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@dsaint31x
Created April 24, 2019 03:13
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Zoros and Poles : Freq. Response\n",
"\n",
"## Pole and Freg. Response\n",
"\n",
"* Pole 은 resonance freq. 에서 gain을 증가시키는 주파수 선택적 동작 수행. \n",
"* Amplitude spectrum에서 peak 생성.\n",
" * gain의 변화율은 resonance freq. 부근에서 더 심해짐.\n",
" * Pole이 imaginary axis에 가까울수록 gain이 증가.\n",
" * 중복극은 위의 주파수 선택 효과를 향상시킴\n",
" \n",
"## Zero and Freg. Response\n",
"\n",
"* Zero는 resonance freq.부근에서 gain을 억제시키는 주파수 선택적 동작\n",
"* Amplitude spectrum에서 valley 생성.\n",
" * gain의 변화율은 resonance freq. 부근에서 더 심해짐.\n",
" * Zero가 imaginary axis에 가까울수록 gain이 증가.\n",
" * 중복극은 위의 주파수 선택 효과를 향상시킴\n",
"\n",
"## Zeros, Poles, and Freq. Response\n",
"\n",
"### Amplitude Spectrum\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"|H(\\Omega)|&=b_n\\left.\\frac{|(s-z_1)||(s-z_2)|\\cdots|(s-z_n)|}{|(s-p1)||(s-p2)|\\cdots|(s-p_n)|}\\right|_{s=j\\Omega} \\\\\n",
"&=b_n\\left.\\frac{\\displaystyle{\\prod^n_{i-1}|j\\Omega-z_i}|}{\\displaystyle{\\prod^n_{i-1}|j\\Omega-p_i}|}\\right|_{s=j\\Omega} \n",
"\\end{align*}\n",
"$$\n",
"\n",
"### Phase Spectrum\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"H(\\Omega) &= b_n\\left.\\frac{(s-z_1)(s-z_2)\\cdots(s-z_n)}{(s-p_1)(s-p_2)\\cdots(s-p_n)}\\right|_{s=j\\Omega} \\\\\n",
"\\angle H(\\Omega) &= \\left. \\{ \\angle(s-z_1)+\\angle(s-z_2)+\\cdots +\\angle(s-z_n) \\} -\\{\\angle(s-p_1)+\\angle(s-p_2)+\\cdots +\\angle(s-p_n)\\} \\right|_{s=j\\Omega} \\\\\n",
"&= \\displaystyle{\\sum_{i=1}^n \\angle (j\\Omega-z_i) - \\sum_{i=1}^n \\angle (j\\Omega-p_i)}\n",
"\\end{align*}\n",
"$$\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.0007692307692307697"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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CCnwz6wP86Jz7/ZzQakByltc7AtuyO8dQM0sws4SUlJRgyim8ihQhasL7vFP8T5yVnsqggZkcOeJ3USISbnIMfDObY2Zrsnn0BUYCj2T3tmy2Zdv77Jwb55yLd87FV6xYMXfVR5K4OKq89xzvpP+BNWujuPtuvwsSkXCTY+A757o655r+/gFsAeKAlWa2FagOfG9m5+C16GtkOU11QGNMgtW3Lz3ub8lfeJaxY2HiRL8LEpFwcsZdOs651c65Ss652