##// END OF EJS Templates
added spacecraft potential filtering design...
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1 {
2 "cells": [
3 {
4 "cell_type": "markdown",
5 "metadata": {
6 "slideshow": "notes"
7 },
8 "source": [
9 "# LFR electric potential low pass filter design\n",
10 "## overview\n",
11 "Initially LFR provides electrical potential trough HK packets at 1Hz frequency by decimating F3 dataflow. Then we implemented as moving average to reduce aliasing this turned out to be a poor design choice. \n",
12 "This notebook will present the LFR IIR filter design used to produce HK potential from F3 datastream."
13 ]
14 },
15 {
16 "cell_type": "code",
17 "execution_count": 51,
18 "metadata": {
19 "collapsed": true
20 },
21 "outputs": [],
22 "source": [
23 "from scipy import signal\n",
24 "import matplotlib.pyplot as plt\n",
25 "import numpy as np\n",
26 "import peakutils\n",
27 "import pandas as pds\n",
28 "plt.rcParams['figure.figsize'] = (14, 10)"
29 ]
30 },
31 {
32 "cell_type": "markdown",
33 "metadata": {},
34 "source": [
35 "## Filter comparaison\n",
36 "We will compare first three filters, **moving average** , **FIR** filter and **IIR** filter."
37 ]
38 },
39 {
40 "cell_type": "code",
41 "execution_count": 52,
42 "metadata": {},
43 "outputs": [
44 {
45 "data": {
46 "image/png": 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584+BjENQcfs/ZL/QN5wezb14belR9l3Iv+3HN0f2Bnve7Pomk9pNYmXKSsat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SHEQl488vxNy94z6o/WTXxsxHxyHkFPsOko/Ccur+CpuVX8woP7bY0uthOvwOM//OBRzC6n8VdP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\ngiAIgiAIgiC0Bf8fiHhexEslcCIAAAAASUVORK5CYII=\n",
47 "text/plain": [
48 "<matplotlib.figure.Figure at 0x7fdd1da404e0>"
49 ]
50 },
51 "metadata": {},
52 "output_type": "display_data"
53 },
54 {
55 "data": {
56 "image/png": 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FqHEIYSsSs5bKfXIDqlcjL5aODMLVwY4Bv2xh8vrjpMsyyBYpc5UglREmRDeu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D8AAAAAvED5AQAAAOAFyg8AAAAAL1B+AAAAAHjh/wOtFix8TZu2RAAAAABJ\nRU5ErkJggg==\n",
57 "text/plain": [
58 "<matplotlib.figure.Figure at 0x7fdd1d9ee080>"
59 ]
60 },
61 "metadata": {},
62 "output_type": "display_data"
63 }
64 ],
65 "source": [
66 "#FIR Filter\n",
67 "coef=signal.firls(33,(0,0.1,0.5,8),(1,1,0,0),nyq=8)\n",
68 "w, h = signal.freqz(coef,whole=False)\n",
69 "\n",
70 "#IIR Filter\n",
71 "b, a = signal.iirfilter(5, 0.07, rs=60, btype='lowpass',analog=False, ftype='cheby2')\n",
72 "w_rec, h_rec = signal.freqz(b,a,whole=False)\n",
73 "\n",
74 "#Moving average\n",
75 "w_, h_ = signal.freqz(np.ones(16)/16,whole=False)\n",
76 "\n",
77 "#plot Gain\n",
78 "plt.plot(w*8/np.pi, 20 * np.log10(abs(h)),label=\"FIR\")\n",
79 "plt.plot(w_rec*8/np.pi, 20 * np.log10(abs(h_rec)),label=\"IIR\")\n",
80 "plt.plot(w_*8/np.pi, 20 * np.log10(abs(h_)),label=\"Moving AVG\")\n",
81 "plt.vlines(0.5,-70,1)\n",
82 "plt.legend()\n",
83 "plt.ylim(-70,1)\n",
84 "plt.xlim(0,3)\n",
85 "plt.show()\n",
86 "\n",
87 "#plot phase\n",
88 "plt.plot(w*8/np.pi, np.unwrap(np.angle(h)),label=\"FIR\")\n",
89 "plt.plot(w_rec*8/np.pi, np.unwrap(np.angle(h_rec)),label=\"IIR\")\n",
90 "plt.plot(w_*8/np.pi, np.unwrap(np.angle(h_)),label=\"Moving AVG\")\n",
91 "plt.legend()\n",
92 "plt.xlim(0,3)\n",
93 "plt.show()"
94 ]
95 },
96 {
97 "cell_type": "markdown",
98 "metadata": {},
99 "source": [
100 "With no surprise, the IIR fiter gives the best results with a small amount of computation. But as is this this filter would be quite hard to implement with fixed point arithmetic due to the high dynamic in coeficients and accuracy needs.\n",
101 "We will then try to overcome this issue by transforming this filter in a cascade of 2nd order sections called **SOS**."
102 ]
103 },
104 {
105 "cell_type": "code",
106 "execution_count": 53,
107 "metadata": {},
108 "outputs": [
109 {
110 "name": "stdout",
111 "output_type": "stream",
112 "text": [
113 "[ 1. -4.69325121 8.81955512 -8.294829 3.90424534 -0.73571303]\n",
114 "[ 0.00049678 -0.00139622 0.00090303 0.00090303 -0.00139622 0.00049678]\n"
115 ]
116 }
117 ],
118 "source": [
119 "print(a)\n",
120 "print(b)"
121 ]
122 },
123 {
124 "cell_type": "markdown",
125 "metadata": {},
126 "source": [
127 "## Flat to SOS conversion"
128 ]
129 },
130 {
131 "cell_type": "code",
132 "execution_count": 67,
