJIuX8T\nAFAtzTe63tq19PPPPwE81wt49jFkZhr2JycDKSlUfGpRN7HZU9flhAkhDrEwoSAqDzCVlTTjZsUK\nwM8PGD2ars+RkuL4iyHZg09GfYIt57fgZPpJTPx+Ihb3W4yBYbWsd1IHegT2QLm6HFfuX0FZdRlS\nC1MNbiEe0tOBCNkQLOy1EHP2zYFGUgzX4s6spQIYZqkDQIR3BGupqLVqrP1rLe54xqHybhhKc/zw\n243fWBH74gs6eL/b9Rv4lD6Krqlfo4UoAt0CuuFM1hmkpJbgl184nXHNg7vUG6igc33ultzF2ax/\n4HS/J1y0/uxh9zQ3QfLb0OP0cZVSkms8R8glD6cyTiMhbyMAoNLZuPIxg5OT/pv8cDzPycaOjKT1\nxNauBf7v/6w98YeD+i4nLBKJ8PPPP8PHxweRkZH47LPPmuQ+hED9A4yrK/Dvf9OvggLgjz/o+hwf\nfEAHqZEjgREjgCFDDINXc8Lf3R9rHluDwdsGY2zbsVjUd1GjXLdfPxGiF0zAj1d+xJBWQ9DBt4NV\nd1t6OtAyVIRX+ryCl3u/jPfWlKDonhjOzvyi0tanLa7nXUdZdRnGx9OEAL+0F9A94ilcvfUJLvt8\ngbcffRsAnaS4aRPw3cBBUDjTAbyqCghUBOKp9k9hyu4YVOyIw+OPK6jrySUfSidvlOZSP1RBZQFy\nSu9DpvWCk8iQSn2++nvociMAJRNXAcp0+fBx9UHZ3vdR6nMEUF3ExIQPoNQ+Ald1a5Q730KgIhBZ\nJcwi9wSACM7OQBUAlFLRGj2alvsHDIH7Oqya2yCIVtgnk5Esr91bHSEE48ePN1pO+N//pinqb7zx\nBt54440a25g0aRKef/55qFQqnDp1Ck899RS8vLwwZcqUOt1DXRFEpZmgVNJChRMnUivl8mUqMBs2\nANOm0cJ/I0fSr6go+63FXV/Ky2kZ9WPHaN+jomp3/vSo6SitLsW0qGmNktqcm0uXxu09eQJ+rHgV\nXs5e6OZv7vriwsymB+jbZIC3B1KvAe7ugK8v3c6IAQC0VrZGWlEaNv69Ec5SZ+yZvAc9PpKi8yTg\n4jVfaJQaNjGgvBwIDweOHwfc3ABnZ2rBrl0LrF3wCYZemYtzEXNx/368QVScfZBeoYUIIqjcVbhV\neAMyojAqdf+XejPwZwYwbi4gpb7VcuTBx8UHmRdnAoEKYDKtjFmINDziPhBXNbfQyquVQVTkZaio\ncIezM1AEAGo6Kfa3s5eQkukHwI+1qC1NqGxsaisG9oJZTnjIkCE4evQoxo4dizNnzqBXr142t8Gt\nONK3b1+8/PLL2L17d6OLioO8HwjYE5EI6NgRWLSIxluys4HFi6lvf+JEIDAQmDkT+O47Wm22MVGr\ngb/+At57Dxg8GFCpqPsuJ4fWliooqLkNLiKRCC/0fIGdud7QHDlC36qLLw1ARnEGfrjyA288hcud\nOwZRAegLQEEBLLq/nKROCFQEYuWxlVgWvQxSsRRlZUDr1kB5rh8AoHtgdxBCRaVVK7pio5ubQZze\negsoynfCo1gGBPyDI0foNeCaB08nb6DUH228wxHqGYrU4huQwx0yGdBCv1ieHO5ASRCgdYLUmard\nuSv5yMvwpplcFQa3C5FUolMQzfbipkHDqQiuroDcST9Qq10BeSnwQies++ddw3GSKogkhqKjDzvC\ncsIOjJBSTHFzAx5/HPjkE+D6dfpW26sXsHMnHZD69KEFDk+dsv88AkKAixfpm/OYMbTg4IIFdFBd\nsoROnDt+HNi8GRg7lq4o6MjxoD//pOueJJ2T4IlHnsDh1MPoHtjd6jlcSwWgM+oLC6mouOs9TlxR\nAagLrK1PW/QOon51RlSKc3wRqAiEv7s/qqroeSoVkJpK3aHOzrQoZGUlrTAsK20DeKbjvbMvQdRh\nD+CcD1LmDZSp8L9xV6FyUyG97CacxG6QSgGPe7RSgRP0aqdxgtxFb0K55OPuLR8qKiXGyRAhClqR\nuZWXoTIznOmiK+l++vWPiBh4i7bbwjmAbiIAXohE3jDDomYlVSXIKLZeGaC5U5flhPfu3YuCggIQ\nQpCYmIj169fjCaYKqA3YK6X4gXN/ZWRk4KWXXoJSqUTbtm1ZNeejuZdpqStt2gAvvEC/qqqo+ykh\nAXj+eWrNDBtmiMcEWkmkqqykVhDzdfeu+fe3b9OqtkOHAs8+C2zdanD5mLJmDdCvH12z/V//aph7\nry+HD9NJhCNGAMsjJuDrpK8R6Rdp9Rym7hcDY6nI5fyWCkAzzEI8QliXXlkZfQEovtwbceO+BkCt\nFFdX+jxTU4FHHqGWCjPOFBYCZcUySNEKSV6fQjTwN4BIUVnqDAAoLhJD6aLE/costBZRS4VxgckZ\nUdE6QSLXi4prHpyJNwrUAAoMExsBwNvFByKtHP7uNG4i1rhC56RfyWvMAvrpZBgAtfrUYkIA+NxA\nhc8NDNgyAMdnH8ecfXPw/eXvm8wV5QhwlxP+kQlA1UB8fDzmzJmDqqoqBAcH480338T06dNtvuZD\nW6bl4sWLeOqpp/DMM880uq+wOeLkRAP5Q4bQAH9mJnDgABWZRYuA4GAqMoC5YJSX07fkgAC6bjnz\n1bUrMGoU/T4kBAgKsr0v8fFA375UXLp2rft9JSUBGzfSqrkudqpvmZND10Xp1w8ICwMCKoZhx5M7\n4Cx1tngOIfyWSkEBFQRGVLgxFQCY32O+URtlZfQ8T1cXdPN8DICxqGRmGtxfhbQ8GIqKqMC4ydpB\n7VoFXfYAyHN7sWXttVrAy8kLalIFF7E7pFI6l6UnWYhAUTfsBQCtHGJZNeB2D/DIgJMuAFIpoNEY\nDx1ucldIKgLgJKWpXtLKALy4rAgfLQCgdgZklYCPYe5NeXU50OIqSGE7dtuJdLpGMVOa/2HCHssJ\n79y5017dqRcOISqzZ8/GL7/8Aj8/P1y8eJHdnpCQgFdeeQVarRZz587F0qVL0a9fP4wbNw5btmyp\nlQoL2EZQEF3edtYsut7H33/Tt3O5HOje3SAcAQH0jdvesfHwcOqmmzwZOHu27llrcXHAvn10cal9\n++iAXF8OH6ZroUgkVPAuJckwa9Zkq+fk59MYDPf6SiUd+D09zS0VnQ5YupRabQzV1bQNmYw++5wc\nKiRcUSGEiopEAty/T88rLKSi4q3sgOqCFsDxLyCRAOX635lGA3atG2cpdX9JpcDjok+gVoOKisaJ\nurGWqAAAbld3QCbTLzv81XH4PPMq8pz/hpvMBZLyQDhJ9KJS0hpErrdUrj4JdIoDnAvZezqbewJY\n+F/otpw0el6KpZ0Q4Olj669EwAFxiJjKrFmzkKAPEDJotVosXLgQCQkJuHz5MuLi4nDlyhVs3boV\n7733Hv744w/8YpSAL2BvpFJqNbz5JrVannmGurE6dgS8vRsug2zKFGDQIGD+/LrHVw4cAL7/HujS\nha71wRQ9rA9//kmTCwA6v+KceRUUlJRQ8WG4cYMKJfdZeXrS44qKzEWlrAz48ENqteTn00W9ysqo\nYADUMszRzz/kigpg2VLpUfU6Ai6vhlxuvKqjVmsQFVcJdX/JZFSY2JUotU7Q+Bhe9JQVvQ3l+dP7\nQ1dFi2T2CugHj39ioSPUryUuCYVWVgS45VBBuT6KzSIDgPsV1BrRze5n9PxKXS/h3n2hQNiDjEOI\nSnR0NJRKpdG2xMREhIeHIywsDDKZDFOmTGFT7j7++GMsWLAArVq1stCiwIPOunXUhbXV9qVTWO7d\nA27dogkIH38MTJoEDBgA3LxZvz5xRaVrV35R2bmTJiIwMKLCRSymYpKVZS4qTGWEoiLgn3+oS9JU\nVLL13iFGVPxoQhgbqGdEhbFUgnw8UZnvzYpGeTlYa4MVFZnBUhGLOaKicYLEJxXIoSV6pMVtIJMB\n77xDXXqMiPi6+0CaNtxQTr/SC2pJEdBlG/252g2QVrDPoFhtOc2vWkZv8H75fYvHCDguDuH+4iMz\nMxMhHEd0cHAwTp8+jaioKOzevdvKmQa4gfrmvFhXc8TVFdi1i1oZvXtT68hWDh6kgz/zRr1sGX2b\nj44Gfv/dsNZ6bcjKom4lZh5Nly7A+fPUXcWduPfrrzTDrrKSDvB8ogJQFxjXUmFiKhX6cbeggH7l\n59fOUqmqMhcVPz9D+rJIRM9TKIxFxV1m2VLRKVLxbLdBUB65gD/zaF/ffpu6Fn/WiwqNs9BlBwBA\nV+GBG+V/A0p96rHaDZAZRKVEbXCFmaIT0fTiF397EXFP1W4JcYHaY6/FuRgcVlTsMZFNyP56sOnQ\ngb6pT5pEYzvWFoHicuAA8Nhjxtuee45aMJ9+Smeg15bDh4FHHzUIiLc34ONDRaNtW7qtspIeFxgI\nXLlCrZnr1837AtAYi1RqKGFiaqkUFhpEpbTUkHrMJyrMuvBublQ0mLk+jPvL15eKCuOyJIQKHtf9\n5S53B9FbKoyoiEQA0cpRKr2DAEUARjxBXYqMwEmlgA5a9nuNBpjeeTrkEjn+e9gdBzK/B3rob7ja\nDZAaMhGqdZysBBOIXlS0OsEN1hiYvnDXN/vLIdxffAQFBSE93bA0anp6OoKDg5uwRwJNwcyZNH7x\n0ku2HU8IFZXhw833tW9vGJBrC9f1xWAaVzlyhFpBAwYAFy7QbdYsFcZyAAyiwrVUCgvp4J6fb91S\nkcmoSJnGVBhLxdeXChMTUwHoeUaWipMbm/3FuL9cXUED9aBlX1xdaUUBrqgQE0sl3Dscyx5dBm2Z\nsTsbajf2W5dC62l91c50Rj7jWhN4sHBYUenRoweuX7+O1NRUVFdXIz4+HuPGjatVG8LkxwcfkYha\nF8eO0bfkmkhOpm/hbdqY7+PGI2rLhQs0+42LaVzll1/oJNNOneiET8CyqHh5GawPwLKlAtCUZGYg\nZ7K/AM7ADyocTJmWggJqbRQUUNdZixa0bca9BdA0a66oKJwM81QYS8XNDYCWioqfmx9cXWlFBOaa\nUimg02dSMKLCoC00ySOv1t+AVoZH7thWklij09R8kI3MmWMQcJFIJHzxeIKa1XoqMTEx6NevH1JS\nUhASEoKtW7dCKpViw4YNGDFiBDp06IDJkycb1baxBWE9leaBQkFdVsuWGQ9cfDBWCp/3lPuWX1tu\n3jQXh65daTAdoBaSqagUFNAYBxNI58JYKgyWYiqAsajwWSoArZAQHEzbqa6m18zIoPuZY7iWipH7\ni4igcHYxCtRXVBhbKkpnJdsHrqgQvftLIjH8bggBtHktjW9YL06o8IZUzF98k0lHZvBxsV9q8bff\n0s8WLQjgmgvEAogF7hTeod87FbGl4x+mLy72Wk/FIWIqcXH8wbhRo0Zh1KhRdW6XERVBWB58mDph\n331HC2Ra4sABGj/ho66iUljILw49ewJnztDlBoYNo4N5p07UCrlwwSBEfAJnKip8lgrjxjIVFdPs\nLwDYsYN+3rlDP/396fU9PQ1xG5nMkKLNtVSGlm6FSwuRUaC+rEzftl4MPJ094aofLZi+yGQA9CnF\nXEtFowHEpSEwcl7p12QBEVkUlZZeLdl1ZCZ3nAyVu4r3uLpAZKVAlTutf1ZhiNVUa/VlDCT0s7IS\nOHqU333a3LFXwN4hLJWGQrBUmg8iEbB8OS1Eaak+WWUlcPIkrQ7Ah0JBs7WYGeW2cvMmrbtlKg4q\nFb3e7t00s+zxx+kxISH0Tf/UKX7XF0CFh09UGEuFcX85ORmLip8fjWvodMaiwsAIiL+/IfPL2dlw\nDVP3l0gkQquiGXB2BmupMO4vKipy2l9nL3h6Gs4F6LGeB3bj2eLLEIupYOl09D6cJE5seX4AQGZP\n+ikikHFFJY8+oOhDOlSWGiwVF5EnKtSGbLH6Ur1YAXjfoMInNpi7X21jauNQtd25k5bgeRgRVn4U\neOgYOpRmMO3axb//xAm68JOl2fMiUd2slZs3+WM0ANCuHc34WrvWkEwgEtF+7NljWVRqslQY91er\nVsaiwtQLy8/nFxVGQIKC6Dnr1xtbKlz3F2NZMOnP3EC9qfvL08mTFRNmSWCpFNAVq+BD2kMkMlgr\najVtR+nMCdZXMr8UAqmE4yA5qzcriQi59wzD0dcbApB1vww38m/wP8C6IC/Bvag3gKhv2U37f9e/\nYYioqDjKkhAPMoKoCDwwMNbKu+/yWyuWsr642FtUADoIP/ssTYFmiIqi2WCWRKVLF2rdMHBjKi4u\nBvdXmzbGogIYgvXWLJUWLahFM2CAsaUip4YHXFwMz5ARFdNAPdf9xQT0AcMcFqmUCggzEHNFRS4H\nWwcMAKChiiSV6QyWyokl8C0bzLYp0g9HbkXdgJIA7Lr5BSI+ieB/gHXBLRcYsBoY8D676WJfvQUF\nQ8JBbRkxAtiyxQ79ayY0a1ERsr+aH8OHAx4ewA8/mO9rKlHho1MnOmhbEpX+/YFXXzX8zLVUAgIM\nlkrr1tRdx80UY+7Bmqi4uBjcVHyWCuP+AvgtFTb7Sw+3aGZNosJkmjlLnSGXyIGPbwJ3+gMAPDw5\nokLEcHamJ5eUAKE3VgK/f4QOx88CxLBqV1J2Ev9DtJFHNjxCv5mu92sRHnNEb6nUdrGwPXsMJYEA\n+iyKiurY0SamWWV/NRRCTKX5IRIB//kPLROi40SCc3Jo+feaFsqzllas0xliGlzqKiqAZVExhU9U\nCgupqADGA7w1UWGsEmdO4WTuBEuZjD5DuZxfVBhLRaPRt60vrcJNQWViUoyoMBNCpVIqpIyl4ix1\npi6wgtYA6PkEBHJm6WWdBOpqg6i0KBgJ/PUabV9nGN2Xxm3HrLcTUakx1A6zlV3Ju9jgP4uIp6Dc\nI/uQXpRea1HZuJF+qtXA3ZK7gEhnUVR0OoN1eO1a7WN7DY0QUxF4aBk1ir5p79lj2MaUZqnJfWHN\nUtmzh87eN4UvnbgmOnWi5wQE2HY8N1AfEEBL2cvl1NUFmIsKs/SANUuFgUkTZiwVxs1l6v5SKmk8\nihlYXV1hVFqFwVZLxUniZOQ2A/SiIjVYKtqsKGDPNty9S5MeAP1gSwxD019nyvG1tDd2JVsIpplQ\nVERFasH+BZi8m6eKtAtP3bGRLyN0XSjE4tpVMGXE+48/gMD/CwQ6b0PLlvzHzpplqL7Qrh0t1Noc\ncYiUYgGB2sDEVpYto6swisW2ub4AOiBfvsy/7/Ztmk6q1RoG1qoqWt6Fux6KLXh60hIttsLEVBhL\nJTubBtu99aWzamupcEVFJKLtM9YJIyqmlsrs2fRnJhFCLgdweyh6wrC2y/bthgXHGAHnispff9Hz\nWUvFxXhmPSEEMiZQTyRwlkuBpGcBGFueXPdX8X1XoK3t81a6dKHPK/npz2w6HgBd7wUAEWkBSJGc\nbLne3MCBNGb1ww88gX0+wdJz9Ci1ptPS6M+OZqnYC8FSEXggefxxOojt22e9NIsp1iyVrCyahstZ\n0ge3b1NBqUsAtzZwLRXGOlEqay8qfJYKs51rqXAnKzKiIhbTL0ZQZTJAUh6AJ6SGYmnTp9NBFTAX\nlexs4Ikn6ERDmQzopOqEGZ1nGPVDR3Ss+6trFzEY7zQ3DVwshpH7i3Gd2UJBAR24U1JqPJSXYk0u\nAOtxkaNHgd9+M9nokkc/Wx61eJ6aljRj4y9qNS1A2twQREXggYQbW7l4kQ66TPzBGtwyJ6ZkZlL3\nz/Hjhm11iafUBW5MxcOD3o+XF7+oWMv+4rNUmO1MTMWS+4uBiZEw4mMpzmAqKty3dpkMCPUMNVrB\nEtCLit795eUhYV1p3PsTi8FaKt5Ovuw6LLbEVJiYGjOA15Z516ysn81BrQbm/PQc9l84Rjcs1Vf1\nbLcXAF051RTmeS9ZQj9/+om+HFni3j2g8+gzuFt8z6Y+OQqCqAg8sIwbR10mr77KXwmYj5oslQkT\naJ0xhsYWlYoKOsB7edXNUmHiJ1yRAMwtFT73FwMjIkzQXmxhlGBEhdlfWmrYZ+lNnxuol8vFrKhw\nhUskAmup9FENAfRr3VdpLVc2Zrhhp2ktNWUIarQ6bEn6Ahg3j3e/LYVASkqs7//iC+BC756Ytov/\nGo5KsxYVIaW4ecNYK4cO2V5Ww5qoZGbSZYyPHzeUM2ksUeHGVBhR8fKiVotYbC4qmZnUVce3HICz\nM7/7i2up8Lm/GGy1VJj0ZMZC4YoPXxYdoI+p6NXISSZBWJj5uRoNWEvFTeYOOBUDAH69/mujLdw1\nYYLlfSIRAJHe7BDzmEQSfvGr7SqmzPEaXR3NrloipBTbgJBS3PwZPx5YvJjW3rIFDw9qEbCLUOkh\nhFoqAwbQ72/fptubwlJxcaFWilJJB1t/f+MqAQEBNK5RXg62dAoXJyd+9xcjKHK5fS0VRlS44mOp\nlI6O6OCkd3/JZWJ8/DF9Y+eeS0WFXtRF4gY40Vf6by9+i1azlvM33IgQAkCkzyrwvmV+wGNL7Xq9\no8fVNVo19uChTSk+fvw4FixYgHnz5qF///5N3R2BJkYsBtasMS55Yg1LpVoKCuhA7OpKZ7ozcZUb\nNxo/psJ1fwF0WWUVp7aiVArExxuvHMnFFkuFiam8+SZ1W/GJSm1jKlzx4ROVvh4TMTlyMmRSsf58\nApnMeGIne67e/eUscQPkhhG1VJfH35m6klfLXHEGMecGRSY368YfAzGzkIMSgZfMrx8bSzPs2OPb\nHMS1a3XrZlPwwInKgAEDsGnTJowZMwYzZ85s6u4IPIDwiUpmJl2xEaDWyrFjdHBLTbUtAaC+8Fkq\njHXCrOxoiqU6Va6uxu4ywBBTYYSFcX+9r69Yws1u405mrI2lwj1Ox7O+1uKW32Pb+G3seRKZ4SDu\nkgZc95eLxB2Qc3JvI+P5O1NXiAXFrAn3u4bvl5ukBjpbTis2ou3PgPdNs83r1wPpYf/Fhryx7DZL\nlp8j4hCiMnv2bKhUKnQyWTw8ISEB7dq1Q0REBFavNl7YZ+fOnZg6dWpjdlOgmcAnKllZBlFhLJXM\nTLpksK3LGNcH05jKv/5F03PrwoED5tYVX/aXRkMnjJr+G3EtFW6KsSmmgXquyHEHQe46K9zzJFId\n7/FcS+Xgr+6AjOOrLLQws7C2MBaKTx1zj1+2YuG427gS3MD3eDcXFACI2gE8sp/d9iAVunQIUZk1\naxYSTHLwtFotFi5ciISEBFy+fBlxcXG4cuUKAODOnTvw9PSEm+nrmICADViyVIL0ixV26gTcvUtL\n1zeG6wswt1R696YViusCX5l+vuwvrZYO9HPmGB9bV0uFC1ckTEWJFSMJv6hwLZXkc25UVEoCEJz1\nL6DMF88/b1jAzGb+ns+/na9kixXYAd8aAedr1WZzwyFEJTo6Gkql8czbxMREhIeHIywsDDKZDFOm\nTMHevTQHfMuWLZjNTP8VEKglfHNVuJaKRAL07UtnjzeWqMhkxinF9oYbqOdaKtzqAQx1jalw4XPX\nmFoqIk5cwmgpYi0MRR/VrrT+WHYXhN6bDzgV4/PPCU6csH6/ZnGNP1bRzyobgm/KmxbjIpMmAQg4\nW3MblvDIAGJFhkXLLFFLsXMkHLZMS2ZmJkI4tTGCg4Nx+vRpALA5Q4F7nLACpACDSgWzwGdWlnFZ\njgEDaCkYOyTD2IRYTAfb0lLzILs9WLSIWjAHDhjHVKyJSk2WCp/bi4EvpsJgEBVzS6VNG7oMMptd\npfyAbSUAACAASURBVJVTS0UrgxQuQIsUYFEQKiqyLF8g7E9gpslKbTop8Ns6oNodeGKuYdA+uBIY\n9pbxsaxry3xgz8sDwLM8tDkEvJUAPNLp59Qx7KZFiwk++pBzrPd1oIXxH2hDur/steIjg8OKisgO\nT9Ee6XECzQ+Vipba4JKZaTyBMjqaDnSNZakA1EVVVNQwlkrfvvTT1P3FJyq2zlPhC9Az8FkqHh70\nk00K4FgqzPFiMY0tsasz6mSAWAdo5ZCJ9DVoFHctzoMBAAx8x/B92gCg5XEaozn9Mt32xFywgkEs\nO2uqqw3rzzCIxTAInjXcswHwVBOd249+hvzFbvq/P7/ER+BMcIxeVXP7dsT0hXvFihX1as8h3F98\nBAUFIT09nf05PT0dwcHBtWpDmPwowAdf+Xuu+wug68/LZI0rKnI5LTLYEJYK9xrceSqNZamkpxtE\nm89SYdxf7LVYUdEfrJPBTRfErkRpUVRGvQS0Omz4+aevjdth4HMvlfka/fjRR4Zaagw6eSFv5WYz\nBhgnFhUWWjlWeRtLuVNbum6tuf0GoNlPfuzRoweuX7+O1NRUVFdXIz4+HuPGjatVG8LkRwE+agrU\nA3Rg//proHPnxusX81bcEJYKw2OPAatWWXd/cS0Va9lf1kTF1FIJDjYcx87E53F/mYmKlh6scJNB\nKhEBWT0AABqNhZhD70+Mf9boH6al1GGu2MQbr/z2v/9Ra4XLuRFKoPsX/G1xERuCRBkZhjlHvBAx\nPv2UfstbuDSjd83XswPNavJjTEwM+vXrh5SUFISEhGDr1q2QSqXYsGEDRowYgQ4dOmDy5Mlo3759\nU3dVoBlgKioaDV16lzvBEKCptqZvqg2JXG5YQKuhUCjossfW3F+2Wip8hSQZrD03azEVc0uFioqO\naPT9omKig40TN1hRMb0JApx5HkjmrLdixRVWaziiUmOJe52Etex456PYs1+NgEPEVOLi4ni3jxo1\nCqNsqcxmAcZSEawVAS5eXnQ+CDMnJCeHTjBk3qCbCrmc9qcx5iTYI/vLkqXStauhvLula9MTzbO/\nLLm/qnz+gSQbbBxGi2rYNnxZeJgiAuw3WW/FZPC+lJEGoCWqqurwctFjMwCT9mMt9EUntT65sZFE\nxV4B+wdLAmuJ4P4S4EMkAvz8DNaKaTylqXByaljXFxeu+8vU5WLrPBVmu+n+Nm2sx6JsslRujAIS\n1rLuL6idqbjphSjnvolfCsDNfPPZ6ah2B8r4ShLwuM9MBu/cZ8IA1QVsrWOIo9vbC2w7kEhocoLF\n/aJGedFoVu4vAYHGhjtXxVFERS5v2CA9F3tYKtbcX9Zg3XsiK6JS5QGceoV1f0HjTPfp11Z5f42x\nqEydCkx70aS4Y7UrTUlek2u8/cQS4ARP0Uc+i8AlD8XFNd8TH+ekHEsl5KTlA7tusd7QA+b+erB6\nKyBgJ7hxFdMgfVPBuL8aAyamotFYDtTXJ/vLGj76VYH5LBUzAdO7v4jGCd98A0CuX7TFpOT8nsxP\ncKqtyfoHlgbj/30A/P2C+fZCnhIGnLTnejk9Br9teR9P/S8jwo4iNT+zHhdvXJq1qAgpxQKW4KYV\nC5aK8T5ba39ZEpWa1g1hCmQSnpiKmUBxRIX7M6Qm/qKQU+YXqs0b/t4vgXIeN5m8lL2fI0dsb84M\ndf0KyC34/Kt6nW8LzT6l2B4IMRUBSziipdJUMZWGyP6yBmOpdPA1ZHMylgp33RgKHdGJTt+JbX8C\nahdAVm4kXlIpX4ykFhWIy335tw990/Y2rMEpDslLi6tWd5dqayjrYgeEmIqAQD3gisrDaqnUd0a9\npUB9TXh5AXhHjRd7/4vdxlgq3t4mc4P07ifCeMqKg4GcKMD7BnYk/mI4TFJz4N0ia3KAa4Yy87jw\njOF7p+Jar9hoik2iO8ZCwUsGsY0p1A6AICoCDyWOKiqNGVOxxVLx9uZfXRKoe0xFIgGIVgqx2HAi\nt6CkUXtsMJ+zsUoBTHkSzyYY6mcREc+SuzobLZUyP+P2uedldzV873XbtvbqQg19rYza0HDXtjMO\nMU9FQKCxcUT3l1xuvRCjPbF1Rv2PP1puo67uLz4Y95eZVZATBQDw9haBdQBVmywVCUAn4SmdUtes\nKe55bX8x9GnCdMvnZEcB/hfqdj0AIBK6xLWsvMZDHR3BUhF4KGFEpaKCznhm/PxNSWPGVGydUW+N\nuloqfCxbRj8JMWlPP8Dnc1cRrjYvX0+kPNPW67qqI8+EyaKiGk4psWzq2uQ+I2Lcvw9g2YO/RlSz\nFhUh+0vAEsw8Fcb15Qgr6zWV+8tUPLjZX9awp6WycGFNR5i4v/ScOUM/dRLDG76HmNaml1oKBgHQ\nr/fHj4mFQwhfAoEJ+RHAexXAyUVmu9q1q+Fc/TXrG7upL0L2lw0I2V8CllAqqYVy65ZjxFOAxg3U\n2+L+stVSqW2gviZ4RYpwNnIslZ49gfv3AY3IICr3Xqd+TZEV95e3t5UOmJyn1jETLWsY9TXOhgoA\ntSX4r5qPaWAe2uwvQgiWLVuGl156Cdu3b2/q7gg8oDClWs6fd4x4CuA4kx9ttVTs6f5i4HtbXz/0\nK+AQZz13k5hKmzYGUXH6+iynTpfl4c2qVUCMbygfN+g3wadtPsciqQP5t0srm9xSsRcPnKj89NNP\nyMzMhFwur/X6KgICXFQq4Nw5x7FUnJwcY/KjrZaKPd1fDHwD67OdZgM5nDxjE1EpVucDnmm0L1qD\nKou1/BMORSIL1YDZThgPiyIiZRo0bCy3ZuqYwF2a2JIlQyQ1iopW92CkFTuEqMyePRsqlQqdOnUy\n2p6QkIB27dohIiICq1fTRW9SUlLQv39/fPjhh9i0aVNTdFegmaBSAf/84zii4uZGS9M3BhIJoFbT\nbDNHslSsXYdFzVVeQlN99SVWRDp9YbENl9Hq+O8W27QqKkz85p859Ccm4M9d3/5uN+NTzuiLR+qz\n1djr6LTAEs6aClefBDJ7mF9SJ0VlpbU+AaczrVhKDoRDiMqsWbOQkJBgtE2r1WLhwoVISEjA5cuX\nERcXhytXriA4OBhe+qiZ2N7OXIGHCpUKSElxHPfXokXAyy83zrWkUioqIpG5KDRF9hcX0/bEYuD9\n9zkbtJw69GItXT5YXz9LRPRKeL89nKr53xbEYhsslc1ngVP0l7GO6Nesl3BLw5h08r4+Gn8pBkiL\nZjerdSbzZ5KeBb742/yazkU4ccJKnx4gHGJUjo6OhtJkabTExESEh4cjLCwMMpkMU6ZMwd69ezFh\nwgT8/vvveOmll4QgvEC9UKmou8VRLBV3d/rVGEildC14vgSp2rq/7Plux+cCEovpGi0s3DpaYg3Q\nbp/hZ457yVp5GauecyLWWyImwiE1L7fPC2c1yWqtyTlWJjl+8IH1ZkWW1oZxMBx28mNmZiZCQkLY\nn4ODg3H69Gm4uLjgyy+/tKkNbiaDsFiXgCn+/vTTUSyVxkQqpYuU8YmKREIFtyaxsLel8v33tETL\n1Knm1+nbl7MhZQxnp8boWJGuZlEBahBMJugu5pmlz8CIw7lZ5mvKc4Qjs9ikujDjSiMiYP8mYKyh\nPMv161b61IDYa3EuBocVFZEd/lLtkR4n0Hxhlg8OCGjafjQFcrllURGLDRWcrVHXKsWWmDjR8nWM\nYk1qVzooi4j5wM8RFUtDSI1DCxOoLzF520iLBloeo9//tA1wyQeUtwD3bP7zAcQnx5v0T//AV+hL\nJ4ytoeZXI2D6wr1ixYp6teewohIUFIT09HT25/T09FpnewnLCQtYQ6Wig1VjBccdCbmcur88POre\nRkNkf/G1Z9Viklh2L9VUXZkXrQzI7E2/L/Mz2clRyzI/+nW/HXB9tOkVDN0hJnV3HHjBrWa/nHCP\nHj1w/fp1pKamorq6GvHx8Rg3blyt2hAmPwpYo3VroFu3mo9rjjCrL1qZdF4jDTX50dJ1eOlhvA48\n0XBSimsQFd7SPO9WA5emWDjRxsJsnDkrrZWtTRuxrQ0eTpxs2IkszWryY0xMDPr164eUlBSEhIRg\n69atkEql2LBhA0aMGIEOHTpg8uTJaN++fc2NCQjYSFgY8LBW8WHShe0hKg2dUszXPrttcKxhYyyB\nTGxwf+VbWIKEOXe0qYFRY0d0dDGvmg9kvwvzCqvlRSyz5foqu7XVkDiE+ysuLo53+6hRozBq1Kg6\ntyu4vwQE+GHWSamPqDSU+4th1ChgwQLjbQMGAKGhAP+IYRyAz8jgP4bpb61jPyIdcC8SWKGp+Vg9\ntZqw6