Merge remote-tracking branch 'origin/master'

3 files changed, 1032 insertions, 0 deletions

diff --git a/notebooks/Test/FIRDelay.ipynb b/notebooks/Test/FIRDelay.ipynb
new file mode 100644
index 0000000..4576f88
--- /dev/null
+++ b/notebooks/Test/FIRDelay.ipynb
@@ -0,0 +1,181 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "acccd8cc",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np \n",
+    "from numpy.fft import fft,ifft,fftshift\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "bee9dae9",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "405fcd96",
+   "metadata": {},
+   "source": [
+    "# Delay as a Convolution System"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "7210e2de",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[0, 0, 0, 1]"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Create the FIR\n",
+    "D = 3 # Delay value\n",
+    "h = [0]*D+[1]\n",
+    "h"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "892c62dd",
+   "metadata": {},
+   "outputs": [
+    {
+     "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": [
+    "d = 3.3\n",
+    "k = np.linspace(-5,10,1000)\n",
+    "h_ideal = np.sinc(k-d)\n",
+    "plt.plot(k,h_ideal)\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "c640e03e",
+   "metadata": {},
+   "outputs": [
+    {
+     "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": [
+    "n = 4\n",
+    "window_sample= np.arange(np.round(d-(n-1)/2),np.round(d+(n+1)/2))\n",
+    "window = []\n",
+    "for ws in window_sample:  \n",
+    "    idx = (np.abs(k-ws)).argmin()\n",
+    "    window.append(idx)\n",
+    "    \n",
+    "plt.plot(k,h_ideal)\n",
+    "plt.plot(window_sample,h_ideal[window],\"*\")\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "17a5bf03",
+   "metadata": {},
+   "outputs": [
+    {
+     "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": [
+    "n = 4\n",
+    "window_sample= np.arange(np.round(d-(n-1)/2),np.round(d+(n+1)/2))\n",
+    "window = []\n",
+    "for ws in window_sample:  \n",
+    "    idx = (np.abs(k-ws)).argmin()\n",
+    "    window.append(idx)\n",
+    "\n",
+    "    \n",
+    "fig = plt.figure()\n",
+    "\n",
+    "plt.plot(k,h_ideal)\n",
+    "plt.plot(window_sample,h_ideal[window],\"o\")\n",
+    "plt.xlim(-5,10)\n",
+    "plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3a82e44c",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.9.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/notebooks/Test/FIR_mehrere.ipynb b/notebooks/Test/FIR_mehrere.ipynb
new file mode 100644
index 0000000..e7f2240
--- /dev/null
+++ b/notebooks/Test/FIR_mehrere.ipynb