133 "metadata": {},
134 "outputs": [
135 {
136 "data": {
137 "image/png": 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SpyjZdOl3Ty1xOgkAAAAQ1ShBUcKXMVWS9OLipQ4nAQAAAKLbmJUgY8yvjTFrjDHvGmMe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\n",
138 "text/plain": [
139 "<matplotlib.figure.Figure at 0x7fdd1dc025c0>"
140 ]
141 },
142 "metadata": {},
143 "output_type": "display_data"
144 },
145 {
146 "name": "stdout",
147 "output_type": "stream",
148 "text": [
149 "==============================\n",
150 "Stage 0 coefs\n",
151 "[ 0.00049678 0.00049678 0. ]\n",
152 "[ 1. -0.90347831 0. ]\n",
153 "==============================\n",
154 "==============================\n",
155 "Stage 1 coefs\n",
156 "[ 1. -1.86369503 1. ]\n",
157 "[ 1. -1.8493484 0.85823409]\n",
158 "==============================\n",
159 "==============================\n",
160 "Stage 2 coefs\n",
161 "[ 1. -1.94681606 1. ]\n",
162 "[ 1. -1.94042451 0.94882247]\n",
163 "==============================\n"
164 ]
165 }
166 ],
167 "source": [
168 "sos=signal.iirfilter(5, 0.07, rs=60, btype='lowpass',analog=False, ftype='cheby2',output='sos')\n",
169 "b, a = signal.iirfilter(5, 0.07, rs=60, btype='lowpass',analog=False, ftype='cheby2')\n",
170 "\n",
171 "w_sos, h_sos = signal.sosfreqz(sos)\n",
172 "w, h = signal.freqz(b,a)\n",
173 "\n",
174 "plt.plot(w*8/np.pi, 20 * np.log10(abs(h)),marker='+',label=\"FLAT\")\n",
175 "plt.plot(w_sos*8/np.pi, 20 * np.log10(abs(h_sos)),label=\"SOS\")\n",
176 "plt.legend()\n",
177 "plt.show()\n",
178 "\n",
179 "for stage,i in zip(sos,range(len(sos))):\n",
180 " print(\"==============================\")\n",
181 " print(\"Stage {} coefs\".format(i))\n",
182 " print(stage[:3])\n",
183 " print(stage[3:])\n",
184 " print(\"==============================\")\n"
185 ]
186 },
187 {
188 "cell_type": "markdown",
189 "metadata": {},
190 "source": [
191 "As we can see the two filters have the same transfer function but the SOS version has also a limited dynamic among each stage.\n",
192 "We should aslo check if the gain is 0dB for each cell"
193 ]
194 },
195 {
196 "cell_type": "code",
197 "execution_count": 68,
198 "metadata": {},
199 "outputs": [
200 {
201 "name": "stdout",
202 "output_type": "stream",
203 "text": [
204 "97.1464739838\n"
205 ]
206 },
207 {
208 "data": {
209 "image/png": 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S4jw6ZXCGphRnaWpRpgZksCU3ACC42B0OANAr4mLcmlIcGP3R+YGNFt7bsl+LNgdGil5b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\nzJSUAAAAAElFTkSuQmCC\n",
210 "text/plain": [
211 "<matplotlib.figure.Figure at 0x7fdd1a0ae898>"
212 ]
213 },
214 "metadata": {},
215 "output_type": "display_data"
216 },
217 {
218 "name": "stdout",
219 "output_type": "stream",
220 "text": [
221 "0.0651897732092\n"
222 ]
223 },
224 {
225 "data": {
226 "image/png": 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0LKuyoKAgEnEAIKkZY3TuvBI9f9NJumZpue5buUen/+JlvbTlsL8NAwCQsCKxGpuRdIek\nTZZl/eKgQ49Lunpg+2pJj432WgCAofN53brlvNl6/MbjlZ3m1jV3vq3vP7pe3X1Bu6MBADAmIjGy\nc5ykz0o61RizduDHOZJ+Iul0Y8xWScsG3gMAxtic8Vl6/Mbj9YXjK/TXlXv0id+8pjV7Wu2OBQBA\n1PFQUQBIIm9sb9I3H3hH9R29+sopU/TVU6fwMFIAQFwZ04eKAgDix9LJ+Xr6Gyfq/Pkl+s3zW3Xx\n79/QtoZOu2MBABAVlB0ASDKZXrd+8an5uu3KhdrT0q1z//tVPVhVbXcsAAAijrIDAEnqnLnjtPzr\nJ2phWY7+7aF1+s7D6+QPhOyOBQBAxFB2ACCJFWZ6dc/nF+srp0zW/W9X6+Lfv6E9zd12xwIAICIo\nOwCQ5JwOo387c4b+dFWlqgemtT2/qd7uWAAAjBplBwAgSVo2q0hPfPUETchN0+fvqtLPntmsUDh2\nVuwEAGC4KDsAgAPK8tL08A1LdfmiCfrdi9v12TtWqrWrz+5YAACMCGUHAHAIr9upn1w8Tz+9ZJ6q\ndrXqwtte145GlqcGAMQfyg4A4LA+VTlBf7tusTr8QV142xt6Y3uT3ZEAABgWyg4A4CMdPTFXj37l\nOBX6PLrqjrf097f32B0JAIAho+wAAD7WhNw0PfzlpVo6JV/ffni9bn1yEwsXAADiAmUHAHBEmV63\n/nx1pa5aMlH/88oOfeneVeruC9odCwCAj0XZAQAMicvp0L+fP0c/PG+Wnt9Ur8tvf1MtrNQGAIhh\nlB0AwLBcc1yF/nhVpbbUdeiSP7yh2rYeuyMBAHBYlB0AwLCdNrNI935hsRo7enXxbW9oa32H3ZEA\nAPgQyg4AYEQWlefqgeuXKGRZuvR/Vmj1nla7IwEAcAjKDgBgxGaOy9TDX1qqrFS3rvzjSr20pcHu\nSAAAHEDZAQCMSllemh780hJV5KfrC3dV6bG1tXZHAgBAEmUHABABhT6v7r/+WC2cmKOv/32tHlpV\nY3ckAAAoOwCAyMj0unXX547RcZPz9W8PvaMH3q62OxIAIMlRdgAAEZOa4tSfrq7UCVML9K2H1+m+\nlXvsjgQASGKUHQBARHndTt3+2aN1yvQCffeR9bpnxS67IwEAkhRlBwAQcV63U3/47NFaNrNIP3hs\no+58fafdkQAASYiyAwCICo/LqduuXKgzZxfp//7zXd3xGoUHADC2KDsAgKhJcTn0208v1NlzivWj\nJ97lHh4AwJii7AAAosrtdOjXly/QqTMK9b1H1+uRNSxLDQAYG5QdAEDUpbgcuu3KhVoyKU83PfCO\nnlq/z+5IAIAkQNkBAIwJr9upP15VqQVlOfqX+9foxc0NdkcCACQ4yg4AYMyke1y683OLNL3Yp+vv