diff --git a/recursive_filters/quantization_of_coefficients.ipynb b/recursive_filters/quantization_of_coefficients.ipynb index 0fd12b2..25b7ca2 100644 --- a/recursive_filters/quantization_of_coefficients.ipynb +++ b/recursive_filters/quantization_of_coefficients.ipynb @@ -62,7 +62,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 64, "metadata": {}, "outputs": [ { @@ -108,6 +108,7 @@ "\n", " return p\n", "\n", + "\n", "def plot_pole_locations(p, Q):\n", " ax = plt.gca()\n", " for n in np.arange(np.ceil(2/Q)+1):\n", @@ -256,12 +257,12 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 59, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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c3cCVwE6gFLjSOff/2qsw6bp69OpL9vXvsSJ+JGMW/4z5T9+hm9SLiIjQ+uu4fQ18AiwGUszs+LYvSQRS0roz+Ka3mJ8ylXFrH2XBY9/HNeo2WSIi0rUFHNzM7Grgv8A7wC/8z3e1T1kiEBeXQP6PX+CTnt9h3LYXWPjodBq93lCXJSIiEjKt2eJ2AzAWWOecmwKMAra3S1UiflEeDxOueYw5fa5i7I5/8ukjF9HgrQ91WSIiIiHRmuBW45yrATCzOOfcKmBw+5QlspdFRTHx6geY0+8H5Je9y2cPfZv6uppQlyUiItLhWhPciswsHXgV+LeZvQZsap+yRPZlZhx95a+Zc/hPGF35ISseOpvaml2hLktERKRDBRTczMyA651zpc65u4CfA08AZ7djbSIHOPrSO5k79A6OqvqErx46nZqqilCXJCIi0mECCm7Odyf6V5u8/9A597pzrq6Fj4m0iwnfuYV5I/6PodWL+fqh06iq2BnqkkRERDpEa3aVzjWzse1WiUgrjD/3ehbl38fA2uVsePg0KkpLQl2SiIhIu2tNcJsCfGJma8zsczNbamaft1dhIocy7owZLJnwW/rXfcmWR0+hvGRbqEsSERFpV9GtGHtau1Uh8g3ln3Y5i2NiGfbRdWz8/Uk0XPM23Xr0DnVZIiIi7aI1t7xa19yjPYsTCcSoqReyasrj9PJuovwPJ1OyeX2oSxIREWkXrb3llUhYOmryuaw5+SkyG7ZR9fgpbCtaE+qSRERE2pyCm3QaRx7zLdZ/61nSG3fS8MSpbC5cFeqSRERE2pSCm3QqQ8edxMaznifR7SLqqWlsXLM01CWJiIi0mdbcZD7OzC42s5+a2Z27H+1ZXJNl/8jMvjCz5WZ2X0csUyLXkNGT2H7uS8RQT8Iz01i95L+hLklERKRNtGaL22vAWYAX2NXk0a7MbIp/uSOcc0cAM9t7mRL5Dh8xkYqL/kkN8fR+5TyWffhiqEsSEREJWmsuB5LjnDu13So5uGuBe5xztQDOOV2sSwLSb/BIts34D5ueOIvB789gUekWxpx1XajLEhER+cbMdzerAAaaPQ484pzr0IOGzGwJvq19pwI1wM3OuQXNjJsBzADIysoaM2vWrHavrbKykuTk5HZfTmfWET2sq95F5oJfM7pxKf9KvYC4kRdhUZ3j8E6tg8FTD4OnHgZPPQxeJPdwypQpi5xz+YGMbU1wWwEMBNYCtYDhu43piG9aaJPvfg/IbmbWHcDdwPvADcBY4HngMNdC4fn5+W7hwoXBlnVIBQUFTJ48ud2X05l1VA9ra6tZ8rvpjC9/h8XJkxhyzTMkJKe1+3Lbm9bB4KmHwVMPg6ceBi+Se2hmAQe31uwqPRV/WPtGVbXAOTf1YPPM7FrgZX9Qm29mjUAmsL2t65DOKy4ugXE/nsXsZ3/BhNW/Zd2Dx5N4+fNk9xsS6tJEREQCdsj9RWb2sf/lcmApsMz/WO5/bm+vAif4axkExALFHbBc6WQsKopjLvsFSyf/mUzvNuL/MpUVs18PdVkiIiIBO2Rwc84d639Occ6lNnmkOOdS279EngQOM7NlwCxgeku7SUUOZeSU89h5yb8otTSGvHs585+4kQZvfajLEhGRcOOtDXUFBwj7I7Sdc3XOuUudc0c650Y7594PdU0S+foNOorMm+awIP00xm14ktX3Hs+2DV+FuiwREQknz5wDz10U6ir2EfbBTaS9JKekMf7G55g3+j761H1N/BOTWPL2k6ANuiIi4hxsWQYpzZ07GToKbtLljT/z++y47D9sis5h5LwbWfKbM9ixZX2oyxIRkVAqXQ+1ZZA9PNSV7KPVwc3MkszM0x7FiIRK38OPYMCtHzP7sBsYUjGX6Mcm8Onrv8M1Noa6NBERCYWt/vMvsyIsuJlZlP8epW+a2TZgFbDZf9/Q+81sYPuXKdL+YmJiOebyX7Ll4v9QFJ3H6E9/yop7p7Bh1aJQlyYiIh1ty1LAIGtYqCvZRyBb3D4ABgC3A9nOuVznXE/gOGAucI+ZXdqONYp0qLzBRzH49o+YM/h2cmq+otdzU1nw2Awqy0pCXZqIiHSULUshYwDEJoW6kn0EcgHeqc65A66V4JzbAbwEvGRmMW1emUgIeTwejr7oNrZvvYwVs25j/OYXKH3wbRYNv4GjzvgR0bFxoS5RpHNYPxfmPQZxKZDQDeLTISG9yetue9/HpkAnuV2dhLmGeij8GAZPC3UlBzhkcGsa2sws2jnnbfK+r3NufXPBTqQz6JHVhx43PMPKTz+i8a1bGbP0/yha/mdKxt3CiJOnY1E63FMkKMtehuWvQnJPqN4JDXUHH2tREJ/WfKhrKfDFp0NMAph13O+SyLb2Q6gphWFnhrqSAwR0yysz+x5wM5BqZgnAp8BPgd8Do9uvPJHwMHT0cbiRH7PwvVl0n3sPR829kTULH6X66Fs4YvIFneam9SIdrqEWknrAzV/6Lr9QX+37g1m9E6pL931dvdP/vsnrnV/vHedaOJnIE3tgqItPh/hUXxjc/Yjb7/3uadGxHdcTCb0Vr/i28B42JdSVHOCQwc3MbgXygUnOuS3+aScDfwL6tm95IuHDoqLIP/livFPOZ+4bj5P72W8Z8N/vUzj715SN+RHDT76CqOjW3P5XRPDWQbT/0AMziE30PVJ7t+57GhuhrmK/gNdC+CvfCNtWQE051Ja3HPoAohOahLnUgwS9VH8YbGZ6TKK2+EWKnYXw+Qtw1IUQEx/qag4QyF+ZK4HhTXeHOufeNbOp+La4iXQp0TExTDjnh9RO+y5z33qC7M9/z1Hzf8LGhTPZOuIahp/2fWLiEkJdpkhkaKjzbQ0LVlTU3qDUrV/rPtvYCHWVvgBXU+Z/NHldW3bg9Kodvj/wu6e3tIsXICr6IEEvDeLSyNtcArHLfMf6xaX4xu153eShwzPaV2MDvHWL75/X5NtDXU2zAto8cJCTE7aa2SNtX5JIZIiLi2fCOT/Ee8b3mf/us6QvepjRS/6XHUseYE3f8xkw7Xq6Z7fyD4hIV9NQu3eLW6hERflDVCqk5Xyz76ivaRL0yn1b9Q4IgPsFw+LV/ukV5NVVwLpZh15ObHLzga7ZoJd68ADo0TmFB/DWwhs3wlfvwGn3t36rbwcJJLitMbNvOefebDrRzH4J3AEo/kuXFh0dzbhp02k85TI+/e+rMO+PjFn3BA1/+AuL0yaTOvmHDBh1gnaTiDTHW9c5QkRMvO+RkvWNPl7wwftMnpgPtRVNHv7duPtMqzhwWuW2facfarcv+Hb9Nhf0YpMgLtn3HLv7ef/XKU1e++dF8jGA3lpY9QYU3AvFX8CkW2H8jFBXdVCBBLcf4LvkxxXAZ0AyMA1YAnzRfqWJRJYoTxSjp5wLU86l8KtlbHz3EYZve53U1/9D4Zt5FA88n0EnfZfUjF6hLlUkfDTUgkeX1/GdMevf6hcM56C+yn/s3kGC3sGmla7z7TKu2+V71FcFvtyoGH/oaybU7fN69/tEX3iMjvOd8Rsdv/c52h+CoxP2PkfHBfc/v875flNVie9Ruh62fwFF82HdHN9vzRgIF/8DBp38zZfTAQK5HMg6MxsLnAIMBcqBS51zn/tPXBCR/eQNPJK8gX+krOxeZr/9J7p/9Q/yV91P3coH+Cz1WGLGXsaQo88mKroTbGkQCUZDfeh3lXYmZnuDEkH+T2Jjgy/Q1O2C2sp9Q90+ryuavG4yr7YSqjbsFwZ3ffN6doe66Dgwj+94P4vyP3sYW10DK/zBt6HO/6j3PddVgrfmwO/MHASjLoVBp/jOII2AYwgDOavUnHMO+Jf/sYdz7t79xohIE2lp6Rxz4f/g3M18sXQ+2z96gqHb3ybj/Q/Z/sEtrOt1Gj0mXky/I4/RrlTpmry1vgP0JfxEefbuRk1po+9sbPSFt7oq8Fb7jg30+h/11U2ea5vM32+ctxZcg++7XIMvYLoGqrZuIal7hm85nlj/I8b3HJsIiZmQlAmJGb7j1zIG+qZHmEB2lX5gZi8Brznn1u+eaGaxwLHAdHy3xXqqPQo0s5HAY0A84AV+4Jyb3x7LEmkvZsbgEeMZPGI8NTXVzH//BaI//zsjNs4i9qVn2fhKLzblTKPPsZfSe5AujShdSDicnCAdJypqbxhsY8sLCpg8eXKbf2+4CSS4nQpcBTxnZv2BUiAB331O3wUedM4tab8SuQ/4hXPubTOb5n8/uR2XJ9Ku4uMTGDdtOkybzvZtm/my4DmSV7/O6HVP4ln/BIWefmzPOYnscd8mZ+gEXdxXOrfOcnKCSAcJ5Bi3GuD3ZvYHYCy+LV9LnXM727u43SUAu4/WTAM2ddByRdpdj5696HHBTcBNbN64njUf/o1ua99gdOETeNb9ma2WSVGPyaSMPJMBY0/FE6MtE9LJNNTp5ASRVrBAD00zs1eBHGADMAyYDVznnGvFaSetZ2ZDgXcAw7eV72jn3Lpmxs0AZgBkZWWNmTUrgOvhBKmyspLk5OR2X05nph42r7JiJ3XrF9Brx3xGej8jweood4ksjxvJzowxxOaMJjqpu/rXBtTD4AXTwwmfXMXObqP4YsiP2riqyKL1MHiR3MMpU6Yscs7lBzK2NcFtNXAJsNg5V2dmV+G7Ddb0b17qnu9+D8huZtYdwInAh865l8zsAmCGc25qS9+Xn5/vFi5cGGxZh1TQRfantyf18NDKK8pZNfufNKx8g0Fls8mgDIDC6P6siR9O7jHfYcCYqXhiw+/WLJFA62DwgurhfQNg2Flw+gNtWlOk0XoYvEjuoZkFHNxac2PFe4BbgaPMrApYCkwys5OAJc657a0v1aelIGZmTwM3+N/+A/jzN12OSCRKTUll3KmXwKmX4PV6Wf7ZJ+z47G3SNn/EcRVvEvvO61S/E8uaxJHU9ZtC9siT6DVwNBYBp7WLtNktr0S6iNYEtzOA55xz55pZGnAUcAJwIb5QN6Yd6gPfMW2TgAL/8r5qp+WIhL3o6GiOGHMcjDkOgLfffouMqFLqvniP3B2f0G/lvbDyXspIZl3yUXhzj6Hn8BPpMzgf87TmX3eRDtJQF9lX3RfpYK35L/nVwF/M7HZgGTAY+Jdz7rvtUtle3wN+a2bRQA3+49hEBBISEhk3eRqccjHOOQrXfsHGJe9h6z4mt3wxuStnw8r7qCCRwqSR1OVMJGPIseQeMRFPbEKoy5euzjnfNbl0coJIwAIObv5doaebWW9gOFDmnJvbbpXtXe7HtN/WPJFOw8zIGzCEvAFDgOtwzrGu8Cs2Ln4P1s0mp2wRfb+YA1/8hrpXo/k67nDKMkYS138iuSMmkZbdP9Q/QbqaRi/gtMVNpBVave/EObcJXZJDJOyZGf36D6Jf/0HAD3DOsWFDIRuXfkj9uvl027GEIza9RPzmWTAHtlsGm1KG09A7n/QB48gZNp7YpPRQ/wzpzLy1vmcd4yYSMB30ItJFmBm5ffuT27c/cAUAVdXVfL50LqVfziZu80JyypfRp7wAVkHjG0aRpzfFqUNpzB5J+mFj6XPEeOKSuoXyZ0hn0lDne9auUpGAKbiJdGGJCQmMGDcFxk0B8G2VK1rPppWfULN+EYnFy8gpXUyv0vdgFfAWbIzqTXHKUBqyjyK530j6DM4nqXtv3WtVWm93cNOuUpGAKbiJyB5mRm5uP3Jz++E7YdwX5oqKNrBp5Vyq1y/whbmyJfQq+w98AbwLpaSyOX4AVd0GE9N7ON0PG0Wvw0fiiUsK6e+RMLdnV6m2uIkESsFNRFpkZuTk9iUnty9wAeALcxs3bWTLV5+ya8NneLavoHvlVwzb9DIJm2fBImhwRlF0b3YkDaQ+YwgJvYeS0X8EPfsNw2J0sWChya5SbXETCZSCm4i0mpnRp08OffrkAGfumV5TW8eXa1ZQvOZT6jctI3HnKrLLV9Gn7EOivnYw2xfotnp6sSMxj7puA4nJGkJ6vyPJPmw4MTp+rmvZvcVNu0pFAqbgJiJtJj4ulkHDRjJo2Mg905xzlJSWsmn1Uso3LKNh2xcklK0hY1chgyrmEbuhAfx3qCu27hTH51Gd2h/LOJykXoPI6DuUbn0Ox6K1O63T0ckJIq2m4CYi7crMyOzWjcyxx8PY4/eZV1ldw5qPQ3+qAAAZHElEQVQ1K9i5bhl1W1YSu/MrulcVcviWt0jZWg0rfOManLHd05Md8bnUpuRhGQNI6jWQjL7DFOoimU5OEGk1BTcRCZnkhHiGHjkajhy9z/R6bwPrN29k+/qV7Nr0Ba5kLXHlX9OtZgOH71rebKjbGZ9LTXJfrFs/4nrkkdZrIJk5A4lN7aEzXsOVTk4QaTUFNxEJOzHRHvrm9qVvbl/glH3m1XsbWLd5I8X+UNdYsob48kLSazaQt2sV3bZV+s529asinuLoLCrie1OXkot160dCj/6k9z6czJxBHfvDZF86OUGk1RTcRCSixER76Jfbl37NhDpvQyMbt2+juGg1lVvWUFfyNZ6yDSTsKiJ91yb6ViwhZXP1Pp8ZQyKFs3uxKz6b+qTekNaHuIy+pPTsR/deh5GYmQuemA78hV2IdpWKtJqCm4h0GtGeKPpkZ9MnOxs49oD5dfUNrN+6mZKir6jcuhZvydfUbf2SDLeD9MoN5JYvJnVL1T6facTYad0oi+lJVUI23uQ+RKX7wl1qVh7de/cnLq0XRHk66Fd2ItpVKtJqCm4i0mXExnjom5ND35wcwHe3iIKCAvInTwagvqGRou3F7Nj8NZXbCqkr2YArLyKmchNJNVtJL/uSrNJPSNxYu8/3evFQEpVBRUwPauJ74E3KJiq1FzHpvUnMyCEtqy9pPfpg8ek63q4pbXETaTUFNxERvxhPFDnZPcnJ7gmMb3ZMda2Xwm2b2bm5kMrthdTvKMLKi4jdtZnE2u2klX1FZuk8UjdVH/DZGmLZ6cmgMiaT2oSeewJeXHofkjL7kNYzl+TMHCw+tX1/aLjQTeZFWk3BTUSkFRLiosnLzSUvNxc4rtkxNfUNFJXsYOe29VRuL6J250YayjcRVbmN2OqtJNUVk169gp47PibRag/4fBXxlHm6sSsmg9q4DBoSekByDzypWcSnZ5Oc0Zu0zD7Ep2dDXHI7/+J2pOu4ibRaWAQ3MzsfuAsYCoxzzi1sMu924LtAA3C9c+6dkBQpIhKg+BgPOdk9yMnuAYw56LhdNfUU7iihdOt6dhVvoHbnZhrLN+Gp3EJsbTGJdTtIrVlDt9JFdLfKZr+jmjjKPd3YFd2dmnhfyHPJPYhOySIuvRfJGb2ahLyU8NpVq12lIq0WFsENWAacC/yx6UQzG4bvTtdHAL2B98xskHOuobULqK+vp6ioiJqamraoF4C0tDRWrlzZZt/XGcTHx5OTk0NMjM7CEzmUpPgYknpnQ+9sYNxBx9V5G9lcXknp9s1U7thE9Y7N1JdvwVVuI6qqmNgaX8hLKSukZ+lndKeCKHMHfg/RlEelUeVJpya2G/Vx3WlM6I4lZRKd0oO41B4kdssiOSObxLSeWGJG+550oZMTRFotLIKbc24l+K6wvp+zgFnOuVrgazNbje+/bp+0dhlFRUWkpKSQl5fX3HK+kYqKClJSUtrkuzoD5xwlJSUUFRXRv3//UJcj0mnERkfRq3sqvbqnAoNbHFvnbWRrxS5Kt2+hsmQjVTu3UF/mC3lWvYOY2h3E1+0gsaqM1MoNdKOCVKtq9rsaMSoshV2eVKpjulEX143G+AxcUiaepAxiU3uSkJ6FZ8dmGnceRlRSBsQkBr5VT9dxE2k1c+7A/ysLFTMrAG7evavUzB4F5jrn/uZ//wTwtnPuxWY+OwOYAZCVlTVm1qxZ+8xPS0tjwIABbRbaABoaGvB4dAmAppxzrFmzhrKysoDGV1ZWkpwcwcfohJj6F7yu3EPnHDUNsKumjvrqchqqy3A1ZUTVleOpKye2vpx4bxmJDRUkN5aT6srpRgXdqCDaGpv9zlpiqCCZyqgUqqJSqPYkUxedQn1MCg0xqTTGpUBsClHxqRxe8j59tr3Pfye93MG/PPx05fWwrURyD6dMmbLIOZcfyNgO2+JmZu8B2c3MusM599rBPtbMtGaTpnPuceBxgPz8fDfZf3r/bitXriQ1tW3P1NIWt+bFx8czatSogMYWFBSw/z8rCZz6Fzz1sHVq6hvYvquG0pJiKndupbp0K+u+/JyeydFQvYOomp3E1JYSV19GoreM9PoiUqmgG5XNhr0yl8Stc7x0S4wlLSGGbomxdEuKIT0xlnT/+/TEGLol+d6n+9/HeKJC8Ovbj9bD4HWVHnZYcHPOTf0GHysCcpu8zwE2tU1FkamwsJA5c+Zw8cUXA7Bw4UKefvppHn744RBXJiJdQXyMh17pSfRKTwL6AVAQndLiH8xabwMlu+ooL91BZelWasq2U1tejLeyhC1kMim6B6VV9ZRW1bNmeyU719VTWlWHt/Hge4SS46JJS4ghNSGGtATf6/0fqXvm7/vobKFPupawOMatBa8DfzezB/CdnDAQmB/akkKrsLCQv//973uCW35+Pvn5AW1dFREJibhoD1lpCWSl9YF+fQL6jHOOXXUN7NxV5wt11XXsrPIFup27fO/Lquspr66nvNpLYXEVZdX1lFXXU13f8vlribGefcJdc6Fv3/nRe8bFRevwGAmtsAhuZnYO8AjQA3jTzJY4505xzi03sxeAFYAX+OE3OaM0nDz99NPMnDkTM2PEiBH86le/4qqrrmL79u306NGDv/zlL/Tt25crrriC1NRUFi5cyJYtW7jvvvs477zzuO2221i5ciUjR45k+vTpjBo1ipkzZ/LGG29w1113sX79etauXcv69ev58Y9/zPXXX09hYSGnn346y5YtA2DmzJlUVlZy1113sWTJEq655hqqqqoYMGAATz75JN26dWPy5MnMnDmT/Px8iouLyc/Pp7CwkOXLl3PllVdSV1dHY2MjL730EgMHDgxxV0WkszEzkuOiSY6LJrd76z5b622gvNq7J8iV+58P9tiwo4rl/te76lr+ExMfE7U31MX7gl1KfDSp8f7nZt6n7nkfQ3xMVJseay1dT1gEN+fcK8ArB5l3N3B3Wy7vF/9czopN5UF/T9OTE4b1TuV/zziixfHLly/n7rvvZvbs2WRmZrJjxw6mT5/O5ZdfzvTp03nyySe5/vrrefXVVwHYvHkzH3/8MatWreLMM8/kvPPO45577tkT1MC3T7+pVatW8cEHH1BRUcHgwYO59tprW6zp8ssv55FHHmHSpEnceeed/OIXv+Chhx466PjHHnuMG264gUsuuYS6ujoaGiI6R4tIJxQX7aFHioceKa2/zEh9Q2OzQa+5aRU1XrZV1LBmu5dy//uWdu8CxHiMlPj9wl18DLtKa/mocsVBQ+DuaSnx0URrV2+XFhbBrat4//33Oe+888jMzASge/fufPLJJ7z8su+Mqssuu4xbbrllz/izzz6bqKgohg0bxtatWwNaxre+9S3i4uKIi4ujZ8+eLX6urKyM0tJSJk2aBMD06dM5//zzW/z+iRMncvfdd1NUVMS5556rrW0i0qnEeKLISI4jI7n1oc85R3V9AxU1viBXXuOlvKZ+z/uKGi8VNfUHTFtbXElxWQOfbl9/yC1+4NvV29IWPl/A823pS47zvfY9+x5JcdE6zi+CdcngdqgtY4Fq7VmlzrlDbiJvOj8ubu9/OAK9bEvTz3g8HrxeL9HR0TQ27j2bK5CLEDf9TNPxF198MePHj+fNN9/klFNO4c9//jMnnHBCQLWJiHRmZkZibDSJsdFkpca36rO7z4j0NjRSWeulosa7Z6ueL+z5n6v3C3819ezYVUdh8a497+sbDv33Ij4myrflLy6aZH+g8+2a3rtlb0/oi48mxR/8kvcLg54o7fbtaF0yuIXKiSeeyDnnnMONN95IRkYGO3bs4Oijj2bWrFlcdtllPPvssxx77LEtfkdKSgoVFRWtWm5WVhbbtm2jpKSE5ORk3njjDU499VTS0tLo1q0bH330EccddxzPPPPMnq1veXl5LFq0iHHjxvHii3svm7d27VoOO+wwrr/+etauXcvnn3+u4CYi0kaiPVH+S57E7nNJhUA556j1+nb3VtR6qazx+oOgL+jtDoW7nytq6qn0jyuuqNoztrLWyyH2+gK+rX97Qp8/CO59H91sONy9RXD3mOTYaKIUAAOm4NaBjjjiCO644w4mTZqEx+Nh1KhRPPzww1x11VXcf//9e05OaMmIESOIjo7mqKOO4oorrgjoemkxMTHceeedjB8/nv79+zNkyJA98/7617/uOTnhsMMO27P8m2++mQsuuIBnnnlmn2D2/PPP87e//Y2YmBiys7O58847v2E3RESkrZkZ8TEe4mM89Azie5xzVNU1+EPe7i1/3j0hr7xJ4NsTBP2hb2t5zT4BMRC7T0RpulUvtUm4O1jo2x0Kk+OiaQyjGwq0p7C6c0Jbyc/PdwsXLtxn2sqVKxk6dGibLkcX4G1ea3rdVS6Y2F7Uv+Cph8