Fxg+P6LU8C8Pka7U7UNm3Pc7N1f9kBwfwkIWIZZhKuuNPQ8lV9/BcaONd7XrRvw7bcmJ1wb\nCySsBWB8P0OHWm///9u7++CoynsP4N+kGzAqChaMkF0MJZFk25RYk9oJbAEdG1c0FIvJpu3ITURK\nmARLnSozdgqtaAktrVyjUAcJqHVJrQwriktRr/gy0+T6Qn1JuImWxb1h7sVeoLaBENns/SPZZXfd\ns3vOnmfPy+73M5OBPXvOc345A/vb511ZUAHA2j3aJ5Js9eNQ89dRBwLBJEnliT+f//uSiGa3gWuB\nN+4FDp7f2/4MIpJOGmRU8xcRaW/cOGPXVOKJW7uYtRc4M7psSuTv85XY7gw5ZUGin23Gf4xdJOcj\nc+yBXPoJtrwVsepHvJn0vvnn/37h2Pr+m8fWGntpA/BhnYz7GQuTClGWUptUNF2leIxkk9XYqK/I\na6V+t88/T1xWXbzP8dtvGAtORmd9qKYy8Sj2HN6T+NyIiZLhsk/OjCws+f0MxhB9KunCPhUiaaKS\nSuQH+csvA7NmqYsrJcEvJhWp5JQsqUQdP3YNMO3t869HZCxtr2jYcA5wajow8RPgkjidQDnaJRVR\nfSoZn1SIKL50NH9dd526mGLLiyVZU7n0E0XlyPbPaQAiksr/zJY8NeLOyu4RShwXfarsOsFCX8DV\nTn5k8xdRlho3Lvn6XoloNaQ4kmRSyT8hO5bQOmKyRn99ao85IOMGknurSFWdEu13YL7mLyYVoiyV\njuYvERKVJ7n4Z0yfiscD3HNP/FNDyURW89fLD0gHI8rfE8y/07D5S5SMbv4iIml5eamv0wWkZ5Xi\nRP7+d+DSSyXeHNtAKxSTnMU3ZCWVZMOH4xYg9UCkbmiO1YflYlIhylLjxo3u/pgqrZu/4i6rEvLP\nqbJjSXZOcbH8mOISur5XRCI6do3ActOHzV9EWcqozV9y/HvpB8Cj7wOfja0k3N0q+9rY5q8ZM6Lf\nv+Ya4MYblcVz0UVyzlLY1wJEN3+N+5eCiPST0Ull3bp1QvcJIMokRp38KKe8oovso0umhJqOxmoH\nSpriQknlb3/74nsjMteODEnfsoQRSWXyf6XrJgBGhxTrPqO+o6MDgUAAPp9PdSByvfrqq3A4HGhu\nbsbBgwcTnstlWoikmbmmcj55RN9cTiyxNZNYqfw+0dcoLOCV+xMUrF1HvSGWaRkeHsZf//pX/LfU\nym1pkJubiwkTJuDs2bOK91chovPMOKM+9t5KO7mfffb82mFtbcCf/hT/vLid+GN71ic/X2Ei+PSr\nCd403+gvVf8cpk+fjmPHjuH1119XFURTUxMKCgpQXl4eddzr9aK0tBQlJSVoa2sDMLqf/b59+7Bh\nwwasXbtW1X2JsplRm7+U3Bv/uXJ0S9/Y4xImTgTyx6aFfOUrwPe+F/+8uElF7n4qUsYSYGgba1nG\n1jQzE1VJ5corr8RNN92ESyXH+cnT2NgIr9cbdSwQCKClpQVerxc9PT1wu93o7e0NbzM8ceJEnD17\nVtV9ibJZXp4xJz8qKu/NewHPdtnXyi07/nBjMbUGRb/fyZnA/UNC7qsVVUOKu7q6MGvWLNykeLeb\naA6H4wv9Mt3d3SguLkZRUREAwOVywePx4PDhw9i/fz9OnTqF1lb5Iz6IKJpRaypymtNS3n9ehpwc\niRjk9m+cKlIfRKTAeLHlpZmqpBLqUzl9+nT4w1+UgYEB2Gy28Gur1Yquri6sWbMGixcvllVGZKcT\nF5YkimbUPpWnnwaOHUt8Tjqb3IqKgJ07gYEBoKoq8qbSzV/Rs/AfBF6/D1gzKeYs9UEHg+J/d1EL\nSYaoSiqhPpX3338fc+fOFRUTAISbudTggpJE0kTVVEQrLBz9SeXescePHEk+2iteGVOnjv5Ek1lT\nGckDhiZKvq1mFYMzw8O4cPy41AuII/YLd9oXlHz++efh9/vjvieqTyWewsLCqPv6/X6O9iISSG1S\nMaLYpKK0ASVholQ6vHfvVmXny/D5OZWDBTSQNKl8/PHH+MMf/oA33xzdH7mzsxPt7e04evQo7HY7\ncnNzsXLlSuGBVVZWor+/Hz6fD8PDw+js7EStnAV9InDyI5E0UUlFzTfvVKWrT+WHP0z0rsJf9PML\n1YQSV24a2/00m/w4adIkrFmzBnPmzMEjjzyCBx54AFdccQV27NjxhRFbqWpoaEB1dTX6+vpgs9nQ\n0dEBi8WC9vZ21NTUwG63o76+HmUKp61y8iORNLV71IfokVSkpOUz991/Gytc+heV9QxOjC4qpibG\ncWJbvqKImvyYtE/l5MmT4b/v2rULq1evxpIlS7BkyRJs3rwZNypdJCcOt9sd97jT6YTT6Uy5XO78\nSCQtE5q/Lr8cOH5cfTltbcC990q8OXAtcPUO4IjCHcjORKyA+atTwLkLUg0vTERfsxTNdn6cM2cO\nli9fjtOnT6O/vz9q5FV+fqLNZfTHjnoiaWZOKqHP1th5NqmORLvnngRJpXcxYDkDfOBSVujHN5z/\n+9nz/c5xazVHHcCVCSaRn70YGP8v5AgYQSZFs50fKysrsXnzZrS2tqKvrw8TJ05Ed3c3duzYgaCR\n6r1EpIjanR9DMqlPJa7BAuAvq+O+tWHD6J/xn0H8YL46tirL4GDkPS6Pe264IajvlqRhGoWsvJ6f\nn49rr70Wl1xyCYDRRFNRUYGJE6WHzRGRsWVCTUWPJWIiJRxdJrEu2axZo0nowsh+/NyxjW26JQY9\njZWVzuYvUVL6npKbm4uKigpUVFSIjkco9qkQSbv1VkDEfw0jNVho/Zmb+H4KggmM9cD/31UJy0pn\n85eoPpWM30+FCYUoviuuAOx2vaNITarNX5quUyZRU4mbhN+8J3H5Gmw5bIil74mI9KBpn0qEadOU\n3E9BMJ+PDXq6+H8TlmWG5i8mFSJSRc/mL2M1dwGbN8c52N6bvIzQHJiKjvjnjiWddDZ/icKkQkSm\nk2pNRW0CjL0+dL/Q8VWr4lx06koZBY99FPcvjP/+28tlxWcETCpEpIqZhhSLHO1WVSWjpvTMLnmT\nHj8dWy3kkznx3x9b/t4MzV8CRqkTEWlLakhxss/cZPNylHxmu+TMhfywXmZpOTF/xsQTyJNZjv4y\nuqbCBSWJsouWNZXIeyWrranec+ZEicoCktNsQUkz45BiovQzUvOXlLq60T/TlVTS5fyQ4lxgXXof\ndFYPKR4cHERVVRVeeOEFvUMhynpGSipSNYKZM0f/1CupmKArRBhTJpWNGzeivl5uWyURZZqqqtFt\nh5X2qYheliaVhJrwGg0mOaabIZJKU1MTCgoKUF5eHnXc6/WitLQUJSUlaGtrAwAcOHAAdrsdU6ZM\n0SNUIjIAiwVoaFB+XbKkMnu2/LKU9Kmkyow1HEOM/mpsbERraytuv/328LFAIICWlha89NJLKCws\nRFVVFWpra3Hw4EEMDg6ip6cH+fn5uOmmm0wxzI4oUxlp8qOa0V8jMnfqfe894OtfT/0DX9gsfIMy\nRFJxOBzw+XxRx7q7u1FcXIyisWVAXS4XPB4P1q9fDwDYuXMnpkyZwoRCRGHJ5q8kqqnI/SgJNZJE\nnn/bbUBBgfQ1Uon3W98C/vIX9TEZiSGSSjwDAwOw2Wzh11arFV1dXeHXS5cuTVpG5EgGrlZMlB5m\nWaW4rAyYOlXcPSLv9bOfpVbWa6+ld4tgOUStThxi2KQiogbCnR+J0s8M36ZzcoCeHvFlprLJWWmp\n2DjUiv3CrXbnR8MmlcLCQvj9/vBrv98Pq9WqqAzup0KUXn/+M7BggX73//KXgaNHgeeeA2prNZ47\nAuDmm4E33pB/7dBQkppJzOgvLRO2ZnvU66WyshL9/f3w+XyYNm0aOjs74Xa7FZXBmgpRet1wQ/Jz\n0mn/fuD0aWD69NHXWiaVnJzRPpo5Est1xTN+fPyyjECzPeq10NDQgOrqavT19cFms6GjowMWiwXt\n7e2oqamB3W5HfX09ysrK9A6ViAxk8uTzCQXQ9kNa+L2eehH4sE5wodozRE1FqgbidDrhdDpTLpfN\nX0TZRcvNu5SUKWsww0c3qrqHWhnf/CUCm7+IKF2uktpO3qQyqvmLiEgE1asBK6BkgMKFF6YvDqNh\nUiGijGGkju9Iv/vd6Ez8WMniNervk0hGJxXup0JEgP4fzpdeCsQsbSiL1n0qIroM2KdCRBlD7+Rh\nZuxTISKKoeXoLxGMtMSNKEwqRJQxjJo8sgmTChFltIceApYt0+5+SmofyZLgpk3qYtFDRvepEFF2\nifchfddd2sfx6afnl8gHUq9Bje38YSoZXVPh6C+i7GKU5q/Jk9WXcdll6stQQtTor5xgMBO7ikaX\nzs/QX42I4vj1r0c3vXI4xJUZm6SmTQMOHQIuvzx5M1fktZ2dQF2cZb0CAenl80Pla7FtcSS1n52m\nq6kcPnwYzc3NqKurw+OPP653OERkED/9qdiEAgAqlh6UJdFOlGZluqRSWlqKLVu2YNeuXdi/f7/e\n4RBRBrv+ejHlGKVZTguGSCpNTU0oKChAecyUU6/Xi9LSUpSUlKCtrS18fO/evVi4cCFcLpfWoRIR\nUQKGSCqNjY3wer1RxwKBAFpaWuD1etHT0wO3243e3l4AwC233IIXX3wRO3fu1CNcIiKSYIghxQ6H\nAz6fL+pYd3c3iouLUTQ2ps7lcsHj8eD48ePYvXs3hoaGsEDPfUyJKONxrI9yhkgq8QwMDMBms4Vf\nW61WdHV1Yd68eZg3b56sMiKHx3GzLiJS67vfBSZNAu64Q+9IxBG1OVeIYZNKjoCeLS4oSUSiPPTQ\n+YmU27bpG4tIsV+4M3ZBycLCQvj9/vBrv98Pq9WqqAxOfiQiUdR8zzXD6C9Rkx8Nm1QqKyvR398P\nn8+H4eFhdHZ2ora2VlEZoT3qiYgosfnz52dOUmloaEB1dTX6+vpgs9nQ0dEBi8WC9vZ21NTUwG63\no76+HmVlZXqHSkRZhB31yhmiT8Xtdsc97nQ64VQxpTVUU2FthYjMrro6veWL6rA3RFJJF3bUE1Gm\nmDUrveVz50ciogyycSNwzTV6R6EekwoRkQQt+1QsFuCtt6TfN8MIMiDDkwqHFBOREShJCD/6Ufri\nSCTjhxSLwCHFRGR0hw5Fv549O/q1VjWUjBpSTESUrWKTiNkxqRARGYhUPw77VIiITI6TH5VjUiEi\nkkFpTeGCC5SdH29PejNiUiEikkFNrUXEYpRmSTYZnVQ4pJiIjMAMzWhZPaTY4/Fg+fLlcLlcOHDg\ngOR5HFJMRGoYIRlMmDD6Z7pjyeohxYsWLcJjjz2GrVu3orOzU+9wiIhUk2reeu89beNQyzBJpamp\nCQUFBSgvL4867vV6UVpaipKSErS1tUW9t379erS0tGgZJhFlKb026Zo+XX0ZWjJMUmlsbITX6406\nFggE0NLSAq/Xi56eHrjdbvT29iIYDOLee++F0+lERUWFThETUbZYsQK45Ra9ozAHwyx973A44PP5\noo51d3ejuLgYRUVFAACXywWPx4OXXnoJL7/8Mj777DN89NFH+JFei+UQUVbYskXvCMzDMEklnoGB\nAdhstvBrq9WKrq4uPPzww2htbU16fWSnEzfrIiKljNBRH5Ku5i9Rm3OFGDqp5Kh8ityki4jMxm7X\n9n6xX7gzepOuwsJC+P3+8Gu/3w+r1Sr7es5TISKzCNWK5s3Tp4aUFfNUKisr0d/fD5/Ph+HhYXR2\ndqK2tlb29ZynQkRGYIaRWxk3T6WhoQHV1dXo6+uDzWZDR0cHLBYL2tvbUVNTA7vdjvr6epSVlekd\nKhFliWzoUxHNMH0qbrc77nGn0wmn05lSmaGaCmsrRKSnXMN8fZcmqsPeMEklHdhRT0RqiKqpLFyY\n/By9ayKhL+AZ3VFPRJQJLBn99T0akwoRkQS9aw9mlNFJhUOKiUgNI3XUp5uoIcUZXSljnwoRkTzs\nUyEiSjM1NZXnnxcXB2CepjgmFSKiNLj++uzqoA9hUiEiMoBM6b9hUiEiShORTVZs/iIiMjm1tQcl\n15slaSST0UmFQ4qJiOQRNaQ4JxjMlJa8aDk5OcjQX42INHL//cDPf556jcViAQKB5Nfn5AC//S2w\nenX89zduBG6+WZu9VtR+dpqupnLkyBEsW7YMt912m96hEBFp4p57tN+8K1WmSyozZszAtm3b9A6D\niIjiMERSaWpqQkFBAcrLy6OOe71elJaWoqSkBG1tbTpFR0TZii3oyhkiqTQ2NsLr9UYdCwQCaGlp\ngdfrRU9PD9xuN3p7e3WKkIiI5DBEUnE4HJg0aVLUse7ubhQXF6OoqAh5eXlwuVzweDw4ceIEVqxY\ngUOHDrH2QkSGlo01HcMuIjAwMACbzRZ+bbVa0dXVhcsuuwxbt26VVUbk8DjuAElERqZXAhK142OI\nYZNKjoCZQFylmIjUyIaaRuwX7oxdpbiwsBB+vz/82u/3w2q1KiqDkx+JSE9mmlEvavKjYZNKZWUl\n+vv74fP5MDw8jM7OTtTW1ioqY926dWzyIiKSYf78+ZmTVBoaGlBdXY2+vj7YbDZ0dHTAYrGgvb0d\nNTU1sNvtqK+vR1lZmd6hEhFRAoboU3G73XGPO51OOJ3OlMsN1VRYWyEiSkxUhz3X/iIikrBuHfCL\nX6TeYZ+bO3qt2rW/tJR1a38REZlFNn6vZVIhIiJhMjqpcEgxEZE83E8lCfapEJFaa9cCv/xliHBj\noAAABxZJREFU6s1YobkncvpUNm0CfvKT1O4jEvtUiIjIMJhUiIgkaDnLXe8Z9aIYYp4KEZER3X03\n8O1v6x2FubCmQkQkYcIE4Lrr9I7CXDI6qXD0FxGRPBz9lQRHfxGR3nJyRn9GRpKflykz6k3XpzI4\nOIiVK1di/PjxmD9/Pr7//e/rHRIRUVw9PXpHoD3TNX/t3r0bdXV1eOyxx/Dcc8/pHU7WYDOiOHyW\nYhn5eZaVjf5kE0MklaamJhQUFKC8vDzquNfrRWlpKUpKSsL70UduM/ylL31J81izlZH/45oNn6VY\nfJ7GYoik0tjYCK/XG3UsEAigpaUFXq8XPT09cLvd6O3thdVqDe8IOZKsoTLN1PxjlnttsvMSvS/1\nXrzjscf0+I9qxudp1Gep5r5Krkv1efLf5hd99FHy88zwPA2RVBwOByZNmhR1rLu7G8XFxSgqKkJe\nXh5cLhc8Hg9uvfVWPPvss1i5cqXinSBFM+OHoNTxbPmPy6Qi9jomFTHXtrYCeXnJzzPF8wwaxJEj\nR4Jf+9rXwq+feeaZ4LJly8Kvn3zyyWBLS4vs8gDwhz/84Q9/UvhRw7Cjv3JUrlkQ5HBiIiLNGaL5\nK57CwsJw3wkA+P1+WK1WHSMiIqJkDJtUKisr0d/fD5/Ph+HhYXR2dureh0JERIkZIqk0NDSguroa\nfX19sNls6OjogMViQXt7O2pqamC321FfX4+ybBvwTURkMhm7TAsREWnPEDUVLRw+fBjNzc2oq6vD\n448/rnc4pjc4OIiqqiq88MILeodieq+++iocDgeam5tx8OBBvcMxvWAwiPvuuw+rVq3CE088oXc4\npvbGG2+gubkZd955J+bMmSPrGsOO/hKttLQUW7ZswcjICFwuF+644w69QzK1jRs3or6+Xu8wMkJu\nbi4mTJiAs2fPcjCKAHv27MHAwAAmT57M56nS3LlzMXfuXHg8Hnzzm9+UdY2paypKlncBgL1792Lh\nwoVwuVxah2p4Sp7lgQMHYLfbMWXKFD1CNQUlz9PhcGDfvn3YsGED1q5dq0e4hqfkefb19WHOnDn4\nzW9+gy1btugRrqEp/dwEgKefflr+4r2qZrno7LXXXgu+8847UZMmz507F5w5c2bwyJEjweHh4eDs\n2bODPT09UdfV1tZqHarhKXmW9913X/DHP/5x8Dvf+U5w0aJFwZGRER0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"text": [
"<matplotlib.figure.Figure at 0x7fd890fd6410>"
]
}
],
"prompt_number": 68
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here as we begin to run the calculations for $S_{xx}(f,T)$ and repeat and then average the results we see that the results converge to $S_{xx}(f)$ and the number of repitions (averages) increases."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}