@@ -0,0 +1,658 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "d828ae1c",
+   "metadata": {},
+   "source": [
+    "# FIR Filter Parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "9aed9f51",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np \n",
+    "from numpy.fft import fft,ifft,fftshift\n",
+    "import matplotlib.pyplot as plt\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "9a16a6d2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Anfangs werte noch variabel machen \n",
+    "delays = [3,5,2]\n",
+    "ampl = [0.2,0.5,0.8]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "04de21c9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#if len(delays)!= len(ampl):\n",
+    "# Exeption ? "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "01fe08fe",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[1, 0, 0, 0, 0.2]"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1]+[0 for n in range (0,delays[0])]+[ampl[0]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9ab70ca5",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "f55da062",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "i = len(ampl)\n",
+    "x = [([1]+[0 for n in range (0,delays[i])]+[ampl[i]]) for i in range(0,i)]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5ad0edf9",
+   "metadata": {},
+   "source": [
+    "# Dealy Window\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "bf92d73a",
+   "metadata": {},
+   "outputs": [
+    {
+     "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": [
+    "d =0\n",
+    "k = np.linspace(-5,10,1000)\n",
+    "h_ideal = np.sinc(k-d)\n",
+    "plt.plot(k,h_ideal)\n",
+    "plt.show()\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "dd93e444",
+   "metadata": {},
+   "outputs": [
+    {
+     "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": [
+    "n = 4.5\n",
+    "window_sample= np.arange(np.round(d-(n-1)/2),np.round(d+(n+1)/2))\n",
+    "window = []\n",
+    "for ws in window_sample:  \n",
+    "    idx = (np.abs(k-ws)).argmin()\n",
+    "    window.append(idx)\n",
+    "    \n",
+    "plt.plot(k,h_ideal)\n",
+    "plt.plot(window_sample,h_ideal[window],\"-*\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "12b0c2d2",
+   "metadata": {},
+   "source": [
+    "# FIR"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "efc93b69",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "delay = 3\n",
+    "amplitude = 1\n",
+    "\n",
+    "d_int = int(np.floor(delay))\n",
+    "#d_frac = delay - d_int\n",
+    "\n",
+    "h_int = np.concatenate([np.zeros(d_int-1), [amplitude], np.zeros(3)])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "43372541",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#H_int = fft(h_int)\n",