\nXaU3tjXZHQkAkMAoOwCAMZXpdevuaxerPC9NX7i7Smv2tNodCQCQoCg7AIAxl5ueonu/sFj5GR5d\n+5e3tb2x0+5IAIAERNkBANii0OfV3dceI6fD6Ko73lJ9u9/uSACABEPZAQDYpjw/XXdec4zauvt0\n9Z/f0v6egN2RAAAJhLIDALDV3NIs/c9nK7W9sVNfvLtK/kDI7kgAgARB2QEA2O74qfn6xafm6+1d\nLfra/WsUClt2RwIAJADKDgAgJpx3VIluOXeWntlYrx8+vlGWReEBAIyOy+4AAAAMuua4Cu3b79f/\nvLJDE/PS9IUTJtkdCQAQxyg7AICY8u2zZmhPS7d+/OQmTchN05mzi+2OBACIU0xjAwDEFIfD6JeX\nzddRpdn62v1r9E51m92RAABxirIDAIg5XrdTf7q6UvkZHn3+rirVtHbbHQkAEIcoOwCAmJSf4dFf\nPrdIfcGQrv3L22r38wweAMDwUHYAADFrSqFPf/js0drZ1KUb71ujYChsdyQAQByh7AAAYtrSyfn6\n0flz9Mp7jbr1qc12xwEAxBFWYwMAxLzLjynT5roO3fHaTk0v8ulTiybYHQkAEAcY2QEAxIXvf2Km\njp+Sr+89ul5Vu1rsjgMAiAOUHQBAXHA5HfrtpxdofHaqvnTvKtW29dgdCQAQ4yg7AIC4kZ2Woj9d\nvUi9gbC+eFeVuvuCdkcCAMQwyg4AIK5MKczQbz69QJvr2vXth9fLsiy7IwEAYhRlBwAQd06ZXqhv\nnjld/3xnr+54bafdcQAAMYqyAwCISzecNFlnzi7SrU9t1ortzXbHAQDEIMoOACAuGWP0X5cepfK8\nNN1432rtZcECAMAHUHYAAHHL53Xrfz5bqd5gWDfcu0r+QMjuSACAGELZAQDEtSmFGfqvS4/SOzX7\n9cPHN9odBwAQQyg7AIC4d9acYn355Mm6/+1qPVhVbXccAECMoOwAABLCTWdM15JJefrBYxu0ua7d\n7jgAgBhA2QEAJASnw+jXV8yXz+vWl/+6Wp29PHAUAJIdZQcAkDAKfV795vIF2tXUpZv/wQNHASDZ\nUXYAAAllyeQ83XRG/wNH731zt91xAAA2ouwAABLODSdN1inTC/SjJzZpXU2b3XEAADah7AAAEo7D\nYfSLT81Xgc+jG+9bow5/wO5IAAAbUHYAAAkpJz1Fv758vmrbevS9RzZw/w4AJCHKDgAgYVWW5+ob\ny6bq8Xf26sFVNXbHAQCMMcoOACCh3XDyFC2ZlKdbHtuobQ0ddscBAIwhyg4AIKE5HUa/uny+UlOc\nuvG+NfIHQnZHAgCMEcoOACDhFWV69fNLj9Lmug79x5Ob7I4DABgjlB0AQFI4ZUahPn98he5esVsv\nbK63Ow4AYAxQdgAASeNbZ03XjGKfvvXQOjV19todBwAQZZQdAEDS8Lic+s0VC9TuD+pbD61jOWoA\nSHCUHQBAUplW5NPNZ8/QC5sbdO+bu+2OAwCIIsoOACDpXLO0XCdNK9D/+99NLEcNAAmMsgMASDrG\nGP3s0nlK97j0tfvXKhAK2x0JABAFlB0AQFIq9Hl160VztXFvu377wja74wAAooCyAwBIWmfOLtaF\nC8brdy9u04ba/XbHAQBEGGUHAJDUfnjebOWmp+ibD76j3mDI7jgAgAii7AAAklpWmls/uXiuNtd1\n6DfPb7U7DgAggiJSdowxfzbGNBhjNhy0L9cY86wxZuvAa04krgUAQKSdOqNIlx5dqt+/tF3vVLfZ\nHQcAECGRGtn5i6SzPrDvO5KetyxrqqTnB94DABCTfnDeLBVlenXTg+/IH2A6GwAkgoiUHcuyXpHU\n8oHd50u6a2D7LkkXROJaAABEQ6bXrf+8eJ62NXTql8++Z3ccAEAERPOenSLLsvYNbNdJKjrch4wx\n1xljqowxVY2NjVGMAwDAxztxWoE+vbhMt7+6Q6t2f/Dv8AAA8WZMFiiwLMuSZH3Esdsty6q0LKuy\noKBgLOIAAPCRvnvOTI3PTtU3H1ynnj6mswFAPItm2ak3xoyTpIHXhiheCwCAiMjwuPTTS+ZpZ1OX\nfvrMZrvjAABGIZpl53FJVw9sXy3psSheCwCAiFk6OV9XL5moO1/fpTd3NNsdBwAwQpFaevpvklZI\nmm6MqTHGfF7STySdbozZKmnZwHsAAOLCt8+eoYl5afr2w+tYnQ0A4lSkVmO7wrKscZZluS3LKrUs\n6w7LspotyzrNsqyplmUtsyyLOz0BAHEjLcWlWy+aq93N3TxsFADi1JgsUAAAQDxaOjlflxxdqttf\n2aHNde12xwEADBNlBwCAj/G9c2YqM9Wt7zy8XqHwYRcWBQDEKMoOAAAfIyc9RT84d6bWVrfpryt3\n2x0HADAMlB0AAI7ggvnjdcLUfP306S2q2++3Ow4AYIgoOwAAHIExRv/vgjkKhMK65fENdscBAAwR\nZQcAgCGYmJeury2bqmc21uuZjXV2xwEADAFlBwCAIfriCZM0o9inWx7bqA5/wO44AIAjoOwAADBE\nbqdDt140V/Udfv18+Xt2xwEAHAFlBwCAYVhQlqOrjp2ou1bs0po9rXbHAQB8DMoOAADD9M0zp6vI\n59XN/1ivQChsdxwAwEeg7AAAMEw+r1s//ORsba7r0N0rePYOAMQqyg4AACNw5uwinTitQL969j01\ndvTaHQcAcBiUHQAARsAYo1vOmyV/MKSfPr3Z7jgAgMOg7AAAMEKTCzJ07XEVenBVjVazWAEAxBzK\nDgAAo/DV06aq0OfRDx/fqHDYsjsOAOAglB0AAEYhw+PSd8+ZqXU1+/VAVbXdcQAAB6HsAAAwSufP\nL9Gi8hz99Jkt2t8dsDsOAGAAZQcAgFEyxuiHn5yttu4+/eLZLXbHAQAMoOwAABABs0uydOXiibrn\nzd3atK/d7jgAAFF2AACImJvOmKasVLdueXyjLIvFCgDAbpQdAAAiJDstRd88c7re2tmix9/Za3cc\nAEh6lB0AACLo8kVlmjM+U//x5CZ19wXtjgMASY2yAwBABDkdRrecN1v17b3606s77Y4DAEmNsgMA\nQIQtKs/VWbOL9YeXt6uhw293HABIWpQdAACi4Ntnz1BfMKxfPbfV7igAkLQoOwAAREFFfro+c+xE\n3f/WHm2t77A7DgAkJcoOAABR8i+nTVV6iks/eWqz3VEAIClRdgAAiJLc9BR9+ZQpen5zg97Y3mR3\nHABIOpQdAACi6HPHlasky6v/eHKTwmEeNAoAY4myAwBAFHndTv3bWdO1obadB40CwBij7AAAEGXn\nHzVec8Zn6mfPbJE/ELI7DgAkDcoOAABR5nAYfffsmapt69Ff3thldxwASBqUHQAAxsDSKfk6dUah\nfvfCNrV09dkdBwCSAmUHAIAxcvPZM9TVF9RvX9hmdxQASAqUHQAAxsjUIp8uXliqe1fu1r79PXbH\nAYCER9kBAGAM/ctpU2VZln73IqM7ABBtlB0AAMbQhNw0XbZogv7+drWqW7rtjgMACY2yAwDAGLvx\nlKkyxug3z2+1OwoAJDTKDgAAY6w4y6vPLJ6of6yp1Y7GTrvjAEDCouwAAGCDG06erBSnQ79mdAcA\nooayAwCADQp8Hl1zXLkef2evttR12B0HABISZQcAAJtcf+IkZaS49Mtn37M7CgAkJMoOAAA2yU5L\n0bXHV+jpjXXaULvf7jgAkHAoOwAA2OjzJ1QoK9WtXzC6AwARR9kBAMBGmV63rj9pkl7Y3KBVu1vt\njgMACYWyAwCAza5ZWq78jBT96jlGdwAgkig7AADYLC3FpS+cMEmvbm3Supo2u+MAQMKg7AAAEAOu\nXFymTK9Lt7243e4oAJAwKDsAAMQAn9eta5aW6+mNddpaz3N3ACASKDsAAMSIa46rUKrbqd+/zOgO\nAEQCZQcAgBiRm56iTy8u02Nr96q6pdvuOAAQ9yg7AADEkC+eMEkOI93+yg67owBA3KPsAAAQQ4qz\nvLrk6FL9vapaDR1+u+MAQFyj7AAAEGOuP3GygqGw7nhtp91RACCuUXYAAIgx5fnpOndeie5dsVv7\nuwN2xwGAuEXZAQAgBt1w8mR19YV014pddkcBgLhF2QEAIAbNHJepZTMLdefrO9XdF7Q7DgDEJcoO\nAAAx6sunTFFrd0B/e6va7igAEJcoOwAAxKiFZTk6piJXf35tp4KhsN1xACDuUHYAAIhhXzxhkmrb\nevT0xjq7owBA3KHsAAAQw06bUaiK/HT