Test interpolation angefangen

1 files changed, 389 insertions, 16 deletions

diff --git a/notebooks/FIR_mehrere.ipynb b/notebooks/FIR_mehrere.ipynb
index 710db99..cb4a968 100644
--- a/notebooks/FIR_mehrere.ipynb
+++ b/notebooks/FIR_mehrere.ipynb
@@ -204,7 +204,7 @@
     },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -232,7 +232,7 @@
     {
      "data": {
       "text/plain": [
-       "array([4, 1, 7, 5, 2, 8, 1, 0, 5, 9, 6, 1, 0, 9, 5, 5, 1, 2, 6, 5])"
+       "array([3, 6, 5, 2, 9, 9, 5, 9, 2, 1, 5, 8, 0, 5, 1, 6, 9, 9, 9, 8])"
       ]
      },
      "execution_count": 11,
@@ -274,8 +274,8 @@
     {
      "data": {
       "text/plain": [
-       "array([0., 0., 4., 1., 7., 5., 2., 8., 1., 0., 5., 9., 6., 1., 0., 9., 5.,\n",
-       "       5., 1., 2., 6., 5., 0., 0., 0.])"
+       "array([0., 0., 3., 6., 5., 2., 9., 9., 5., 9., 2., 1., 5., 8., 0., 5., 1.,\n",
+       "       6., 9., 9., 9., 8., 0., 0., 0.])"
       ]
      },
      "execution_count": 13,
@@ -297,7 +297,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 107,
+   "execution_count": 14,
    "id": "d51e107c",
    "metadata": {},
    "outputs": [
@@ -306,7 +306,7 @@
      "output_type": "stream",
      "text": [
       "System frequencies fs=10, T=0.1\n",
-      "Tap with amplitude=4, delay=0.7230000000000001\n",
+      "Tap with amplitude=4, delay=0.7250000000000001\n",
       "Creating filter of order N=15.0\n"
      ]
     },
@@ -316,13 +316,13 @@
        "<StemContainer object of 3 artists>"
       ]
      },
-     "execution_count": 107,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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LwJ7NrGmp1erLzK9l5vOtl/8N7Nj0wpbXs9r/IcDfAfuAxs4MKSnIB4Anl7w+RQODEiAidgFDwAM1l7KaT7FwUp6ruY7V/AYwA/xLa+jnsxHx8rqLWiozp4G/ZaF39hTwk8z8Wr1VXdCvZeZTsNDRAF5Tcz0v5k+Af6+7iJUi4npgOjO/W3ctL6akIF/t6RWN+wsZEa8Avgx8JDN/Wnc9S0XEe4CnM/No3bVcwCXAm4F/yswh4BfUOxxwntY48w3Aa4HtwMsj4v31VlW2iPgEC0OTd9Rdy1IRcSnwCeCv6q7lYkoK8lPAziWvd9CAt7RLRcQ2FkL8jsw8XHc9q7gWuD4ifsjC0NR1EfHFekta5hRwKjMX38kcYiHYm+TtwA8ycyYzzwKHgd+tuaYL+d+IuAKg9e/TNddznoj4IPAe4I+yeTe1/CYLf7C/2/qd2QE8FBGrPZ+hViUF+XeA10XEayPiJSxcYLq75ppeEAvPu/sccCIzP1l3PavJzP2ZuSMzd7Hw/3dfZjamN5mZPwaejIjFx6m/DXisxpJWcxJ4a0Rc2jrmb6NhF2SXuBv4YOvzDwJtPwhmM0TEbuAvgesz8//qrmelzDyema/JzF2t35lTwJtb52mjFBPkrYsiHwbGWfjFuSszH623qmWuBT7AQi/34dbHu+ouqkB/BtwREceANwF/U285y7XeLRwCHgKOs/A7VPtt3BFxEPg2MBgRpyLiQ8BtwDsi4vsszLq4rWH1/SPwSuDe1u/LP9dV34vUWARv0ZekwhXTI5ckrc4gl6TCGeSSVDiDXJIKZ5BLUuEMckkqnEEuSYX7f1AeGtKnD28BAAAAAElFTkSuQmCC\n",
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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -338,25 +338,25 @@
     "period = 1 / samp_rate\n",
     "print(f\"System frequencies fs={samp_rate}, T={period}\")\n",
     "\n",
-    "delay = 7.23 * period\n",
+    "delay = 7.25 * period\n",
     "ampl = 4\n",
     "print(f\"Tap with amplitude={ampl}, delay={delay}\")\n",
     "\n",
-    "order = 2 * np.floor(delay / period) + 1\n",
+    "order = 2 * np.floor(delay / period) + 1 #N\n",
     "print(f\"Creating filter of order N={order}\")\n",
     "\n",
-    "skip = np.floor(delay / period) - (order - 1) / 2\n",
+    "skip = np.floor(delay / period) - (order - 1) / 2 #M\n",