+    "#h = ifft(H_int)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "a32cb580",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<StemContainer object of 3 artists>"
+      ]
+     },
+     "execution_count": 10,
+     "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": [
+    "test = np.random.randint(0, 10, size = 20)# Signal\n",
+    "\n",
+    "y = np.convolve(test.real, h_int)#Faltung\n",
+    "\n",
+    "plt.stem(test, linefmt=\"C0-\")\n",
+    "plt.stem(y, linefmt='C1-')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "39fb3489",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([9, 9, 2, 7, 8, 2, 8, 6, 2, 8, 4, 5, 7, 8, 2, 3, 0, 6, 4, 6])"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "test"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "7fd06347",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0., 0., 1., 0., 0., 0.])"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "h_int"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "a9612999",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0., 0., 9., 9., 2., 7., 8., 2., 8., 6., 2., 8., 4., 5., 7., 8., 2.,\n",
+       "       3., 0., 6., 4., 6., 0., 0., 0.])"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "y"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "706a51b1",
+   "metadata": {},
+   "source": [
+    "# FIR mit Delay \n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "d51e107c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "System frequencies fs=100, T=0.01\n",
+      "Tap with amplitude=4, delay=0.0725\n",
+      "Creating filter of order N=15.0\n",
+      "[-0.12418156  0.14405061 -0.17148882  0.21183913 -0.2770204   0.40014058\n",
+      " -0.72025305  3.60126526  1.20042175 -0.51446647  0.32738775 -0.24008435\n",
+      "  0.18954028 -0.15657675  0.13338019 -0.11616985]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<StemContainer object of 3 artists>"
+      ]
+     },
+     "execution_count": 17,
+     "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 = 100\n",
+    "period = 1 / samp_rate\n",
+    "print(f\"System frequencies fs={samp_rate}, T={period}\")\n",
+    "\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\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 = np.arange(0, order +1) * period - delay\n",
+    "\n",
+    "h = ampl*(np.sin(samp_rate * samples*np.pi) / (samp_rate * samples * np.pi)) #sinc\n",
+    "print(h)\n",
+    "plt.stem(h)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "79e18131",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Tap with amplitude=1, delay=7.5\n",