s652ngh38o5txuYBlwXGK3TDtjvnNuVNyVHuMcf54lL5tLBFnHTDRmsWeN3QSISLvJrHP5MvL8AEoHXgNvy6TqRJyaGohPfZXKV2yl97Cf6900nNdXvokQkHORZ4Ada+j8FfnbOuWHOubrOuWbOuYS8uo4AlSpRdcZrTC5yDUlJMOSaDK2qKSI50kzbcNWiBRe+fxsvuTuYPjOahx/SjCwROTUFfjjr35/b/laFWxjHk08Z77zjd0EiEsoU+GHOHhrJK9csojNzufnGDObP97siEQlVCvxwZ0aRf/+LKRe/TJ2MzfTrdZzERL+LEpFQpMAvDIoWJXba20xveA+kHaBHp6Ps2eN3USISahT4hUWZMtSb+y9mVL6RXTsy6NnpKGlpfhclIqFEgV+YVKtG22+eY0rZm1m1PoZ+PY9w7JjfRYlIqFDgFzYNGtBz3v28WWIYXy4swTUDjpKe7ndRIhIKFPiF0XnnMWTO9bxQ5D4+nFGc6wcdJSPD76JExG8K/MKqQwfu+rw7o2Ie4f2PijP0uiOajSsS4RT4hVnnzjz4+cU8Ej2Kf79fguE3H9EtEkUimAK/sOvShUc/b8e90c/z6pslGHajWvoikUqBHwGsaxee/rwF98X8nVffKsHNVx9Sn75IBFLgRwjr2oWn5rbl0WJP8uakUlzX/4BG74hEGAV+BLGLOvLXBd15uuRjvD+tNAN77OfoUb+rEpGCosCPNK1bc993V/GPMg8zdW5ZenZI1YxckQihwI9EjRtz+4obee+ce/h2eSkubpHK7t1+FyUi+U2BH6ni4rhm9f182uheNiUV4YJm+7XKpkghp8CPZBUq0GPZKL7s+Cj7fzpB++YHWfitxmyKFFYK/EhXsiRtv3qahX94hXJHdtH54nQmvKVvckUKIwW+QHQ0Dcb/lcVPz6NN5mKuvqE4T/xlv2blihQyCnz5zdn33czsT45wbZEJPPz3sgzp+RNHjvhdlYjkFQW+/JdifbrzzvLmPB77AuO/qEDHc1NITva7KhHJCwp8+R/WpDEPbb6eaS0eYdO2YrRukMY3c477XZaIBEmBL9k7+2x6J/yVJTe/Trmju+lyaRSvjEpVv75IGFPgy8lFR3Pua3ez9O0NdI+azfCHynFNl10cOOB3YSJyJhT4kqNy1/Vh2opajKr4EhO/qsT5cSmsWanlNkXCTVCBb2aPmtmPZrYi8Lgsy74HzCzRzDaaWffgSxU/RTVtzINJtzCnx/Ok7sugTasTvP3SL36XJSK5kBct/Bedcy0Cj5kAZtYYGAw0AXoAY8wsOg+uJX4qVYpOn93Lipfm0ZYl/PGuWK7rskOLr4mEifzq0ukLTHDOHXPOJQGJQJt8upYUsHPuGMTs5RV5tNIYxn9ZhZY1UlgyT7NzRUJdXgT+cDNbZWb/NrPYwLZqQNbR2zsC26SQiGnemL9uu5FvBr5CRtohLrgkhidH7NKdtERCWI6Bb2ZzzGxNNo++wKtAXaAFsAt4/te3ZXOqbAf0mdlQM0sws4SUlJQz/Bjii+LFuWDi7az4cAtXFp/OyJer0Kl+Mls2K/VFQlGOge+c6+qca5rN4xPn3B7nXIZzLhN4jf902+wAamQ5TXVg50nOP845F++ci69YsWKwn0d8UK5/Zz7YfiFvtRrNyqQyNG90jH89vkdj9kVCTLCjdKpkedkPWBP4eRow2MyKmVkcUB9YGsy1JLRZxQpcnzCC1S/OpX3UEv7vkcr0bLyNHdu13LJIqAi2D/9ZM1ttZquATsBdAM65tcAkYB3wOTDMOae/8ws7M2re2Z8vkhrySpMxzN9QgaZ1DvHWs3vV2hcJAeZC6F9ifHy8S0hI8LsMyQvOkfjsR9wwsgrfZnSga72t/GtGdeo0iPG7MpFCx8yWOeficzpOM20lf5hR774BzEuqxZjzxrIksTzNzj3BC3claySPiE8U+JKvompU49YV/8fafy2gc5Fv+fNLNWhffTsrFmmhfZGCpsCXAlFjaE+m7TqfCV1eY+vu4rTuUJS7+iSStj90uhRFCjsFvhQYiy3HoDm3sGHGFoaW/5B/fFqHRpV/ZsI/NIRTpCAo8KXAlb+sHa/u6c/iOyZQ5cR2rr6zMt3q/sDGlVqeQSQ/KfDFHzExtHnpDyzdWpmXW79JQtLZNGsRxT19NrE/Vc19kfygwBdfRdeoyrCEG9g4ZQ3XxU7nhU/rUb9SKq8/sl2jeUTymAJfQkLlARfy+t4+fPfAVBq4TdzyeE3Or7yN+Z/87HdpIoWGAl9CR0wMrZ8cwPy9DfngsndJ2RfFRVeUZ0CTDWxaqWGcIsFS4EvIsdhyDJ4xhI0rjvK3huOZta4aTVrEMLzzWvbuTPe7PJGwpcCXkFXyvPo8vOEaEj9Zxy2VpzH2q4bUrXGMJ67dwKGD+mJXJLcU+BLyKvdpy5hd/Vk7+ku6lVzAw+MbUf/sfbz650SOH/e7OpHwocCX8GBGwxGX8tHPnfj2z1Op47Zw2wv1aFRuF28/mqQRPSKnQYEv4aVIES74ez/m/9KUmTdOIfb4Xv74WBzNYpOZ8vw2MrX8vshJKfAlLFmpkvR840oS9sUxZdBkOHSIq+6pRXyFJD55ebuWahDJhgJfwpqVLcOACVexencl3uk1ibTUTK4YUZOW5bfy0Ytq8YtkpcCXQiG6YnmGfDqQDTvL8nbvyRzen86Au2vRInYrk59NUvCLoMCXQibmnApcN+0q1u8pz3v9pnDi4DEG3hdHs7LbGf9YIukaxi8RTIEvhVJ0xfJc89GVrNlbmQlXfYgdPsS1j9ajfuldvDJsHYcPqZNfIo8CXwq16LPLMWjSAFb9XJ1pN35MlcwfGT6mMbXL/cKoQSv5JUVNfokcCnyJCFFlS9P7jStYkNacb+6fyfnFVvPQpPOoWfko93RdQfImrdUjhZ8CXyKKFStKx6cuY0ZaR1a88CV9yi/gpblNiWtYhD80WUnCZyl+lyiSbxT4Epmiojjvrs6MT7mUxInfc0e9mUxfF8f5l1Xk4sob+OTFLZq9K4WOAl8imxm1B7bh+c192LH8J17oOJVtKSW44u46NCq9g5f/tIoDqUp+KRwU+CIBZVrU4a5v+pG4tywTr5lG+fQURoxrTvXyh7mj4zI2LU31u0SRoCjwRX4npkI5Br7Xh8UHm7Lo8Tn0qrCYV79tRsO25ehRfQ3T/7lFE7kkLCnwRU7Cihah3UNdGb+3G9vnbOax1p+w6sez6X17HeqX+pEXrlvOz7u1PrOEDwW+yGk4p0sTHknoy7Y9xZlw7XSqspM/v9uSalUyuK7p9yyc/KMWbJOQF3Tgm9kIM9toZmvN7Nks2x8ws8TAvu7BXkckFBSpFMugd3sx/1BrVvxzPjfU/oqP19bjgoHVaF4miZdvXsH+n074XaZItoIKfDPrBPQFmjvnmgB/D2xvDAwGmgA9gDFmFh1krSKhIyqK84Z3ZEzSZezccIBxvT+l2LEDjHijBVUqpnNTi2Us/XinWv0SUoJt4d8KPO2cOwbgnNsb2N4XmOCcO+acSwISgTZBXkskJJ3VsBq3TOtNwpEmJLw4n2trzmPiyoa07VeV5qWTeHHI96Rs10xe8V+wgd8A6GhmS8xsnpmdH9heDUjOctyOwDaRwis6mtZ3dmTcth7sXJvKv3pPp9SJVO5+rxXVakUzoO5yZvxjM+kn1OwXf+QY+GY2x8zWZPPoC8QAsUA74C/AJDMzwLI5Vbb/l5vZUDNLMLOElBRNa5fCoUzj6gyd1ovFR85jzRtLuP3cOczfUo1ed9anVsm9PNhtKZuX/Ox3mRJhzAXRyWhmn+N16XwdeP0DXvjfDOCceyqw/QvgUefcolOdLz4+3iUkJJxxPSKh7PjeVGY8soR/TyzJzNQOZBJN+9gNDBlwmEGPNaZ81eJ+lyhhysyWOeficzou2C6dj4HOgQs2AIoCPwHTgMFmVszM4oD6wNIgryUS1opWKke/sd359JeOJM/dzDMXzeDAAcdtr7finGpR9I9bzsdPruP4MXX5SP4INvD/DdQxszXABOB651kLTALWAZ8Dw5xzWpBEJKBq50bcO+9yVh1pwPJXFzG80VwWbq1Kv5GNqVIylWHnL2Xx5GSN8pE8FVSXTl5Tl45EsvTUg8x+Ygnvjjem7m7PUUpQt1gygzvu5OoH42jSqZLfJUqIOt0uHQW+SAhK27iLDx9ZyQeflWPugfPJJJpmpX7g6m77GPxwfeJaxfpdooSQgurDF5F8UKZhFW6Y2INZae3YuWAro3t+xlkZaTz4cRvqtI6lfex6Rg/5jl2bD/pdqoQRtfBFwoVzbJ25jonPbuODRbVYeaIJRiYXVVjHVZcfof/Ic6lS/yy/qxQfqEtHpDDLzGTd+yuYOHoPk5fXZX16A4xMLiy/nqsuP8yABxtStVEZv6uUAqLAF4kUmZmsG7+cya/sZfKyONamN8LIpEPsBq667CADHmhI9SZl/a5S8pECXyQSZWayfuIqpvxzF5MTarP6xLkAtC27nn6d9tPvz3VocKFG+xQ2CnyRSOccGyevYso/dzL1u+osO9YMgHNLJNGv3W76Da9G6341sewWQpGwosAXkf9wju1zNvHJS0lM/eZsvjnYkgxiqB6zmytabKXfTeW56Kb6xBRR+ocjBb6InNS+FclMf249U78oyRf7WnOUEsRGpdKz7iZ69y9KjzsbUe4cre0TLhT4InJaDm37iVl/X8Unn8CM5Gb8REViOEHHChvo3eUwve+oQ732Ff0uU05BgS8iuZZx6ChLxi7n0/FpfLq6NmvTGwLQqHgSveN30euGSnQYUlddPyFGgS8iwXGOLTM3MH3Mdj79NpZ5aS04QVFio1LpHreJnpdH0+OOhlSqo8leflPgi0ieSkvcyxfPr2HGTOPz5MbscZUBiC+9gZ5tfqbnHyvTZnAdomPU+i9oCnwRyTeZR4+z/O1VfPbePj77vhKLDzcnk2jKR/1C97jN9OwVTffb1fovKAp8ESkwP6/+kVn/3MhnXxifJzdhr6uEkUnr0pu4tPU+Lh18Nu2vb0DR4lqvMT8o8EXEF5lHj/P926v57L19zFpegUWHmpNBDKU4yCVVNnHpJce59JZaNLykiiZ95REFvoiEhLTEvXw1Zj2zZqYzO7E2mzPqAlAjZieXNthGt17F6HpbA86upe6fM6XAF5HQ4xxJX2xi9hvbmTW/BHP3NCGVWIxMWp21ic7N99Glf1kuvLEBpWKL+l1t2FDgi0jISz94lIQ3VzNr4i/MXXk2iw424wRFKcJx2sVupEt8Gp0HVaDtH+pRtES03+WGLAW+iISdQ8k/s+D19cz99DBz11fh+6ONcURRioN0rLyJzu2P0uXaKpzXt7aGf2ahwBeRsPfLul18PW4TX846wdzNtVifXh+AWPuFi6slcnH7E1x8dVWa964V0b8AFPgiUrg4x67F2/jyjS3M/dKYtz2OLRm1AShnqXSsksgl7Y9x8aAqtOgXF1G/ABT4IlK4OceO+UnMe2crX39tzNtai80ZdQAoY2l0rLyZi9se5ZLB59CyfxwxRQvvHAAFvohEFufYuWgb895KYt7Xjq+TarIxvR4Ape0AHSpu5sJWh+nY92za/KEeJcoU8bngvKPAF5GIt/u7ZL558we+/jKT+UnVWHPcW/2zCMeJL7OZC5v8Qscepbjgj/UpXzN85wEo8EVEfueX9btZ8M4PfDv7CPM3VOC7Q405gTfev0nxH7iw/h46dorhwiFx1IoPn3sAKPBFRHJwZE8a3723kW+npzJ/VRkW/tyINMoC3kzgDtWT6dA2nQ5XVOa8K+IoUjw05wIo8EVEcinjyHFWT97At1NTmL+0GIt21yY5szoAJTjM+bF9dF+hAAAGBElEQVSJdGi8n/bdzqL9tXWpWLeMzxV7CiTwzWwi0DDwshyQ6pxrEdj3AHATkAHc7pz7IqfzKfBFJKQ4x44F21g0cRsL56Wz8IdKLD/c8LduoPpFt9K+1i46tHd0uLIqjXv6Mx+gwFv4ZvY8sN859zczawx8ALQBqgJzgAbOuYxTnUOBLyKh7sieNJZ9sJGFM/ezaGVJFqbUY6+rBHjDQc8vv4W2jQ/QtnMp2l5dh8oNy+V7TQUa+GZmwHags3Nuc6B1j3PuqcD+L4BHnXOLTnUeBb6IhBuXkcmW2T+waMqPLPjWsWRbZVYdbUAGMQDUitlB22o/0rbVCdpeXoFWV9ahRNm8XRjudAM/Jo+u1xHY45zbHHhdDVicZf+OwDYRkULFoqOo26M+dXvU59rAtsO79vP9xM0smZXKkpXFWZxcm0nbqsNUiLn5BM1LbaBt3Z9o2yGGtgOq06BTNaKi878rKMfAN7M5wDnZ7BrpnPsk8PPVeF04v70tm+Oz/VPCzIYCQwFq1qyZUzkiIiGvZJWyXHhnPBfeGdjgHLsTklkyaRtLvjnKko3leG9Vc15dVQbGQlnbz4OXreTe6Rfla105Br5zruup9ptZDNAfaJ1l8w6gRpbX1YGdJzn/OGAceF06OdUjIhJ2zDjn/Br0Pb8GfQObMo6eYMOn61gybQ9LlkJc3fyf+ZsXXTpdgQ3OuR1Ztk0D3jezF/C+tK0PLM2Da4mIFArRxYvQ5KrGNLmqMTcW0DXzIvAH89/dOTjn1prZJGAdkA4My2mEjoiI5K+gA98598eTbB8FjAr2/CIikjcK73qhIiLyXxT4IiIRQoEvIhIhFPgiIhFCgS8iEiEU+CIiESKk1sM3sxRgWy7eUgH4KZ/KKSj6DKFBnyE06DOcmVrOuRxv0RVSgZ9bZpZwOivEhTJ9htCgzxAa9Bnyl7p0REQihAJfRCRChHvgj/O7gDygzxAa9BlCgz5DPgrrPnwRETl94d7CFxGR0xS2gW9mPcxso5klmtn9fteTW2b2bzPba2Zr/K7lTJlZDTP7yszWm9laM7vD75pyy8yKm9lSM1sZ+AyP+V3TmTCzaDNbbmbT/a7lTJnZVjNbbWYrzCzsbm5tZuXMbIqZbQj8m2jvd02/F5ZdOmYWDWwCuuHdXes74Grn3DpfC8sFM7sIOAi845xr6nc9Z8LMqgBVnHPfm1lpYBlwRZj9dzCglHPuoJkVAb4F7nDOLc7hrSHFzO4G4oEyzrleftdzJsxsKxDvnAvLcfhm9jYw3zn3upkVBUo651L9riurcG3htwESnXNbnHPHgQnw253DwoJz7hvgZ7/rCIZzbpdz7vvAzweA9YTZzeqd52DgZZHAI6xaQWZWHbgceN3vWiKVmZUBLgLeAHDOHQ+1sIfwDfxqQHKW1zsIs6ApbMysNtASWOJvJbkX6A5ZAewFZjvnwu0zvATcC2T6XUiQHDDLzJaZ2VC/i8mlOkAK8Gaga+11Myvld1G/F66Bb9lsC6tWWWFiZmcBHwJ3OufS/K4nt5xzGc65FkB1oI2ZhU0Xm5n1AvY655b5XUseuMA51wroCQwLdHuGixigFfCqc64lcAgIue8WwzXwdwA1sryuDuz0qZaIFuj3/hAY75z7yO96ghH4E/xroIfPpeTGBUCfQP/3BKCzmb3nb0lnxjm3M/C8F5iK13UbLnYAO7L8dTgF7xdASAnXwP8OqG9mcYEvRwYD03yuKeIEvvB8A1jvnHvB73rOhJlVNLNygZ9LAF2BDf5Wdfqccw8456o752rj/Tv40jl3rc9l5ZqZlQp88U+gK+RSIGxGsDnndgPJZtYwsKkLEHKDF4K+ibkfnHPpZjYc+AKIBv7tnFvrc1m5YmYfAJcAFcxsB/BX59wb/laVaxcAQ4DVgT5wgAedczN9rCm3qgBvB0Z+RQGTnHNhO7QxjFUGpnptCGKA951zn/tbUq6NAMYHGqFbgBt8rud/hOWwTBERyb1w7dIREZFcUuCLiEQIBb6ISIRQ4IuIRAgFvohIhFDgi4hECAW+iEiEUOCLiESI/wcEU8dlLP61qgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy import signal\n",
"import matplotlib.pyplot as plt\n",
"\n",
"w0, mag0, phase0=signal.bode(([],[-3+10j,-3-10j],3))\n",
"w1, mag1, phase1=signal.bode(([],[-1+10j,-1-10j],3))\n",
"\n",
"w = w0*np.pi*2/len(w0)\n",
"\n",
"\n",
"fig = plt.figure()\n",
"plt.plot(w,mag0, color='red')\n",
"plt.plot(w,mag1, color='blue')\n",
"\n",
"fig = plt.figure()\n",