     "assert skip >= 0\n",
     "\n",
     "samples = np.arange(0, order + 1) * period - delay\n",
-    "h = ampl*(np.sin(samp_rate * samples) / (samp_rate * samples))\n",
+    "h = ampl*(np.sin(samp_rate * samples) / (samp_rate * samples)) #sinc\n",
     "\n",
     "plt.stem(h)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 110,
+   "execution_count": 15,
    "id": "c89c83ae",
    "metadata": {},
    "outputs": [
@@ -366,13 +366,13 @@
        "<StemContainer object of 3 artists>"
       ]
      },
-     "execution_count": 110,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -394,9 +394,382 @@
    ]
   },
   {
+   "cell_type": "markdown",
+   "id": "15f663c6",
+   "metadata": {},
+   "source": [
+    "#  Test Delay  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "afb9e748",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "System frequencies fs=10, T=0.1\n",
+      "Tap with amplitude=4, delay_freq=0.7250000000000001, delay_int=7\n",
+      "Creating filter of order N=15.0\n",
+      "samples_freq[-0.725 -0.625 -0.525 -0.425 -0.325 -0.225 -0.125 -0.025  0.075  0.175\n",
+      "  0.275  0.375  0.475  0.575  0.675  0.775]\n",
+      "samples_int[0 1 2 3 4 5 6]\n",
+      "h_freq[ 0.45411359 -0.0212347  -0.65442628 -0.84234293 -0.13316324  1.38324124\n",
+      "  3.03675078  3.95846335  3.63540672  2.24911074  0.55514326 -0.60966541\n",
+      " -0.84150972 -0.35358545  0.26669278  0.51334131]\n",
+      "h_ideal[ 3.10262780e-02  2.99830750e-02  2.88692595e-02  2.76870500e-02\n",
+      "  2.64388245e-02  2.51271158e-02  2.37546068e-02  2.23241246e-02\n",
+      "  2.08386353e-02  1.93012375e-02  1.77151562e-02  1.60837364e-02\n",
+      "  1.44104353e-02  1.26988161e-02  1.09525398e-02  9.17535764e-03\n",
+      "  7.37110346e-03  5.54368515e-03  3.69707648e-03  1.83530854e-03\n",
+      " -3.75389411e-05 -1.91734645e-03 -3.79996360e-03 -5.68121819e-03\n",
+      " -7.55692534e-03 -9.42289669e-03 -1.12749496e-02 -1.31089164e-02\n",
+      " -1.49206538e-02 -1.67060518e-02 -1.84610433e-02 -2.01816127e-02\n",
+      " -2.18638056e-02 -2.35037373e-02 -2.50976019e-02 -2.66416805e-02\n",
+      " -2.81323506e-02 -2.95660937e-02 -3.09395037e-02 -3.22492951e-02\n",
+      " -3.34923102e-02 -3.46655271e-02 -3.57660666e-02 -3.67911991e-02\n",
+      " -3.77383512e-02 -3.86051122e-02 -3.93892397e-02 -4.00886655e-02\n",
+      " -4.07015008e-02 -4.12260407e-02 -4.16607694e-02 -4.20043635e-02\n",
+      " -4.22556964e-02 -4.24138408e-02 -4.24780722e-02 -4.24478711e-02\n",
+      " -4.23229246e-02 -4.21031285e-02 -4.17885880e-02 -4.13796183e-02\n",
+      " -4.08767448e-02 -4.02807029e-02 -3.95924372e-02 -3.88131000e-02\n",
+      " -3.79440498e-02 -3.69868493e-02 -3.59432624e-02 -3.48152516e-02\n",
+      " -3.36049739e-02 -3.23147774e-02 -3.09471966e-02 -2.95049475e-02\n",
+      " -2.79909227e-02 -2.64081855e-02 -2.47599639e-02 -2.30496441e-02\n",
+      " -2.12807638e-02 -1.94570050e-02 -1.75821866e-02 -1.56602563e-02\n",
+      " -1.36952827e-02 -1.16914466e-02 -9.65303250e-03 -7.58441946e-03\n",
+      " -5.49007187e-03 -3.37453002e-03 -1.24240037e-03  9.01654268e-04\n",
+      "  3.05292479e-03  5.20666595e-03  7.35810667e-03  9.50246043e-03\n",