98dWdsizL7jgAEFcoOwAAxDCHw+ja4yv0TnWbqna32h0H\nAOIKZQcAgBh3ycJSZae59adXd9gdBQDiCmUHAIAYl5ri1GcWT9Tyd+u1q6nL7jgAEDcoOwAAxIGr\nlkyUy2F4yCgADANlBwCAOFCY6dUn5o7Tg1U16uzlIaMAMBSUHQAA4sTVS8vV2RvUw6tq7I4CAHGB\nsgMAQJxYUJajoyZk664VuxQOsww1ABwJZQcAgDjyuaXl2tHYpVe3NdkdBQBiHmUHAIA4cs7cccrP\n8Ogvr++0OwoAxDzKDgAAcSTF5dCVi8v04pZG7W5mGWoA+DiUHQAA4swVx5TJ6TC6b+Ueu6MAQEyj\n7AAAEGeKs7w6fWaRHqiqlj8QsjsOAMQsl90BAADA8F15bJme3linpzfU6YIF4+2OAyBOhMOWgmFL\nobClkGXJsixZkixL/duWZEkKH9ju3+FxOZWV5rY7/rBFvewYY86S9GtJTkl/sizrJ9G+JgAAie64\nyfkqz0vwtCMPAAAgAElEQVTTvW/upuwAMciyLPUGw+ruC6m7L6ievtDAdkj+YEi9gbB6gyH1BcPq\nC4XVGzj4NfSB9+9/tnfgRzAUVihsKRDqLy7BcHjg1VIwNFhowgfeD35mpKvWXzC/RL+6fEFkf5HG\nQFTLjjHGKel3kk6XVCPpbWPM45ZlvRvN6wIAkOgcDqMrF0/Uj5/cpM117ZpRnGl3JCDuBUNhdfiD\n6vAH1e4PDGwH1NkbPLDdfyyort6guvtC6gkMvB5UZnr6guoJhEZcLFwOI4/LoRSXQx6Xc+DVcchr\nuscll8PI6XD0vzqN3B9473IYuRwOuZxGTocZ+Lw58D2nQzIyMkYyxshIMkZymIF96t/hMFJFXnoE\nf6XHTrRHdo6RtM2yrB2SZIy5X9L5kig7AACM0iVHl+pny7for2/u0Y8umGN3HCBmBEJhtXUH1Nbd\np9bugFq6+g5st3X3qaXr/e3W7r4DBadnCPfAeVwO+bxuZXicSk1xKS3FqQyPSwUZHqWlvL+vf9up\nNLdTaSmu/u2BfV63U56BIuM5pMj0Fxunw4zBr1JyiHbZGS+p+qD3NZIWR/maAAAkhZz0FH1i7jg9\nuqZW3z1nplJTnHZHAqImFLbU0tWnxo5eNXT41djRq8bO3v7Xjl41dPSqaWBfhz/4kedJcTmUm5ai\nnPQU5aS5Nb3Yp0yvWz6vS76DXjM8LmUesq9/O8XF+l7xxPYFCowx10m6TpLKyspsTgMAQHy5bNEE\nPbKmVk9t2KeLFpbaHQcYkXDYUlNXr/a2+bW3rWfgR//2vv092rvfr+bO3sNOC8vwuFTg86ggw6OZ\n4zJ1QkZ/kclNT1F2Wn+hyTmo3KS6nTKGkZNkEe2yUytpwkHvSwf2HWBZ1u2SbpekysrKEc5sBAAg\nOS2uyFV5Xpruf7uasoOY1uEPaHdzt/a0dGtXc5d2N3Vrd0uX9rb5tW9/jwKhQ/8YmJbiVEl2qsZl\neTWjOFOFmZ4DpaYw06OCDK/yfSlKS7H97+4Rw6L9b8fbkqYaYyrUX3Iul/TpKF8TAICkYYzRpxZN\n0E+f3qIdjZ2aVJBhdyQksUAorN3NXdpa36mtDZ3a1dTVX2yau9Xc1XfIZ/MzPCrLTdX8Cdk6Z+44\nlWR7VZKVqpLsVJVke5WV6mYEBqMW1bJjWVbQGHOjpGfUv/T0ny3L2hjNawIAkGwuWViqny9/Tw9U\n1eg7Z8+wOw6SQCAU1vbGzgOlZltDh7bWd2pnU5eCA3PNjJFKslJVlpumM2YXqSw3XeV5aZqYl66y\nvDRleBiRQfRF/d8yy7KelPRktK8DAECyKsz06pTphXp4dY2+ecY0uZzcQI3I8QdC2lzXoQ21+7Vx\nb7s27t2vzXUd6guGJUkOI03MS9eUwgydPqtI04p8mlKYockFGSyaAdtRqQEASACXLZqg5zbV68Ut\njTp9VpHdcRCnwmFLWxs6tXpPq1btbtW6mjZtb+xSaGC0JivVrdklmbpmablmjcvU9GKfKvLT5XVT\nahCbKDsAACSAU6YXKD/Do4dX1VB2MGTt/oDW7mnTqt2tWr2nVWv3tKmjt3/Z5tz0FB1VmqUzZxdr\ndkmWZpdkqjQnlftoEFcoOwAAJACX06Hz55fo7hW71Nbdp+y0FLsjIQb19IVUtbtFb2xv1hvbm7W+\npk1hq38q2rQinz45v0QLy3K0cGKOyvPSKDaIe5QdAAASxEULx+uO13bqn+/s1WeXlNsdBzEgHLa0\nYe9+vbSlUa9va9KaPW3qC4XlchgtKMvWjadM0TEVeTpqQpZ8XrfdcYGIo+wAAJAgZpdkaUaxTw+v\nrqXsJLEOf0CvbW3SC5sb9OKWRjV19soYaU5Jlj53XLmWTM7TovJcpbMaGpIA/5YDAJBALl5Yqh8/\nuUnbGzs1mWfuJI3mzl49s7FeT23Ypzd3NCsQspTpdenEaQU6dUahTppWoLwMj90xgTFH2QEAIIGc\nP79Etz61Sf9YXaN/O5Nn7iSywYLz5Pp9WrGjWaGwpfK8NF17fIVOnV6ooyfmsAw5kh5lBwCABFKY\n6dWJ0wr0yOpa3XT6dDkc3GCeSPyBkJa/W6+HVtXo9W1NCoUtVeSn60snTdI5c8dp1rhMFhUADkLZ\nAQAgwVwwf7y+/ve1qtrdqmMqcu2Og1GyLEvravbrwVXVenztXrX7gxqfnarrT5ykc+eVaOY4HwUH\n+AiUHQAAEszps4rkdTv0+Du1lJ041tUb1D/W1OreFbu1pb5DHpdDZ88p1qWVE7RkUh6jdsAQUHYA\nAEgw6R6Xls0s0pPr63TLebPl5r6NuLKzqUt3r9ilh6pq1NEb1NzxWfqPC+fq3KPGKZPloYFhoewA\nAJCAPnlUiZ5Yt0+vb2vSydML7Y6DIXh7V4t+/9J2vbC5QW6n0SfmjtNVS8u1YEI209SAEaLsAACQ\ngE6aXqBMr0uPv7OXshPDLMvSy+816rYXt+utXS3KTU/RN5ZN0xWLJ6jQ57U7HhD3KDsAACQgj8up\ns+YU68n1dfIHQvK6nXZHwkEsy9IzG+v13y9s1ca97SrJ8uqW82bp8kVlSk3hnxUQKZQdAAAS1Pnz\nx+uBqhq9uLlBZ88dZ3ccDHhjW5P+85kteqe6TRX56frpJfN0wfzxSnFxbxUQaZQdAAAS1LGT8pSf\nkaL/Xb+PshMDNtTu138+vVmvbm1SSZZXP71kni5aMJ4HfwJRRNkBACBBOR1GZ8wu1qNrapnKZqPm\nzl791/Ituv/tamWnuvX9T8zUZ46dyD8PYAxQdgAASGDnzBmn+1bu0SvvNeqM2cV2x0kqwVBY9765\nW7949j1194V07XEV+tqyqSwfDYwhyg4AAAls8aRcZae59dSGOsrOGFpX06ZvPbROm+s6dPyUfN1y\n3ixNLfLZHQtIOpQdAAASmNvp0BmzivTU+jr1BkPyuJg6FU3+QEi/em6rbn9luwp8Hv3hMwt15uxi\nnpMD2IQ74gAASHBnzx2njt6gXt/WZHeUhLZqd4vO+c2r+sPL23Xp0RO0/Bsn6aw54yg6gI0Y2QEA\nIMEdNzlfPq9LT62v06kziuyOk3ACobB++ex7+v3L21WSlap7Pn+MTphaYHcsAKLsAACQ8FJcDp0+\ns0jL363XraEwSx1HUHVLt/7l/jVas6dNl1VO0A/Om6UMD3+8AmIFv9sBAJAETp9VpP09AVXtbrU7\nSsJ4av0+nfObV7WtvlP/fcUC/ecl8yg6QIzhv0gAAJLAidMKlOJ06Nl363XspDy748S1UNjSz5dv\n0W0vbddRE7L12ysWaEJumt2xABwGIzsAACSBdI9LS6fk6blN9bIsy+44cWt/T0Cfv+tt3fbSdl1x\nTJkeuP5Yig4Qwyg7AAAkidNnFWl3c7e2NnTaHSUu7Wjs1AW/e12vb2vSjy+co1svmstS3kCMo+wA\nAJAkls3sX4nt2XfrbU4Sf9bsadUlf1ih9p6A7vvisbpy8US7IwEYAsoOAABJoijTq6NKs/TcJsrO\ncDy/qV5X/PFNZXhceviGpVpUnmt3JABDRNkBACCJLJtZpLXVbWro8NsdJS488Ha1rrtnlaYW+vTw\nDUtVnp9udyQAw0DZAQAgiSybVSTLkl7a3Gh3lJh3z5u79a2H12np5Dzdf92xKvB57I4EYJgoOwAA\nJJEZxT4VZ3r10nsNdkeJafe8uVs/eHSDTptRqD9dXal0np8DxCXKDgAAScQYo5OmFejVrU0KhsJ2\nx4lJg0Vn2cxC3faZhay4BsQxyg4AAEnm5OkF6vAHtXpPm91RYs59K/ccKDq/u5KiA8Q7yg4AAEnm\nuKn5cjmMXtrCVLaDPbl+n7736HqdMr2AogMkCMoOAABJJtPr1sKJOXppC4sUDFqxvVlfv3+tFpbl\n6LYrj6boAAmCsgMAQBI6eXqB3t3XroZ2lqDeUteh6+6u0sS8NN1xdaVSUyg6QKKg7AAAkIROnlYo\nSXrpveQe3Wnu7NXn73pb3hSn7rr2GGWnpdgdCUAEUXYAAEhCM8f5VJTp0ctJXHb6gmHd8NfVauzo\n1R+vqlRJdqrdkQBEGGUHAIAkZIzRcVPytWJ7s8Jhy+44trjl8Q16a2eLfnrJPM2fkG13HABRQNkB\nACBJHTc5Xy1dfdpc12F3lDH30Koa/e2tan355Mk6f/54u+MAiBLKDgAASeq4KfmSpNe3NdmcZGxt\nqevQ9x9dryWT8nTTGdPtjgMgiig7AAAkqeIsryYXpOv17clTdrp6g7rhr6uU4XHr11fMl9Nh7I4E\nIIooOwAAJLHjpuTrrZ0t6guG7Y4yJn74+EbtaurSb66Yr0Kf1+44AKKMsgMAQBJbOjlf3X0hra1u\nsztK1C3fWKcHV9XoyydP0dLJ+XbHATAGKDsAACSxJZPy5DCJf99OU2evbv7Hes0al6l/OW2q3XEA\njBHKDgAASSwrza2547MSuuxYlqXvPbJeHf6gfnnZfKW4+OMPkCz4rx0AgCS3dEq+1la3qbsvaHeU\nqHhi3T49s7FeN50xTdOLfXbHATCGKDsAACS5YypyFQxbWrsn8e7bafcH9O9PvKu547P0hRMm2R0H\nwBij7AAAkOSOnpgjh5FW7myxO0rE/fyZLWrq7NWPL5zDMtNAEqLsAACQ5DK9bs0qydRbCVZ21tW0\n6e43d+uqYydqXmm23XEA2ICyAwAAtKg8V6v3tCbM83ZCYUvfe2SD8jM8uunM6XbHAWATyg4AANDi\nilz1BsNaX7vf7igR8Y/VNVpfu1/f/8RMZXrddscBYBPKDgAA0KLyXElKiKls/kBIP1/+no4qzdIn\njyqxOw4AG1F2AACA8jI8mlyQrrd2NtsdZdTueG2n6tr9uvmcmTKGRQmAZEbZAQAAkqRjKvJUtatV\nobBld5QRa+7s1e9f2q5lMwt17KQ8u+MAsBllBwAASJKOqchRR29Qm+va7Y4yYv/9wjb1BEL6ztkz\n7I4CIAZQdgAAgCSpcmL/fTtr4vThonvbevTXlbv1qcpSTSn02R0HQAyg7AAAAElSaU6q8jNS4rbs\n3P7KDlmW9JVTptgdBUCMoOwAAABJkjFG8yfkaE11q91Rhq2xo1d/e2uPLlwwXqU5aXbHARAjKDsA\nAOCABWXZ2tHYpbbuPrujDMsdr+1UIBTWDSdPtjsKgBhC2QEAAAcsKMuWJK2tjp+pbG3dfbpnxS59\nYl6JJhVk2B0HQAyh7AAAgAPmlWbLYeJrkYI7X9+lrr6QvnIKozoADkXZAQAAB2R4XJpW5NOaOBnZ\n8QdCumvFLi2bWaQZxZl2xwEQYyg7AADgEAvKcrR2T6vCcfBw0X++s1dt3QFde3y53VEAxCDKDgAA\nOMSCsmy1+4Pa0dRld5SPZVmW7l6xW1MLM7RkUp7dcQDEIMoOAAA4xMKBRQrW7IntJajXVrdpfe1+\nXbVkoowxdscBEIMoOwAA4BCT8jOUnuLUhtr9dkf5WPes2K0Mj0sXLiy1OwqAGEXZAQAAh3A4jGaX\nZGnD3na7o3yk5s5ePbFuny5aOF4ZHpfdcQDEKMoOAAD4kNnjM/Xu3naFYnSRgr9XVasvFNZnj51o\ndxQAMYyyAwAAPmROSZZ6AiHtbOq0O8qHhMOW7lu5R0sm5Wlqkc/uOABiGGUHAAB8yJzxWZKkDbWx\nN5XtzZ3Nqmnt0eXHTLA7CoAYR9kBAAAfMrkgXR6XQ+tjcJGCh1fVyudx6czZxXZHARDjKDsAAOBD\nXE6HZo7LjLkV2bp6g3pqwz59Yt44ed1Ou+MAiHGjKjvGmEuNMRuNMWFjTOUHjt1sjNlmjNlijDlz\ndDEBAMBYmzOwSEE4hhYpeHpDnbr7Qrr4aJabBnBkox3Z2SDpIkmvHLzTGDNL0uWSZks6S9Jtxhj+\n+gUAgDgypyRLHb1B7WnptjvKAY+/s1elOamqnJhjdxQAcWBUZceyrE2WZW05zKHzJd1vWVavZVk7\nJW2TdMxorgUAAMbWgUUK9sbGVLbWrj69vq1J584rkTHG7jgA4kC07tkZL6n6oPc1A/sAAECcmFqU\nIbfTxMwiBU9vrFMwbOnceePsjgIgThzxkcPGmOckHW65k+9ZlvXYaAMYY66TdJ0klZWVjfZ0AAAg\nQjwupyYXZGhLXYfdUSRJT6zbq4r8dM0uybQ7CoA4ccSyY1nWshGct1bSwYvflw7sO9z5b5d0uyRV\nVlbGzh2QAABAM4p9emtni90x1NzZqxXbm/WVU6YwhQ3AkEVrGtvjki43xniMMRWSpkp6K0rXAgAA\nUTKt2Ke9+/1q9wdszfH85gaFLfFsHQDDMtqlpy80xtRIWiLpf40xz0iSZVkbJT0g6V1JT0v6imVZ\nodGGBQAAY2t6kU+StLXe3qlsz75br5IsL1PYAAzLaFdje8SyrFLLsjyWZRVZlnXmQcd+bFnWZMuy\npluW9dToowIAgLE2baDsbKnrtC1DT19Ir25t1OmzipjCBmBYojWNDQAAJIDx2alKT3HqPRtHdl7d\n2ih/IKzTZzGFDcDwUHYAAMBHcjiMphX7bF2R7flNDfJ5XVo8Kde2DADiE2UHAAB8rOlFPm2p75Bl\njf2iqZZl6eX3GnXi1AK5nfyxBcDw8LsGAAD4WNOKfGrp6lNTZ9+YX/u9+k7Vtft14rT8Mb82gPhH\n2QEAAB9renH/IgV23Lfz8nsNkqQTpxWM+bUBxD/KDgAA+Fjvr8g29mXnlfeaNK0oQ+OyUsf82gDi\nH2UHAAB8rAKfR3npKWM+stPdF9RbO1t0EqM6AEaIsgMAAI5oSmHGmJedt3a2qC8U1glTKTsARoay\nAwAAjmhSQYZ2NXeP6TXf3NEit9OosjxnTK8LIHFQdgAAwBFNyk9XS1ef2rrHbkW2N3c066jSbKWl\nuMbsmgASC2UHAAAcUUV+uiRpZ1PXmFyvszeo9bX7deykvDG5HoDERNkBAABHVFHQX3Z2NI5N2ana\n1aJQ2KLsABgVyg4AADiistw0OR1mzEZ2Bu/XWTgxe0yuByAxUXYAAMARuZ0OleWmjWHZ4X4dAKNH\n2QEAAENSkZ+uHWNQdvyBkDbU7ldleW7UrwUgsVF2AADAkFTkp2tXU5fCYSuq19lQu1/BsKWFZUxh\nAzA6lB0AADAkFfnp6gmEVNfuj+p11uxpkyQtKOP5OgBGh7IDAACGZFLB2Cw/vaa6VRNyU1Xg80T1\nOgASH2UHAAAMyaT8DEmK+n07q3e3acEERnUAjB5lBwAADElRpkepbqd2RvFZO/v296iu3c/9OgAi\ngrIDAACGxBgzsCJbZ9SusXo39+sAiBzKDgAAGLKK/HTtbu6O2vnXVrcqxeXQzHGZUbsGgORB2QEA\nAENWmpOq2raeqC0/vXFvu2YW+5Ti4o8oAEaP30kAAMCQleakqi8YVlNnb8TPbVmWNu5t16wSRnUA\nRAZlBwAADFlpTpokqbq1J+Lnrm3r0f6egGaVZEX83ACSE2UHAAAMWWlOqiSppjXy9+1s3NsuSZrN\nyA6ACKHsAACAIRt/oOxEfmRn4952OYw0s5iyAyAyKDsAAGDI0lJcyktPiUrZeXfvfk0qyFBqijPi\n5waQnCg7AABgWEpzUqM2jY0pbAAiibIDAACGpTQnTbURHtlp6erTvv1+yg6AiKLsAACAYekf2Yns\ns3Y27+tfnGDWOFZiAxA5lB0AADAspTmp6guF1RjBZ+1sbeiUJE0ryojYOQGAsgMAAIZl8Fk7kbxv\nZ2tDh3xelwp8noidEwAoOwAAYFhKo7D89LaGTk0tzJAxJmLnBADKDgAAGJZoPGtnW0OnphQyhQ1A\nZFF2AADAsLz/rJ3ITGNr7epTU2efphb6InI+ABhE2QEAAMM2uCJbJGxr7F+cgJEdAJFG2QEAAMNW\nmpMWubLTQNkBEB2UHQAAMGxFmV7Vt/sjcq6t9Z1KdTs1Pjs1IucDgEGUHQAAMGxFmR5194XU2Rsc\n9bm2NXZqcmG6HA5WYgMQWZQdAAAwbEWZXkmKyOjOtvoOTSlgChuAyKPsAACAYSvM7H/452jLjj8Q\n0t79flXkU3YARB5lBwAADNvgyE5De++ozjO4fPXEvLRRZwKAD6LsAACAYSv0RWZkZ09Lf9mZkEvZ\nARB5lB0AADBsGR6X0lKcaugY3cjOnub+slNG2QEQBZQdAAAwbMaYiCw/vbulW2kpTuVnpEQoGQC8\nj7IDAABGpNDnGfU9O9Ut3SrLTZMxLDsNIPIoOwAAYESKMr2q7xj9PTvcrwMgWig7AABgRIoyPapv\n98uyrBF937Is7RkY2QGAaKDsAACAESn0eeUPhNXRGxzR9xs7euUPhFl2GkDUUHYAAMCIDD5YtGGE\nixSw7DSAaKPsAACAERl8sGj9CBcp2M2y0wCijLIDAABG5P2yM/KRHWOk0pzUSMYCgAMoOwAAYEQK\nff3T2EY6slPd0q3iTK88LmckYwHAAZQdAAAwIukel3welxpGuPx0bVuPxmczqgMgeig7AABgxAoy\nR/5g0fp2v4qyvBFOBADvo+wAAIARK/J5R3TPjmVZqmv3qziTsgMgeig7AABgxAozPaofwTS29p6g\n/IGwxjGyAyCKKDsAAGDEctNT1NYVGPb36gZGg4oY2QEQRZQdAAAwYrlpKeroDaovGB7W9wbLTjEj\nOwCiiLIDAABGLDs9RZLU1tM3rO/V7e+RJO7ZARBVlB0AADBiOWluSVLrMKey1e3vX8GtMNMT8UwA\nMIiyAwAARiw3rX9kp7V7mCM77X7lpafwQFEAUUXZAQAAI5Y9WHa6hld26tv9LE4AIOooOwAAYMRy\n0wdHdoY7jc3P4gQAoo6yAwAARix78J6dYU5jY2QHwFig7AAAgBHzup1KS3EOaxpbbzCk5q4+HigK\nIOooOwAAYFRy0lLUMoyRnYb2/pXYWHYaQLRRdgAAwKjkpLvVNox7dgYfKFrEyA6AKKPsAACAUclJ\nS1HLMKax1e3vLzuM7ACINsoOAAAYley0FLUNYxpb/eDIDg8UBRBllB0AADAquWnuYY3stHb3yeUw\nykp1RzEVAFB2AADAKGWnpajdH1QwFB7S51u6AspJT5ExJsrJACQ7yg4AABiVwQeLtvUMbZGClq5e\n5aalRDMSAEii7AAAgFEafLDoUO/bae0KKCedKWwAom9UZccY8zNjzGZjzDpjzCPGmOyDjt1sjNlm\njNlijDlz9FEBAEAsGhzZaeka4shOd9+B7wBANI12ZOdZSXMsy5on6T1JN0uSMWaWpMslzZZ0lqTb\njDHOUV4LAADEoJyBKWmtQx7Z6TvwHQCIplGVHcuylluWFRx4+6ak0oHt8yXdb1lWr2VZOyVtk3TM\naK4FAABi0+A0ttYhrMgWDltqZWQHwBiJ5D0710p6amB7vKTqg47VDOz7EGPMdcaYKmNMVWNjYwTj\nAACAsTBYXFq7jzyNrd0fUNgSIzsAxoTrSB8wxjwnqfgwh75nWdZjA5/5nqSgpL8ON4BlWbdLul2S\nKisrreF+HwAA2CvV7VSKyzGkaWyDz+NhZAfA/2/v/kIsP886gD/P+TebnakmsRvU/LGVhNSCUiWK\n0KtgL1IpDdibilAsxRJIr0UR9EKCgneiVCJKFIpSikhaCv658saivQjStAqh0DZR8U9ikp1k98w5\n5/VizpmdnT07M7vnnd975sznA0N2z5zzO282mYfz3fd9nl8XTgw7pZSPHPf9zPzliPhYRPxcKWUR\nVl6LiIcPPe2h+WMAwIbJzLj/8uhUx9iEHaBLq05jeyoifjUiPl5KeefQt16MiE9m5lZmvj8iHouI\nf1rlvQCA9XXv5eGpjrEJO0CXTtzZOcEfRMRWRPzd/C7IXyulPFNKeTkzvxgR34z9423PllKmK74X\nALCm7t8eneoY2+I59wk7QAdWCjullEeP+d5zEfHcKtcHAM6H+y6P4lv/+daJz1vci+d+AwqADtSc\nxgYAXFA7W4O4em1y4vPeeGccl4a9uGfk9nvA2RN2AICVbW8NYvf6yWHn9d2xXR2gM8IOALCyna1+\n7I6nMZsdfxeJN3bH+nWAzgg7AMDKtrf224Df2Tt+HtHr74xNYgM6I+wAACtbhJ2TjrK9vivsAN0R\ndgCAle3Mw87VU4Sd+/TsAB0RdgCAlZ1mZ2dvOou3r03s7ACdEXYAgJVtb+2Pkj5uZ8cNRYGuCTsA\nwMp2DnZ2bj+g4A03FAU6JuwAACs7zTG2xc7OvZeHnawJQNgBAFZ2sLMzvn3YWQShxXMBzpqwAwCs\n7DQ7O4t+nm1hB+iIsAMArOzycDGg4PY9O4t+Hjs7QFeEHQBgZb1exvaof+zOzu7Bzk6/q2UBF5yw\nAwBUsb01ODbsvL0IOyM7O0A3hB0AoIqdrcGx99nZvT6Jy6N+9HrZ4aqAi0zYAQCqOGlnZ/f6RL8O\n0ClhBwCoYnurf+xNRa8KO0DHhB0AoIrTHGMzdhrokrADAFSxvTU44aaiU5PYgE4JOwBAFSf17DjG\nBnRN2AEAqjjxGNvYMTagW8IOAFDF9mgQ1/ZmMZnOln7/6jVhB+iWsAMAVLHox9kdL5/I5hgb0DVh\nBwCoYrFrs6xvZzKdxfXJLLZHwg7QHWEHAKjiuLCzuP+OaWxAl4QdAKCKnXmQWTak4Op8JPV7LtnZ\nAboj7AAAVSyOqC12cQ5b7PYYUAB0SdgBAKo4OMa25MaiV4UdoAFhBwCoYufYnp3JTc8B6IKwAwBU\ncfyAgvnOjmlsQIeEHQCgisWuzdUlPTtvX7OzA3RP2AEAqrg07EUvT9jZMXoa6JCwAwBUkZmxvTVY\nOnp6d7y4z46dHaA7wg4AUM3O1mDpzs7V65MY9DK2Bj56AN1RcQCAara3BktHT+9en8TOpUFkZoNV\nAReVsAMAVLN/jO3WAQVXr09MYgM6J+wAANXsbPVvO6DAJDaga8IOAFDNPcNBvDu+dWdn9/rUJDag\nc8IOAFDNaJCxN53d8vjV6xOT2IDOCTsAQDXDfu+2YccxNqBrwg4AUM1+2Cm3PL5rZwdoQNgBAKoZ\n9kKhJzsAAAoASURBVHsxtrMDrAlhBwCoZmtw6zG2Usp8Z8eAAqBbwg4AUM2wn7E3uTnsXNubxayE\nY2xA54QdAKCaZcfYrk/2R1HfM7SzA3RL2AEAqlkMKCjlxpCCRfgZ9n3sALql6gAA1YwG+x8tDk9k\nW/x6JOwAHVN1AIBqhv2MiLhpSMGih2c4yCZrAi4uYQcAqGZxVO2msOMYG9CIqgMAVLM4xnZ4SIGe\nHaAVVQcAqObGzo6eHaA9VQcAqGYRaMYTx9iA9lQdAKCapT07iwEFfQMKgG4JOwBANYtAc3hn56Bn\nZ+BjB9AtVQcAqGY4WDaNTc8O0IaqAwBUM1o6oEDPDtCGqgMAVDNaurOjZwdoQ9gBAKoZLpnGNp7Y\n2QHaUHUAgGoOBhQs6dkRdoCuqToAQDWjZaOnHWMDGhF2AIBqlt5nx+hpoBFVBwCo5mD09OTGNLbF\nkTajp4GuqToAQDVLe3YmenaANlQdAKCaZT07k9ksehnR7+nZAbol7AAA1Szus3PT6OnpzK4O0ITK\nAwBUs3RAwaTo1wGaUHkAgGoGvUXPzo0BBXvTmUlsQBMqDwBQTWbGqN+7ZfS0e+wALQg7AEBVw37G\nnp4dYA2oPABAVcPB0Z0dPTtAGyoPAFDVsN87cp8dOztAGyoPAFDVqN+L8eTogAI9O0D3hB0AoKrR\nkWNsenaAVlaqPJn525n5L5n5Umb+bWb+8PzxzMzfz8xX5t//qTrLBQDW3bCfS6axCTtA91atPL9X\nSvmJUsqHIuIrEfGb88c/GhGPzb8+GxGfX/F9AIBzYnjL6GkDCoA2Vqo8pZS3Dv12OyIWB3Sfjog/\nL/u+FhH3ZuYPrfJeAMD5sD+g4EjPjvvsAA0MVr1AZj4XEZ+KiDcj4sn5ww9GxPcOPe3V+WP/seT1\nn4393Z945JFHVl0OANDYqN+7+T47prEBjZxYeTLz7zPzG0u+no6IKKX8Rinl4Yj4QkR87k4XUEp5\nvpTyRCnliStXrtz5vwEAsFaGg7x59PR0FsOBsAN078SdnVLKR055rS9ExFcj4rci4rWIePjQ9x6a\nPwYAbLhRvxdvX5sc/F7PDtDKqtPYHjv026cj4l/nv34xIj41n8r2sxHxZinlliNsAMDmGfZ7MZ4c\nncamZwfo3qo9O7+bmY9HxCwivhMRz8wf/2pE/HxEvBIR70TEp1d8