+      "Creating filter of order N=15.0\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<StemContainer object of 3 artists>"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD4CAYAAADvsV2wAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAASXklEQVR4nO3df6xf913f8edr1wm4Q527xV0bO52DlJqaNm2629AuYhTSzklATUAIpR2lsLEQ1HQtYm6TViBNkyDDE6PTwjKrZANRNYzUcyPm1hTKmBBLGqcucRPj1kpVxz+63tKZIPBw7Lz3x/frcn3zvff6+p57v+d7P8+HdOXvOd/PPZ/31+d8X/d8P+d8z0lVIUla+/7WuAuQJK0OA1+SGmHgS1IjDHxJaoSBL0mNWDfuAhZyxRVX1JYtW8ZdhiRNjMcff/zrVbVx1HO9DvwtW7awf//+cZchSRMjyVfme84hHUlqhIEvSY0w8CWpEQa+JDXCwJekRvT6LB1ptew5cJyd+w5z4tRprtywnh3bt3LbdZt6szypCwa+mrfnwHHu2X2Q08+dA+D4qdPcs/sgwCWFdNfLk7rikI6at3Pf4W+G83mnnzvHzn2He7E8qSsGvpp34tTpJc1f7eVJXTHw1bwrN6xf0vzVXp7UFQNfzduxfSvrL5u6YN76y6bYsX1rL5YndcWDtmre+QOp73/oCc6ce55NyzyrpuvlSV0x8CUGIf2xzx4F4Ld+6k29W57UBYd0JKkRnQR+kpuSHE5yJMnd87R5c5LPJ3kyyR920a8k6eIte0gnyRRwH/BW4BjwWJKHq+qpWW02AL8K3FRVR5O8dLn9SpKWpos9/OuBI1X1dFWdAR4Ebp3T5h3A7qo6ClBVX+ugX0nSEnQR+JuAZ2ZNHxvOm+2VwEuS/M8kjyf5sfkWluSOJPuT7J+ZmemgPEkSdBP4GTGv5kyvA/4h8P3AduDnkrxy1MKqaldVTVfV9MaNI2/LKEm6BF2clnkMuGrW9GbgxIg2X6+qvwT+Msn/Al4LfLGD/iVJF6GLPfzHgGuSXJ3kcuB24OE5bT4BfHeSdUleBHwXcKiDviVJF2nZe/hVdTbJXcA+YAp4oKqeTHLn8Pn7q+pQkk8BTwDPAx+pqi8st29J0sXr5Ju2VbUX2Dtn3v1zpncCO7voT5K0dH7TVpIaYeBLUiMMfElqhIEvSY0w8CWpEQa+JDXCwJekRhj4ktQIA1+SGmHgS1IjDHxJaoSBL0mNMPAlqREGviQ1wsCXpEYY+JLUCANfkhph4EtSIwx8SWqEgS9JjTDwJakRBr4kNcLAl6RGGPiS1AgDX5IaYeBLUiMMfElqhIEvSY0w8CWpEQa+JDXCwJekRhj4ktQIA1+SGmHgS1IjDHxJaoSBL0mNMPAlqRGdBH6Sm5IcTnIkyd0LtHtDknNJfriLfiVJF2/ZgZ9kCrgPuBnYBrw9ybZ52v1bYN9y+5QkLV0Xe/jXA0eq6umqOgM8CNw6ot17gI8DX+ugT0nSEnUR+JuAZ2ZNHxvO+6Ykm4AfBO5fbGFJ7kiyP8n+mZmZDsqTJEE3gZ8R82rO9K8AH6iqc4strKp2VdV0VU1v3Lixg/IkSQDrOljGMeCqWdObgRNz2kwDDyYBuAK4JcnZqtrTQf+SpIvQReA/BlyT5GrgOHA78I7ZDarq6vOPk/xX4HcMe0laXcsO/Ko6m+QuBmffTAEPVNWTSe4cPr/ouL0kaeV1sYdPVe0F9s6ZNzLoq+rHu+hTkrQ0ftNWkhph4EtSIwx8SWqEgS9JjTDwJakRBr4kNcLAl6RGGPiS1AgDX5IaYeBLUiMMfElqhIEvSY0w8CWpEQa+JDXCwJekRhj4ktQIA1+SGmHgS1IjDHxJaoSBL0mNMPAlqREGviQ1wsCXpEYY+JLUCANfkhph4EtSIwx8SWqEgS9JjTDwJakRBr4kNcLAl6RGGPiS1AgDX5IaYeBLUiMMfElqhIEvSY0w8CWpEQa+JDWik8BPclOSw0mOJLl7xPP/NMkTw58/TvLaLvqVJF28ZQd+kingPuBmYBvw9iTb5jT7MvA9VXUt8G+AXcvtV5K0NF3s4V8PHKmqp6vqDPAgcOvsBlX1x1X1f4eTjwCbO+hXkrQEXQT+JuCZWdPHhvPm88+BT873ZJI7kuxPsn9mZqaD8iRJ0E3gZ8S8Gtkw+V4Ggf+B+RZWVbuqarqqpjdu3NhBeZIkgHUdLOMYcNWs6c3AibmNklwLfAS4uar+rIN+JUlL0MUe/mPANUmuTnI5cDvw8OwGSV4B7AbeWVVf7KBPSdISLXsPv6rOJrkL2AdMAQ9U1ZNJ7hw+fz/w88DfA341CcDZqppebt+SpIvXxZAOVbUX2Dtn3v2zHv8k8JNd9CVJujR+01aSGmHgS1IjDHxJaoSBL0mNMPAlqREGviQ1wsCXpEYY+JLUiE6+eCUtZM+B4+zcd5gTp05z5Yb17Ni+lduuW+iCqloNrpf2GPhaUXsOHOee3Qc5/dw5AI6fOs09uw8CGC5j5Hppk0M6WlE79x3+Zqicd/q5c+zcd3hMFQlcL60y8LWiTpw