FTD4PXWXvY2OjYVXfwrXwVNd49Wwb3TK/1Ul7jpdL/vqLGS1UAx/5B8wGw6W7g/cPe3t3CMXumhWIXsJmF350TREREpGuJitp9Fm1MUN/jbWhkV13Dnl2+u2q9++wKrqzxsuyL1WRk5+wTACtqvGwuq9k7LsAtgImxHob2SuUnJw3i6MMzg6q9rSm4iYiISFiL9kSRluC7ht7BFDSuZ/LkYS1+z+4tgHt3+e59vXuXcGWtl/JqL68sLuLRD1YruImIiIiEwj5bANNaHvt1cSXbK2s7prBW0IVcRERERPaTmhBDRU1gu1Y7koKbiIiIyH5S42Mor64PdRkHUHATERER2U9KfDTlNd6AL4DfURTcOpmHHnqIqqqqPe+nTZtGaWlpUN9ZUFDA6aefHmxpIiIiESM1IYaGRt9tzMKJglsns39we+utt0hPTw9hRSIiIpEn1X8Jk/Lq8DrOTcGtg919990MHjyYqVOnctFFFzFz5kwmT57M7gsGFxcXk5eXB0BhYSHHHXcco0ePZvTo0cyZMwfYe6HG8847jyFDhnDJJZfgnOPhhx9m06ZNTJkyhSlTpgC+W1cVFxfz2GOPMXLkSEaOHEn//v33zH/33XeZOHEio0eP5vzzz6eyshKAf/3rXwwZMoRjjz2Wl19+uYO7JCIiElop8b4Lb5TXhNdxbmFxORAzOx+4CxgKjHPOLfRPPwm4B4gF6oD/cc69H/QC374NtiwN+msSGrzg8bcwezicdk+L4xctWsSsWbNYvHgxXq+X0aNHM2bMmIOO79mzJ//+97+Jj4/nq6++4qKLLtoT8BYvXszy5cvp3bs3xxxzDLNnz+b666/ngQce4IMPPiAzc9/rzlxzzTVcc8011NfXc8IJJ3DTTTdRXFzMr371K9577z2SkpK49957eeCBB7jlllv43ve+x/vvv8/hhx/Od77zneAaJSIiEmFSE3ZvcVNwa84y4Fzgj/tNLwbOcM5tMrMjgXeAPh1dXFv56KOPOOecc0hMTATgzDPPbHF8fX091113HUuWLMHj8fDll1/umTdu3DhycnIAGDlyJIWFhYe8QT3ADTfcwAknnMAZZ5zBG2+8wYoVKzjmmGMAqKurY+LEiaxatYr+/fszcOBAAC699FIef/zxb/SbRUREIlGqf4tbuF0SJCyCm3NuJfhujrvf9MVN3i4H4s0szjkX3BXxDrFlLFDV3+Bepfv/RoDo6GgaGxsBqKmp2TP9wQcfJCsri88++4zGxkbi4+P3zIuLi9vz2uPx4PUeesV66qmnWLduHY8++ijgu4nwSSedxHPPPbfPuCVLljRbp4iISFex+zZd4barNJKOcfs2sDjo0BZCxx9/PK+88grV1dVUVFTwz3/+E/Adh7Zo0SIAXnzxxT3jy8rK6NWrF1FRUTzzzDM0NBz6zJaUlBQqKioOmL5o0SJmzpzJ3/72N6KifP/YJ0yYwOzZs1m9ejUAVVVVfPnllwwZMoSvv/6aNWvWABwQ7ERERDq71AT/MW5ddVepmb0HZDcz6w7n3GuH+OwRwL3AyS2MmQHMAMjKyqKgoGCf+Wlpac0GmmA0NDS06jsHDhzI2WefzYgRI8jNzWXChAnU1tZy7bXXMn36dJ566imOP/54nHNUVFRw+eWXc9lllzFr1iyOP/54kpKSqKiooKqqCq/Xu2fZdXV11NTU7PnMKaecQnZ2Nm+++SbOOSorK3nwwQcpKSlh0qRJAIwaNYpHH32U3//+91xwwQXU1dUB8POf/5xevXrx0EMPcdppp5GRkcHEiRPZuXNnwL+1pqbmgP4fTGVlZcBj5UDqX/DUw+Cph8FTD4PX1j2sa/Bdv+2zFV+SW1vYZt8bLAunC8uZWQFw8+6TE/zTcoD3gSudc7MD+Z78/Hy3+yD+3VauXMnQoUPbsFqo+Aa7Spu66667SE5O5uabb27DqkKvNb3efYasfDPqX/DUw+Cph8FTD4PXHj0c9LO3ufKYPG4/rW3zw/7MbJFzLj+QsWG9q9TM0oE3gdsDDW0iIiIibSE1PjrsruMWFicnmNk5wCNAD+BNM1vinDsFuA44HPi5mf3cP/xk59y2EJXapu66665QlyAiIiIHkRofE3YnJ4RFcHPOvQK80sz0XwG/6viKREREpKtLSYjR5UBCyTmny1y0s3A6ZlJERCQYv7t4FPExnlCXsY+wPsatLcXHx1NSUqJg0Y6cc5SUlOxzvTkREZFIldMtkczkuEMP7EBdZotbTk4ORUVFbN++vc2+s6amRiFlP/Hx8Xvu6CAiIiJtq8sEt5iYGPr379+m31lQUMCoUaPa9DtFREREDqbL7CoVERERiXQKbiIiIiIRQsFNREREJEKE1S2v2oqZbQfWdcCiMoHiDlhOZ6YeBkf9C556GDz1MHjqYfAiuYf9nHM9AhnYKYNbRzGzhYHeW0yapx4GR/0LnnoYPPUweOph8LpKD7WrVERERCRCKLiJiIiIRAgFt+A8HuoCOgH1MDjqX/DUw+Cph8FTD4PXJXqoY9xEREREIoS2uImIiIhECAW3QzCzU83sCzNbbWa3NTM/zsye98+fZ2Z5HV9leAugh1eY2XYzW+J/XB2KOsOZmT1pZtvMbNlB5puZPezv8edmNrqjawxnAfRvspmVNVkH7+zoGsOdmeWa2QdmttLMlpvZDc2M0XrYggB7qHWxBWYWb2bzzewzfw9/0cyYTv13WcGtBWbmAX4HnAYMAy4ys2H7DfsusNM5dzjwIHBvx1YZ3gLsIcDzzrmR/sefO7TIyPAUcGoL808DBvofM4A/dEBNkeQpWu4fwEdN1sFfdkBNkcYL/MQ5NxSYAPywmX+XtR62LJAegtbFltQCJzjnjgJGAqea2YT9xnTqv8sKbi0bB6x2zq11ztUBs4Cz9htzFvBX/+sXgRPNzDqwxnAXSA/lEJxz/wV2tDDkLOBp5zMXSDezXh1TXfgLoH9yCM65zc65T/2vK4CVQJ/9hmk9bEGAPZQW+NetSv/bGP9j/4P1O/XfZQW3lvUBNjR5X8SB/5LtGeOc8wJlQEaHVBcZAukhwLf9u1ZeNLPcjimtUwm0z3JwE/27X942syNCXUw48+96GgXM22+W1sMAtdBD0LrYIjPzmNkSYBvwb+fcQdfDzvh3WcGtZc0l9P2TfSBjurJA+vNPIM85NwJ4j73/pySB03oYnE/x3XLmKOAR4NUQ1xO2zCwZeAn4sXOufP/ZzXxE6+F+DtFDrYuH4JxrcM6NBHKAcWZ25H5DOvV6qODWsiKg6dafHGDTwcaYWTSQhnbJNHXIHjrnSpxztf63fwLGdFBtnUkg66ochHOufPfuF+fcW0CMmWWGuKywY2Yx+ALHs865l5sZovXwEA7VQ62LgXPOlQIFHHj8aqf+u6zg1rIFwEAz629mscCFwOv7jXkdmO5/fR7wvtPF8Zo6ZA/3OwbmTHzHfUjrvA5c7j+rbwJQ5pzbHOqiIoWZZe8+BsbMxuH7b2NJaKsKL/7+PAGsdM49cJBhWg9bEEgPtS62zMx6mFm6/3UCMBVYtd+wTv13OTrUBYQz55zXzK4D3gE8wJPOueVm9ktgoXPudXz/Ej5jZqvxJfoLQ1dx+Amwh9eb2Zn4zrjaAVwRsoLDlJk9B0wGMs2sCPhffAfl4px7DHgLmAasBqqAK0NTaXgKoH/nAdeamReoBi7sTP+hbyPHAJcBS/3HFwH8FOgLWg8DFEgPtS62rBfwV/8VC6KAF5xzb3Slv8u6c4KIiIhIhNCuUhEREZEIoeAmIiIiEiEU3EREREQihIKbiIiISIRQcBMRERGJEApuIiIiIhFCwU1EREQkQii4iYgcgpnlmdlbZvaFmX1pZreHuiYR6ZoU3EREWmBmUfjuLfmYc24wMBzIN7MZoa1MRLoi3TlBRKQFZnYacLVz7ttNpvUCPnTODQpdZSLSFWmLm4hIy4YCnzWd4L9xeqqZxYamJBHpqhTcRERa1gAkN51gZgYkAt6QVCQiXZaCm4hIywqAaf6wtttJwKfOucbQlCQiXZWCm4hIC5xznwGLgV8CmFkW8ADw01DWJSJdk4KbiEgLzOw2IB/4mZmdAPwB6Af83szyQliaiHRBOqtUREREJEJoi5uIiIhIhFBwExEREYkQCm4iIiIiEULBTURERCRCKLiJiIiIRAgFNxEREZEIoeAmIiIiEiEU3EREREQixP8HSy8PBkIfg/QAAAAASUVORK5CYII=\n", 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\n", 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" ] @@ -288,6 +289,7 @@ "w = 16 # wordlength of filter coefficients\n", "N = 7 # order of filter\n", "\n", + "\n", "def