HwDgnBgOjk5j07MDtLFS2Cml\nfOI2j5eIeHaVawMA59Oo34u9Q9PYDCgAWlF5AICqbr2paImRAQVAAyoPAFCVnh1gXQg7AEBV+zcV\n3Q87s1mJyaw4xgY0ofIAAFWNDg0o2Jvt/1PYAVpQeQCAqg4PKFj80312gBZUHgCgqmG/F9NZiems\nxGS62NnRswN0T9gBAKoaDvaDzd50dtC7MzSNDWhA5QEAqlocWdubzg6OsenZAVpQeQCAqhbBZjyZ\nxd58BLWeHaAFlQcAqGp4sLNTDqay2dkBWlB5AICqFsMIburZMaAAaEDYAQCqGs2HEYz17ACNqTwA\nQFU3DyhwjA1oR+UBAKo66NmZlIMBBY6xAS0IOwBAVcODY2xT99kBmlJ5AICqFrs440k56Nkxehpo\nQeUBAKrSswOsC5UHAKhquDTs6NkBuifsAABVLUZP701nMZ7Y2QHaUXkAgKoWwWY8PdSzY0AB0IDK\nAwBUddCzM9GzA7Sl8gAAVQ0H82lsenaAxoQdAKCqwwMKxnZ2gIZUHgCgqoOencks9iblpscAuqTy\nAABV3bjPTom96Sz6vYx+zzE2oHvCDgBQ1aI/Z3GfHf06QCvCDgBQ1aDfi17e6NlxhA1oRfUBAKob\n9nv7PTvT2cGxNoCuqT4AQHWjfm9/9PSk2NkBmlF9AIDqhoPejZ6dgZ4doA1hBwCobtjP2JuU2JvZ\n2QHaUX0AgOqG/fnOzkTPDtCO6gMAVHfQs2MaG9CQ6gMAVDca7E9jG7vPDtCQsAMAVDca9OLdvamd\nHaAp1QcAqO7HfvD74qXv/l+8O57GaODjBtCG6gMAVPfkB67E29cn8fK/v2VnB2hG9QEAqvvwo++N\nQS9jMit6doBmhB0AoLr3XBrGT7/v/ogIOztAM6oPAHAmnvzAlYgI99kBmlF9AIAz8eTjD0SEnR2g\nHdUHADgTjz6wEx96+N549IGd1ksBLqhB6wUAAJspM+Ovn/1w62UAF5idHQAAYCMJOwAAwEYSdgAA\ngI0k7AAAABtJ2AEAADaSsAMAAGwkYQcAANhIwg4AALCRhB0AAGAjCTsAAMBGEnYAAICNJOwAAAAb\nSdgBAAA2krADAABsJGEHAADYSMIOAACwkYQdAABgIwk7AADARhJ2AACAjSTsAAAAG0nYAQAANpKw\nAwAAbCRhBwAA2EhZSmm9hgOZ+d8R8Z3W62jo+yP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227 "text/plain": [
228 "<matplotlib.figure.Figure at 0x7fdd1dc82080>"
229 ]
230 },
231 "metadata": {},
232 "output_type": "display_data"
233 },
234 {
235 "name": "stdout",
236 "output_type": "stream",
237 "text": [
238 "0.0989684499371\n"
239 ]
240 },
241 {
242 "data": {
243 "image/png": 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04VCb2nqYygYAUxVhBwCQlm5ZVKGIlZ7ZedLpUgAADiHsAADS0vyKHNUW+bV+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\nQmCC\n",
244 "text/plain": [
245 "<matplotlib.figure.Figure at 0x7fdd56b43048>"
246 ]
247 },
248 "metadata": {},
249 "output_type": "display_data"
250 }
251 ],
252 "source": [
253 "for cel,i in zip(sos,range(len(sos))):\n",
254 " w_cell, h_cell = signal.sosfreqz([cel])\n",
255 " plt.plot(w_cell*8/np.pi, 20 * np.log10(abs(h_cell)),label=\"SOS cell{}\".format(i))\n",
256 " print(1/max(abs(h_cell)))\n",
257 " plt.semilogx()\n",
258 " plt.legend()\n",
259 " plt.show()"
260 ]
261 },
262 {
263 "cell_type": "markdown",
264 "metadata": {},
265 "source": [
266 "The first cell attenuate the signal by 40dB while the two later stages amplifies the signal by 20dB each."
267 ]
268 },
269 {
270 "cell_type": "code",
271 "execution_count": 69,
272 "metadata": {},
273 "outputs": [
274 {
275 "data": {
276 "image/png": 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hqIjNHJhqWVa+SwEAAACKBiGoiMWiAY1NTWtoIpnvUgAAAICiQQgqYjMT4tgXBAAAAFw8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\n4ubQUXKGEgQAAACgR3m2UDMOGEcJAgAAAJAcJx1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277 "text/plain": [
278 "<matplotlib.figure.Figure at 0x7fdd1a0df2b0>"
279 ]
280 },
281 "metadata": {},
282 "output_type": "display_data"
283 },
284 {
285 "name": "stdout",
286 "output_type": "stream",
287 "text": [
288 "==============================\n",
289 "Stage 0 coefs\n",
290 "[ 0.04793969 0.04793969 0. ]\n",
291 "[ 1. -0.90347831 0. ]\n",
292 "==============================\n",
293 "==============================\n",
294 "Stage 1 coefs\n",
295 "[ 0.064 -0.11927648 0.064 ]\n",
296 "[ 1. -1.8493484 0.85823409]\n",
297 "==============================\n",
298 "==============================\n",
299 "Stage 2 coefs\n",
300 "[ 0.1575 -0.30662353 0.1575 ]\n",
301 "[ 1. -1.94042451 0.94882247]\n",
302 "==============================\n"
303 ]
304 }
305 ],
306 "source": [
307 "sos[0][0:3]=sos[0][0:3]*96.5\n",
308 "sos[1][0:3]=sos[1][0:3]*0.064\n",
309 "sos[2][0:3]=sos[2][0:3]*0.1575\n",
310 "\n",
311 "w_sos, h_sos = signal.sosfreqz(sos)\n",
312 "\n",
313 "plt.plot(w_sos*8/np.pi, 20 * np.log10(abs(h_sos)),label=\"SOS\")\n",
314 "plt.legend()\n",
315 "plt.show()\n",
316 "\n",
317 "for stage,i in zip(sos,range(len(sos))):\n",
318 " print(\"==============================\")\n",
319 " print(\"Stage {} coefs\".format(i))\n",
320 " print(stage[:3])\n",
321 " print(stage[3:])\n",
322 " print(\"==============================\")"
323 ]
324 },
325 {
326 "cell_type": "markdown",
327 "metadata": {},
328 "source": [
329 "Now we can work on coeficients ronding to convert them as integers."