6vaT5Wh2ulzYZ+FpRV25Yv6T5Wh2ulzYZ+FpRO7ZvZf1lUxfMW3/ZFDu2bx1TRQLXS6s8aKsVdf4A4PsfeoIz555nk2eD9ILrpU0Gvlbcbddt4mOfPQrAb/3Um8Zcjc5zvbTHIR1JaoSBL0mNMPAlqREGviQ1wsCXpEZ4ls4a4EWwtBa5XXfPwJ9wXgRLa5Hb9cpwSGfCeREsrUVu1yvDwJ9wXgRLa5Hb9cow8CecF8HSWuR2vTIM/EXsOXCcG+79DFff/T+44d7PsOfA8XGXdAEvgqW1aFK2677nw1wetF3AJBw48iJYWosmYbuehHyYy8BfwEIHjvq0Qr0Iltaivm/Xk5IPszmkswAPHEmazyTmg4G/AA8cSZrPJOaDgb+ASTlwJGn1TWI+OIa/gEk4cCRpPCYxHwz8RfT9wJGk8Zm0fHBIR5IaYeBLUiMMfElqRCeBn+SmJIeTHEly94jnk+Q/DJ9/Isnru+hXknTxlh34SaaA+4CbgW3A25Nsm9PsZuCa4c8dwH9abr+SpKXp4iyd64EjVfU0QJIHgVuBp2a1uRX4jaoq4JEkG5K8vKpOdtD/C3z1F36Bvz70p50t78dPPgvAV/7oxZ0ts2t9r7Hv9UH3Nbb4mrvW9/pgZWr8lld9By/74Ac7W955XQT+JuCZWdPHgO+6iDabgBcEfpI7GHwK4BWveMUlFfTJgyd52cyzbHt5Nyugq+Wc99RwA+lyuX2vsev6oP819n2ddL0s6P86gf7X+NTJZ/nq2ZP8RKdLHegi8DNiXl1Cm8HMql3ALoDp6emRbRbzqTe/A+jvebHv/8//G+hvfWCNfTQJr9cal+98fSsR+F0ctD0GXDVrejNw4hLaSJJWUBeB/xhwTZKrk1wO3A48PKfNw8CPDc/WeSPw5ys1fi9JGm3ZQzpVdTbJXcA+YAp4oKqeTHLn8Pn7gb3ALcAR4K9YmU8rkqQFdHItnarayyDUZ8+7f9bjAt7dRV+SpEvjN20lqRFrLvD3HDjOgaOnePTL35iImwpL0nkrnV9rKvDP31T4zLnngb+5qbChL6nvViO/1lTgL3RTYUnqs9XIrzUV+JN4U2FJgtXJrzUV+JNwU2GPMUjj0+f332rk15oK/L7fVNhjDNL49P39txr5taYC/7brNvGLP/QaNm1YT4BNG9bziz/0mt7cVNhjDNL49P39txr5teZuYn7bdZt6E/BzeYxBGp9JeP+tdH6tqT38vpuEYwzSWuX7z8BfVX0/xiCtZb7/1uCQTp+d/6i2c99hTpw6zZUb1rNj+9beDkFJa4nvPwN/1fX5GIO01rX+/nNIRy/Q53OV1V9uN/1n4OsCfT9XWf3kdjMZDHxdoO/nKquf3G4mg4GvC0zCucrqH7ebyWDg6wKeq6xL4XYzGQx8XcBzlXUp3G4mg6dl6gKeq6xL4XYzGQx8vUDr5yrr0rjd9J9DOpLUCANfkhph4EtSIwx8SWqEgS9JjTDwJakRBr4kNcLAl6RGGPiS1AgDX5IaYeBLUiMMfElqhIEvSY0w8CWpEQa+JDXCwJekRhj4ktSIZQV+kr+b5NNJvjT89yUj2lyV5A+SHEryZJL3LqdPSdKlWe4e/t3A71fVNcDvD6fnOgv8bFW9Cngj8O4k25bZryRpiZYb+LcCvz58/OvAbXMbVNXJqvrc8PFfAIcAb3wpSatsuYH/96vqJAyCHXjpQo2TbAGuAx5doM0dSfYn2T8zM7PM8rRW7TlwnANHT/Hol7/BDfd+hj0Hjo+7pBXV2uvVyli3WIMkvwe8bMRTH1pKR0m+Dfg48L6qena+dlW1C9gFMD09XUvpQ23Yc+A49+w+yJlzzwNw/NRp7tl9EIDbrlt7Hx5be71aOYvu4VfVW6rq1SN+PgH8nyQvBxj++7VRy0hyGYOw/2hV7e7yBag9O/cd5vRz5y6Yd/q5c+zcd3hMFa2s1l6vVs5yh3QeBt41fPwu4BNzGyQJ8GvAoar65WX2J3Hi1OklzZ90rb1erZzlBv69wFuTfAl463CaJFcm2TtscwPwTuD7knx++HPLMvtVw67csH5J8ydda69XK2dZgV9Vf1ZVN1bVNcN/vzGcf6Kqbhk+/qOqSlVdW1WvG/7sXXjJ0vx2bN/K+sumLpi3/rIpdmzfOqaKVlZrr1crZ9GDtlLfnD9QuXPfYU6cOs2VG9azY/vWNXsAs7XXq5WTqv6eCDM9PV379+8fdxmSNDGSPF5V06Oe81o6ktQIA1+SGmHgS1IjDHxJaoSBL0mN6PVZOklmgK/MmX0F8PUxlHOx+l4f9L/GvtcH1tiFvtcH/a9xVH3/oKo2jmrc68AfJcn++U456oO+1wf9r7Hv9YE1dqHv9UH/a1xqfQ7pSFIjDHxJasQkBv6ucRewiL7XB/2vse/1gTV2oe/1Qf9rXFJ9EzeGL0m6NJO4hy9JugQGviQ1YuICP8nrkjwyvJHK/iTXj7umUZK8J8nhJE8m+aVx1zOfJP8qSSW5Yty1zJZkZ5I/TfJEkv+eZMO4awJIctNwvR5Jcve465kryVVJ/iDJoeG2995x1zRKkqkkB5L8zrhrGSXJhiQPDbfBQ0neNO6a5kryM8N1/IUkH0vyrYv9zsQFPvBLwL+uqtcBPz+c7pUk3wvcClxbVd8J/LsxlzRSkqsY3Kns6LhrGeHTwKur6lrgi8A9Y66HJFPAfcDNwDbg7Um2jbeqFzgL/GxVvQp4I/DuHtYI8F7g0LiLWMCHgU9V1XcAr6VntSbZBPxLYLqqXg1MAbcv9nuTGPgFvHj4+O8AJ8ZYy3x+Gri3qv4aoKpG3ty9B/498H4G/6e9UlW/W1Vnh5OPAJvHWc/Q9cCRqnq6qs4ADzL4w94bVXWyqj43fPwXDIKqV3dKSbIZ+H7gI+OuZZQkLwb+MYN7cVNVZ6rq1FiLGm0dsD7JOuBFXEQWTmLgvw/YmeQZBnvOY9/zG+GVwHcneTTJHyZ5w7gLmivJ24DjVfUn467lIvwz4JPjLoJBcD4za/oYPQvT2ZJsAa4DHh1zKXP9CoMdjefHXMd8vh2YAf7LcNjpI0n+9riLmq2qjjPIv6PASeDPq+p3F/u9Xt7iMMnvAS8b8dSHgBuBn6mqjyf5EQZ/hd+ymvXBojWuA17C4CP1G4D/luTba5XPgV2kxg8C/2Q165lrofqq6hPDNh9iMEzx0dWsbR4ZMa93n44Aknwb8HHgfVX17LjrOS/JDwBfq6rHk7x5zOXMZx3weuA9VfVokg8DdwM/N96y/kaSlzD4dHk1cAr47SQ/WlW/udDv9TLwq2reAE/yGwzG/wB+mzF9LFykxp8Gdg8D/rNJnmdwkaOZ1aoP5q8xyWsYbCh/kgQGwyWfS3J9VX113PWdl+RdwA8AN672H8t5HAOumjW9mR4OKSa5jEHYf7Sqdo+7njluAN6W5BbgW4EXJ/nNqvrRMdc12zHgWFWd/2T0EIPA75O3AF+uqhmAJLuBfwQsGPiTOKRzAvie4ePvA740xlrms4dBbSR5JXA5PbriXlUdrKqXVtWWqtrCYAN//WqG/WKS3AR8AHhbVf3VuOsZegy4JsnVSS5ncJDs4THXdIEM/oL/GnCoqn553PXMVVX3VNXm4XZ3O/CZnoU9w/fBM0m2DmfdCDw1xpJGOQq8McmLhuv8Ri7iwHIv9/AX8S+ADw8PVPw/4I4x1zPKA8ADSb4AnAHe1ZM91EnyH4FvAT49/BTySFXdOc6CqupskruAfQzOinigqp4cZ00j3AC8EziY5PPDeR+sqr3jK2kivQf46PAP+9PAT4y5ngsMh5oeAj7HYMjzABdxmQUvrSBJjZjEIR1J0iUw8CWpEQa+JDXCwJekRhj4ktQIA1+SGmHgS1Ij/j8LwkpcCafaXwAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "\n",
+    "delay = 7.5\n",
+    "ampl = 1\n",
+    "print(f\"Tap with amplitude={ampl}, delay={delay}\")\n",
+    "\n",
+    "order = 2 * np.floor(delay) + 1 #N\n",
+    "print(f\"Creating filter of order N={order}\")\n",
+    "\n",
+    "samples = np.arange(0, order +1) - delay\n",
+    "\n",
+    "h = ampl*(np.sinc(samples)) #sinc\n",
+    "\n",
+    "plt.stem(samples, h)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "c89c83ae",
+   "metadata": {},
+   "outputs": [
+    {
+     "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": [
+       "[<matplotlib.lines.Line2D at 0x7fbfbc612d60>]"
+      ]
+     },
+     "execution_count": 27,
+     "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": [
+    "t = np.arange(200)\n",
+    "\n",
+    "signal = np.sin(2 * np.pi * t * 0.05)\n",
+    "\n",
+    "signal_shifted = np.convolve(h, signal, mode='full')\n",
+    "\n",
+    "plt.plot(t, signal)\n",
+    "plt.grid(True)\n",
+    "plt.show()\n",
+    "plt.plot(signal_shifted)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "15f663c6",
+   "metadata": {},
+   "source": [
+    "#  Test Delay  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "afb9e748",
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "samp_rate = 100\n",
+    "period = 1 / samp_rate\n",
+    "\n",
+    "#samp_rate_2 = 100\n",
+    "#period_2 = 1 / samp_rate_2\n",
+    "\n",