+      "  1.16349357e-02  1.37507466e-02  1.58451231e-02  1.79133223e-02\n",
+      "  1.99506380e-02  2.19524121e-02  2.39140447e-02  2.58310043e-02\n",
+      "  2.76988383e-02  2.95131833e-02  3.12697744e-02  3.29644561e-02\n",
+      "  3.45931908e-02  3.61520691e-02  3.76373182e-02  3.90453114e-02\n",
+      "  4.03725766e-02  4.16158043e-02  4.27718560e-02  4.38377715e-02\n",
+      "  4.48107764e-02  4.56882893e-02  4.64679278e-02  4.71475148e-02\n",
+      "  4.77250846e-02  4.81988877e-02  4.85673958e-02  4.88293061e-02\n",
+      "  4.89835454e-02  4.90292733e-02  4.89658850e-02  4.87930140e-02\n",
+      "  4.85105339e-02  4.81185596e-02  4.76174484e-02  4.70078001e-02\n",
+      "  4.62904572e-02  4.54665036e-02  4.45372638e-02  4.35043009e-02\n",
+      "  4.23694144e-02  4.11346372e-02  3.98022324e-02  3.83746893e-02\n",
+      "  3.68547189e-02  3.52452494e-02  3.35494203e-02  3.17705767e-02\n",
+      "  2.99122632e-02  2.79782166e-02  2.59723589e-02  2.38987898e-02\n",
+      "  2.17617778e-02  1.95657526e-02  1.73152954e-02  1.50151300e-02\n",
+      "  1.26701130e-02  1.02852236e-02  7.86555385e-03  5.41629729e-03\n",
+      "  2.94273859e-03  4.50242226e-04 -2.05575891e-03 -4.56977505e-03\n",
+      " -7.08627130e-03 -9.59967955e-03 -1.21044105e-02 -1.45948660e-02\n",
+      " -1.70654508e-02 -1.95105853e-02 -2.19247178e-02 -2.43023365e-02\n",
+      " -2.66379819e-02 -2.89262594e-02 -3.11618507e-02 -3.33395267e-02\n",
+      " -3.54541587e-02 -3.75007304e-02 -3.94743496e-02 -4.13702594e-02\n",
+      " -4.31838493e-02 -4.49106660e-02 -4.65464241e-02 -4.80870163e-02\n",
+      " -4.95285232e-02 -5.08672230e-02 -5.20996007e-02 -5.32223566e-02\n",
+      " -5.42324150e-02 -5.51269319e-02 -5.59033024e-02 -5.65591677e-02\n",
+      " -5.70924219e-02 -5.75012172e-02 -5.77839701e-02 -5.79393658e-02\n",
+      " -5.79663626e-02 -5.78641958e-02 -5.76323807e-02 -5.72707150e-02\n",
+      " -5.67792814e-02 -5.61584481e-02 -5.54088703e-02 -5.45314899e-02\n",
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+      " -5.17123024e-02 -5.29105853e-02 -5.39847788e-02 -5.49332105e-02\n",
+      " -5.57544922e-02 -5.64475214e-02 -5.70114826e-02 -5.74458468e-02\n",
+      " -5.77503715e-02 -5.79250997e-02 -5.79703582e-02 -5.78867552e-02\n",
+      " -5.76751777e-02 -5.73367882e-02 -5.68730201e-02 -5.62855740e-02\n",
+      " -5.55764119e-02 -5.47477517e-02 -5.38020613e-02 -5.27420517e-02\n",
+      " -5.15706699e-02 -5.02910910e-02 -4.89067105e-02 -4.74211357e-02\n",
+      " -4.58381763e-02 -4.41618356e-02 -4.23963006e-02 -4.05459318e-02\n",
+      " -3.86152529e-02 -3.66089403e-02 -3.45318117e-02 -3.23888155e-02\n",
+      " -3.01850186e-02 -2.79255956e-02 -2.56158163e-02 -2.32610339e-02\n",
+      " -2.08666732e-02 -1.84382181e-02 -1.59811995e-02 -1.35011830e-02\n",
+      " -1.10037565e-02 -8.49451808e-03 -5.97906349e-03 -3.46297419e-03\n",
+      " -9.51805147e-04  1.54892714e-03  4.03375648e-03  6.49727867e-03\n",
+      "  8.93416300e-03  1.13391635e-02  1.37071299e-02  1.60330187e-02\n",
+      "  1.83119032e-02  2.05389840e-02  2.27095991e-02  2.48192326e-02\n",
+      "  2.68635248e-02  2.88382803e-02  3.07394768e-02  3.25632727e-02\n",
+      "  3.43060149e-02  3.59642460e-02  3.75347103e-02  3.90143607e-02\n",
+      "  4.04003640e-02  4.16901060e-02  4.28811966e-02  4.39714734e-02\n",
+      "  4.49590059e-02  4.58420983e-02  4.66192922e-02  4.72893687e-02\n",
+      "  4.78513501e-02  4.83045006e-02  4.86483272e-02  4.88825791e-02\n",
+      "  4.90072479e-02  4.90225658e-02  4.89290044e-02  4.87272725e-02\n",
+      "  4.84183133e-02  4.80033015e-02  4.74836396e-02  4.68609537e-02\n",
+      "  4.61370892e-02  4.53141056e-02  4.43942707e-02  4.33800555e-02\n",
+      "  4.22741272e-02  4.10793427e-02  3.97987415e-02  3.84355384e-02]\n"
+     ]
+    },
+    {
+     "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": {
+      "text/plain": [
+       "<StemContainer object of 3 artists>"
+      ]
+     },
+     "execution_count": 19,
+     "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"
+    }
+   ],
+   "source": [
+    "samp_rate = 10\n",
+    "period = 1 / samp_rate\n",
+    "print(f\"System frequencies fs={samp_rate}, T={period}\")\n",
+    "\n",
+    "delay_freq = 7.25 * period\n",
+    "delay_int = int(np.floor(delay_freq/period))\n",
+    "ampl = 4\n",
+    "print(f\"Tap with amplitude={ampl}, delay_freq={delay_freq}, delay_int={delay_int}\")\n",
+    "\n",
+    "order = 2 * np.floor(delay / period) + 1 #N\n",
+    "print(f\"Creating filter of order N={order}\")\n",
+    "\n",
+    "skip = np.floor(delay / period) - (order - 1) / 2 #M\n",
+    "assert skip >= 0\n",
+    "\n",
+    "samples_freq = np.arange(0, order + 1) * period - delay_freq\n",
+    "print(f\"samples_freq{samples_freq}\")\n",
+    "\n",
+    "samples_int = np.arange(0,delay_int,1)\n",
+    "print(f\"samples_int{samples_int}\")\n",
+    "\n",
+    "h_freq = ampl*(np.sin(samp_rate * samples_freq) / (samp_rate * samples_freq)) #sinc\n",
+    "\n",
+    "#h_ideal = np.exp(-1j*delay_int*2*np.pi*samp_rate)\n",
+    "print(f\"h_freq{h_freq}\")\n",
+    "print(f\"h_ideal{h_ideal}\")\n",
+    "\n",
+    "t_freq = np.linspace(0, delay_freq + period, samp_rate)\n",
+    "t_int = np.linspace(0, delay_int + period, samp_rate)\n",
+    "\n",
+    "f_freq = np.sin(2 * np.pi * samp_rate * t_freq)#test Signal\n",
+    "f_int = np.sin(2 * np.pi * samp_rate * t_int)#test Signal\n",
+    "\n",
+    "f_shift_freq = np.convolve(h_freq , f_freq)[:len(f_freq)]#Faltung freq \n",
+    "f_shift_int = np.convolve(h_int , f_int)[:len(f_int)]#Faltung int \n",
+    "\n",
+    "\n",
+    "\n",
+    "#h_int = np.concatenate([np.zeros(delay_int-1), [ampl], np.zeros(3)])\n",
+    "#y1 = np.convolve(test.real, h_int)\n",
+    "plt.grid(True)\n",
+    "plt.stem(t_freq, f_shift_freq, linefmt=\"C0-\")\n",
+    "plt.stem(t_int, f_shift_int, linefmt='C1-')\n",
+    "plt.show()\n",
+    "plt.grid(True)\n",
+    "plt.stem(f_shift_freq, linefmt=\"C2-\", label='freq')\n",
+    "plt.stem(f_shift_int, linefmt='C3-', label = 'int')\n",
+    "#plt.legend(loc=\"upper left\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e5f23991",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
    "cell_type": "code",
    "execution_count": null,
-   "id": "68a63dbd",
+   "id": "f224987a",
    "metadata": {},
    "outputs": [],
    "source": []