330 ]
331 },
332 {
333 "cell_type": "code",
334 "execution_count": 112,
335 "metadata": {},
336 "outputs": [
337 {
338 "name": "stdout",
339 "output_type": "stream",
340 "text": [
341 "==============================\n",
342 "Stage 0 coefs\n",
343 "[ 0.04785156 0.04785156 0. ]\n",
344 "[ 1. -0.90332031 0. ]\n",
345 "==============================\n",
346 "==============================\n",
347 "Stage 1 coefs\n",
348 "[ 0.06396484 -0.11914062 0.06396484]\n",
349 "[ 1. -1.84960938 0.85742188]\n",
350 "==============================\n",
351 "==============================\n",
352 "Stage 2 coefs\n",
353 "[ 0.15722656 -0.30664062 0.15722656]\n",
354 "[ 1. -1.93945312 0.94921875]\n",
355 "==============================\n"
356 ]
357 },
358 {
359 "data": {
360 "image/png": 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LkCSp4WueQ/z0GxgVn8E/3pzHhClLok4kSarHLEGSpMbh7C8SJ8EnCidGnUSS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\nI6i1pZnWlmbu+9pPyW7PsWnZ4rhLGpJhhaAQwruArwIzgRUhhIejKHp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361 "text/plain": [
362 "<matplotlib.figure.Figure at 0x7fdd1db8c3c8>"
363 ]
364 },
365 "metadata": {},
366 "output_type": "display_data"
367 },
368 {
369 "name": "stdout",
370 "output_type": "stream",
371 "text": [
372 "1.01020408163\n"
373 ]
374 },
375 {
376 "data": {
377 "image/png": 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idW5+is4tSNXYnAS5mfIaAGATyg4AoMtafH59sq9aS4oqtXhnpTaUVitgSdERTk0amKxz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\nRK5CYII=\n",
378 "text/plain": [
379 "<matplotlib.figure.Figure at 0x7fdd1dc7fcf8>"
380 ]
381 },
382 "metadata": {},
383 "output_type": "display_data"
384 },
385 {
386 "name": "stdout",
387 "output_type": "stream",
388 "text": [
389 "0.888888888889\n"
390 ]
391 },
392 {
393 "data": {
394 "image/png": 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v5TPU0ObTNX9cqq/84SOtKa+3Ox4AABGPsgMAEc7hMLrwmHy9+d1Tdcf5k7Vud73m3f++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\n5TU7xk4Drag+AMBaLMOOsdNAK8IOALAWy21sI50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395 "text/plain": [
396 "<matplotlib.figure.Figure at 0x7fdd1a098278>"
397 ]
398 },
399 "metadata": {},
400 "output_type": "display_data"
401 },
402 {
403 "name": "stdout",
404 "output_type": "stream",
405 "text": [
406 "0.75708762513\n"
407 ]
408 },
409 {
410 "data": {
411 "image/png": 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mA0xBDQAYRtgBAKSF5dX5CnhdemEfU1ADAIYRdgAAacHtdOjy2iK9sK+VKagB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\nYII=\n",
412 "text/plain": [
413 "<matplotlib.figure.Figure at 0x7fdd1df94358>"
414 ]
415 },
416 "metadata": {},
417 "output_type": "display_data"
418 }
419 ],
420 "source": [
421 "sos_int=sos.copy()\n",
422 "sos_int[0][:3]=np.round(sos[0][:3]*(2**12))/2**12\n",
423 "sos_int[0][4:]=np.round(sos[0][4:]*(2**10))/2**10\n",
424 "\n",
425 "sos_int[1][:3]=np.round(sos[1][:3]*(2**11))/2**11\n",
426 "sos_int[1][4:]=np.round(sos[1][4:]*(2**9))/2**9\n",
427 "\n",
428 "sos_int[2][:3]=np.round(sos[2][:3]*(2**10))/2**10\n",
429 "sos_int[2][4:]=np.round(sos[2][4:]*(2**9))/2**9\n",
430 "\n",
431 "i=0\n",
432 "for stage in sos_int:\n",
433 " print(\"==============================\")\n",
434 " print(\"Stage {} coefs\".format(i))\n",
435 " print(stage[:3])\n",
436 " print(stage[3:])\n",
437 " print(\"==============================\")\n",
438 " i+=1\n",
439 "\n",
440 "w_sos_int, h_sos_int = signal.sosfreqz(sos_int)\n",
441 "\n",
442 "plt.plot(w_sos*8/np.pi, 20 * np.log10(abs(h_sos)),marker='+',label=\"SOS\")\n",
443 "plt.plot(w_sos_int*8/np.pi, 20 * np.log10(abs(h_sos_int)),label=\"SOS rounded\")\n",
444 "plt.legend()\n",
445 "plt.semilogx()\n",
446 "#plt.ylim(-8,2)\n",
447 "plt.show()\n",
448 "\n",
449 "for cel,i in zip(sos_int,range(len(sos_int))):\n",
450 " w_cell, h_cell = signal.sosfreqz([cel])\n",
451 " plt.plot(w_cell*8/np.pi, 20 * np.log10(abs(h_cell)),label=\"SOS int cell{}\".format(i))\n",
452 " print(1/max(abs(h_cell)))\n",
453 " plt.semilogx()\n",
454 " plt.legend()\n",
455 " plt.show()"
456 ]
457 },
458 {
459 "cell_type": "markdown",
460 "metadata": {},
461 "source": [
462 "As we can see we can easily encode coeficients on a 16 bits integer."
463 ]
464 },
465 {
466 "cell_type": "code",
467 "execution_count": 96,
468 "metadata": {},
469 "outputs": [
470 {
471 "name": "stdout",
472 "output_type": "stream",
473 "text": [
474 "static const int32_t b[3][3]={{196,196,0},{131,-244,131},{161,-314,161}};\n",
475 "static const int32_t a[3][3]={{1,-925,0},{1,-947,439},{1,-993,486}};\n",
476 "static const int32_t b_gain[3]={12,11,10};\n",
477 "static const int32_t a_gain[3]={10,9,9};\n"
478 ]
479 }
480 ],
481 "source": [
482 "sos_int_C=sos.copy()\n",
483 "\n",
484 "gains=[(2**12,2**10),(2**11,2**9),(2**10,2**9)]\n",
485 "\n",
486 "for i,G in zip(range(3),gains):\n",
487 " sos_int_C[i][:3]=np.round(sos[i][:3]*G[0])\n",
488 " sos_int_C[i][4:]=np.round(sos[i][4:]*G[1])\n",
489 "out_b=\"static const int32_t b[3][3]={\"\n",
490 "out_a=\"static const int32_t a[3][3]={\"\n",
491 "out_b_g=\"static const int32_t b_gain[3]={\"\n",
492 "out_a_g=\"static const int32_t a_gain[3]={\"\n",
493 "\n",
494 "for stage,G in zip(sos_int_C,gains):\n",
495 " out_b+= \"{\" + str(int(stage[0])) +\",\"+ str(int(stage[1])) +\",\"+ str(int(stage[2])) + \"},\"\n",
496 " out_a+= \"{\" + str(int(stage[3])) +\",\"+ str(int(stage[4])) +\",\"+ str(int(stage[5])) + \"},\"\n",
497 " out_a_g+=str(int(np.log2(G[1]))) + \",\"\n",
498 " out_b_g+=str(int(np.log2(G[0]))) + \",\"\n",
499 " \n",
500 "out_b=out_b[:-1]+\"};\"\n",
501 "out_a=out_a[:-1]+\"};\"\n",
502 "out_b_g=out_b_g[:-1]+\"};\"\n",
503 "out_a_g=out_a_g[:-1]+\"};\"\n",
504 "print(out_b)\n",
505 "print(out_a)\n",
506 "print(out_b_g)\n",
507 "print(out_a_g)"
508 ]
509 },
510 {
511 "cell_type": "markdown",
512 "metadata": {},
513 "source": [
514 "Let's compare C implementation impulse response with Python one."
515 ]
516 },
517 {
518 "cell_type": "code",
519 "execution_count": 120,
520 "metadata": {},
521 "outputs": [
522 {
523 "data": {
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gKAEAAACAB0UpgzWFo6praFPf4LDrKAAAAEBayXMdAHMn1tqo+sM75DcRxXwr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\njbM+JgAAwGxwjZJDjAVHuom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525 "text/plain": [
526 "<matplotlib.figure.Figure at 0x7fdd1a056e48>"
527 ]
528 },
529 "metadata": {},
530 "output_type": "display_data"
531 }
532 ],
533 "source": [
534 "imp=signal.sosfilt(sos_int,signal.unit_impulse(400))\n",
535 "plt.step(np.arange(len(imp)),imp,label=\"Rounded\")\n",
536 "df=pds.read_csv(\"/home/jeandet/Documents/prog/sparc/build-LFR_POT_Filter-Desktop-Default/test.txt\",header=None)\n",
537 "plt.step(df.index,df[0]/(32768),label=\"C implementation\")\n",
538 "plt.legend()\n",
539 "plt.show()"
540 ]
541 },
542 {
543 "cell_type": "markdown",
544 "metadata": {},
545 "source": [
546 "## C filter implementation example\n",
547 "\n",
548 "```c\n",
549 "\n",
550 "#include <stdio.h>\n",
551 "#include <stdint.h>\n",
552 "\n",
553 "static const int32_t b[3][3]={{196,196,0},{131,-244,131},{161,-314,161}};\n",
554 "static const int32_t a[3][3]={{1,-925,0},{1,-947,439},{1,-993,486}};\n",
555 "static const int32_t b_gain[3]={12,11,10};\n",
556 "static const int32_t a_gain[3]={10,9,9};\n",
557 "\n",
558 "\n",
559 "\n",
560 "typedef struct filter_ctx\n",
561 "{\n",
562 " int32_t W[3][3];\n",
563 "}filter_ctx;\n",
564 "\n",
565 "int32_t filter(int32_t x,filter_ctx* ctx)\n",
566 "{\n",
567 " //Direct-Form-II\n",
568 " for (int i=0;i<3;i++)\n",
569 " {\n",
570 " x=x<<a_gain[i];\n",
571 " int32_t W=(x - (a[i][1]*ctx->W[i][0]) - (a[i][2]*ctx->W[i][1]))>>a_gain[i];\n",
572 " x=(b[i][0]*W) + (b[i][1]*ctx->W[i][0]) + (b[i][2]*ctx->W[i][1]);\n",
573 " x=(x>>(b_gain[i]));\n",
574 " ctx->W[i][1] = ctx->W[i][0];\n",
575 " ctx->W[i][0] = W;\n",
576 " }\n",
577 " return x;\n",
578 "}\n",
579 "\n",
580 "int main(void)\n",
581 "{\n",
582 " filter_ctx ctx={{{0,0,0},{0,0,0},{0,0,0}}};\n",
583 " printf(\"%d\\n\",filter(32768,&ctx));\n",
584 " for(int i=0;i<400;i++)\n",
585 " {\n",
586 " printf(\"%d\\n\",filter(0,&ctx));\n",
587 " }\n",
588 "}\n",
589 "\n",
590 "\n",
591 "```"
592 ]
593 },
594 {
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596 "execution_count": null,
597 "metadata": {
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600 "outputs": [],
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661 },
662 "nbformat": 4,
663 "nbformat_minor": 2
664 }
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