+    "print(f\"System frequencies fs={samp_rate}, T={period}\")\n",
+    "\n",
+    "delay_freq = 1.25 * 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": "markdown",
+   "id": "892b32f7",
+   "metadata": {},
+   "source": [
+    "# Test 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f224987a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "samp_rate = 10e6\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 = 2\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*samples_int)\n",
+    "h_ideal = ifft(H_ideal)\n",
+    "\n",
+    "plt.stem(H_ideal.real, linefmt=\"C0-\")\n",
+    "plt.stem(h_ideal.real, linefmt='C1-')\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": "6ba475b6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "h_ideal\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b1cfddba",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5b4c5781",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.9.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/notebooks/Test/Untitled.ipynb b/notebooks/Test/Untitled.ipynb
new file mode 100644
index 0000000..0a1a81c
--- /dev/null
+++ b/notebooks/Test/Untitled.ipynb
@@ -0,0 +1,193 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "6b0e891f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np \n",
+    "from numpy.fft import fft,ifft,fftshift\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "f7878dca",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([-4, -3, -2, -1,  0,  1,  2,  3])"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tau = 1\n",
+    "freq = np.arange(-4,4)\n",
+    "freq"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "6b5000a6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1.-9.79717439e-16j, 1.-7.34788079e-16j, 1.-4.89858720e-16j,\n",
+       "       1.-2.44929360e-16j, 1.+0.00000000e+00j, 1.+2.44929360e-16j,\n",
+       "       1.+4.89858720e-16j, 1.+7.34788079e-16j])"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "f_tabs = np.exp((-2j*np.pi*freq*tau))\n",
+    "f_tabs"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "54df500d",
+   "metadata": {},
+   "outputs": [
+    {
+     "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": [
+    "plt.plot(f_tabs.real)\n",
+    "plt.plot(f_tabs.imag)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "bffc82f4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 1.00000000e+00-1.2246468e-16j, -2.95655891e-16+1.2246468e-16j,\n",
+       "        1.22464680e-16-1.2246468e-16j, -5.07265313e-17+1.2246468e-16j,\n",
+       "        0.00000000e+00-1.2246468e-16j,  5.07265313e-17+1.2246468e-16j,\n",