uniform_midtread_quantizer(x, w, xmin=1):\n", " # quantization step\n", " Q = xmin/(2**(w-1))\n", @@ -302,13 +304,35 @@ " \n", " return xQ\n", "\n", + "\n", + "def zplane(z, p, title='Poles and Zeros'):\n", + " \"Plots zero and pole locations in the complex z-plane\"\n", + " ax = plt.gca()\n", + " \n", + " ax.plot(np.real(z), np.imag(z), 'bo', fillstyle='none', ms = 10)\n", + " ax.plot(np.real(p), np.imag(p), 'rx', fillstyle='none', ms = 10)\n", + " unit_circle = Circle((0,0), radius=1, fill=False,\n", + " color='black', ls='solid', alpha=0.9)\n", + " ax.add_patch(unit_circle)\n", + " ax.axvline(0, color='0.7')\n", + " ax.axhline(0, color='0.7')\n", + " \n", + " plt.title(title)\n", + " plt.xlabel(r'Re{$z$}')\n", + " plt.ylabel(r'Im{$z$}')\n", + " plt.axis('equal')\n", + " plt.xlim((-2, 2))\n", + " plt.ylim((-2, 2))\n", + " plt.grid()\n", + "\n", + " \n", "# coefficients of recursive filter\n", "b, a = sig.butter(N, 0.2, 'low')\n", "# decomposition into SOS\n", "sos = sig.tf2sos(b, a, pairing='nearest')\n", "sos = sos/np.amax(np.abs(sos))\n", "# quantization of SOS coefficients\n", - "sosq = uniform_midtread_quantizer(sos, w, xmin=2)\n", + "sosq = uniform_midtread_quantizer(sos, w, xmin=1)\n", "# compute overall transfer function of (quantized) filter\n", "H = np.ones(512)\n", "Hq = np.ones(512)\n", @@ -348,7 +372,7 @@ "* Decrease the word length `w` of the filter. What happens? At what word length does the filter become unstable?\n", "* Increase the order `N` of the filter for a fixed word length `w`. What happens?\n", "\n", - "Solution: The deviations from the continuous (desired) realization of the filter increase with decreasing word length. The filter with order `N=5` becomes unstable for `w = 10`. Increasing the order `N` of the filter for a fixed word length results also in instabilities. Consequently, for a high order filter also a higher word length is required." + "Solution: The deviations from the continuous (desired) realization of the filter increase with decreasing word length. The filter with order `N=5` becomes unstable for `w < 10`. Increasing the order `N` of the filter for a fixed word length results also in instabilities. Consequently, for a high order filter also a higher word length is required." ] }, {