"phase0=np.array(phase0)*np.pi/180\n",
"phase1=np.array(phase1)*np.pi/180\n",
"plt.plot(w,phase0, color='red')\n",
"plt.plot(w,phase1, color='blue')\n",
"#plt.semilogx(w,phase1, color='blue')\n",
"\n",
"fig = plt.figure()\n",
"theta = np.linspace(-np.pi,np.pi,201)\n",
"\n",
"plt.plot(13*np.cos(theta),13*np.sin(theta))\n",
"plt.scatter(np.real(-3+10j),np.imag(-3+10j), color='red')\n",
"plt.scatter(np.real(-3-10j),np.imag(-3-10j), color='red')\n",
"plt.scatter(np.real(-1+10j),np.imag(-1+10j), color='blue')\n",
"plt.scatter(np.real(-1-10j),np.imag(-1-10j), color='blue')\n",
"plt.axes().set_aspect('equal')\n",
"plt.axvline(x=0, color = 'black') # draw x =0 axes \n",
"plt.axhline(y=0, color = 'black') # draw y =0 axes\n",
"10.**(mag[0]/10.)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.0007692307692307697"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from scipy import signal\n",
"import matplotlib.pyplot as plt\n",
" \n",
"w0, mag0, phase0=signal.bode(([-3+10j,-3-10j],[0],3)) #red\n",
"w1, mag1, phase1=signal.bode(([-1+10j,-1-10j],[0],3)) #blue\n",
"\n",
"w = w0*np.pi*2/len(w0)\n",
"\n",
"\n",
"fig = plt.figure()\n",
"plt.plot(w,mag0, color='red')\n",
"plt.plot(w,mag1, color='blue')\n",
"\n",
"fig = plt.figure()\n",
"phase0=np.array(phase0)*np.pi/180\n",
"phase1=np.array(phase1)*np.pi/180\n",
"plt.plot(w,phase0, color='red')\n",
"plt.plot(w,phase1, color='blue')\n",
"#plt.semilogx(w,phase1, color='blue')\n",
"\n",
"fig = plt.figure()\n",
"theta = np.linspace(-np.pi,np.pi,201)\n",
"\n",
"plt.plot(13*np.cos(theta),13*np.sin(theta))\n",
"plt.scatter(np.real(-3+10j),np.imag(-3+10j), color='red')\n",
"plt.scatter(np.real(-3-10j),np.imag(-3-10j), color='red')\n",
"plt.scatter(np.real(-1+10j),np.imag(-1+10j), color='blue')\n",
"plt.scatter(np.real(-1-10j),np.imag(-1-10j), color='blue')\n",
"plt.axes().set_aspect('equal')\n",
"plt.axvline(x=0, color = 'black') # draw x =0 axes \n",
"plt.axhline(y=0, color = 'black') # draw y =0 axes\n",
"10.**(mag[0]/10.)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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