+       "       -1.22464680e-16-1.2246468e-16j,  2.95655891e-16+1.2246468e-16j])"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "i_tabs = ifft(fftshift(f_tabs))\n",
+    "i_tabs"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "12ff730b",
+   "metadata": {},
+   "outputs": [
+    {
+     "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": [
+    "shiftet= fftshift(f_tabs)\n",
+    "plt.plot(shiftet.real)\n",
+    "plt.plot(shiftet.imag)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "a075dd24",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD4CAYAAAD8Zh1EAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAWrElEQVR4nO3df2xd933e8ffDS1ESJVL3WmJUibqXsgP/khNZl+OcDsG6rNlaqy3iFegAe1uDBSk8oXGRYn8s3oBtGAoMG4oNRVE3huZ4bbEuRpqknbup8Ya1XTZ0WS1TP2zZlqPKkUjJNmlJJCVZEkXysz/upcvQpHhJnatzz7nPCyDMe+7h5QPBeHT0Pef7/SoiMDOz7OtIO4CZmSXDhW5mlhMudDOznHChm5nlhAvdzCwnOtP6xdu2bYvdu3en9evNzDLplVdeeT8i+pZ6L7VC3717N4cPH07r15uZZZKkM8u95yEXM7OccKGbmeWEC93MLCdc6GZmOeFCNzPLiRULXdLzksYkvbbM+5L065JOSTouaTD5mGZmtpJGrtB/C3j0Fu/vB+6tfz0JfPX2Y5mZ2WqtWOgR8V3g4i1OeQz4naj5HlCUtCOpgIudfPcy//rQG1ybnm3WrzAzy6QkxtD7gZEFr0frxz5C0pOSDks6PD4+vqZfNnrpAw5+9zSvnptc08+bmeVVEoWuJY4tuWtGRByMiKGIGOrrW3Lm6or2lYsADJ+9tKafNzPLqyQKfRQoL3i9CzifwOcuaevm9eze2s0RF7qZ2Q9JotBfBD5ff9rlR4HJiHgngc9dVrVSYvjsBN4+z8zsLzXy2OLXgf8L3C9pVNIXJR2QdKB+yiHgNHAK+A/ALzYtbV21UmT88g3OTVxr9q8yM8uMFVdbjIgnVng/gC8llqgBg5USAEfOTrCr1H0nf7WZWcvK5EzR+3+khw3rOjhydiLtKGZmLSOThb6u0MHe/iJHRnxj1MxsXiYLHWrj6CfOTXFjxhOMzMwg04VeYnp2jhPnp9KOYmbWEjJc6EUAj6ObmdVlttC3926gv7jRM0bNzOoyW+hQu0o/6it0MzMg84Ve4tzENd6bup52FDOz1GW80IsAXtfFzIyMF/pDO3vpKniCkZkZZLzQ13cWeKi/14VuZkbGCx2gWi5x/NwEN2fn0o5iZpaqzBf64ECR6zfnePOdy2lHMTNLVeYLvTq/8qLXdTGzNpf5Qt+5ZQMf61nP8BkXupm1t8wXuiQGKyWOjEykHcXMLFWZL3SoPY9+5sIHXLhyI+0oZmapyUmh18bRj/oq3czaWC4K/ZP9W+jskBfqMrO2lotC39hV4MEdnmBkZu0tF4UOtXH0YyMTzM5F2lHMzFKRq0K/Oj3LW+95gpGZtafcFPrg/AQjD7uYWZvKTaFX7urmrk1dXkrXzNpWbgpdEtVy0U+6mFnbyk2hAwwOlPiL8atMfnAz7ShmZndcrgq9Wi4CcHR0ItUcZmZpyFWh7y0X6RBeqMvM2lKuCn3z+k7u297jhbrMrC3lqtChtq7L0bOXmPMEIzNrMzks9CJT12c4/f7VtKOYmd1RDRW6pEclnZR0StLTS7y/RdIfSjom6YSkLyQftTHzE4z8+KKZtZsVC11SAXgG2A/sAZ6QtGfRaV8CXo+Ih4HPAP9OUlfCWRtyz7ZN9G7o9IxRM2s7jVyhPwKciojTETENvAA8tuicAHokCdgMXARmEk3aoI4Osa9S8oxRM2s7jRR6PzCy4PVo/dhCvwE8CJwHXgW+HBFziz9I0pOSDks6PD4+vsbIKxusFHnrvctcuZHK3ylmZqlopNC1xLHFj5D8JHAU2AnsA35DUu9HfijiYEQMRcRQX1/fKqM2rlopMRdw3I8vmlkbaaTQR4Hygte7qF2JL/QF4NtRcwp4G3ggmYirt29XEcDPo5tZW2mk0F8G7pV0d/1G5+PAi4vOOQt8FkDSduB+4HSSQVdjS/c6Pt63yTNGzaytdK50QkTMSHoKeAkoAM9HxAlJB+rvPwv8CvBbkl6lNkTzlYh4v4m5VzRYKfE/3xwjIqjdqzUzy7cVCx0gIg4BhxYde3bB9+eBn0g22u2pVkr83iujnL34AQNbN6Udx8ys6XI3U3RetVIEPMHIzNpHbgv9vu09bOoqeIKRmbWN3BZ6oUM8XC660M2sbeS20KE27PLGO1Ncm55NO4qZWdPlutAHKyVm5oJXz02mHcXMrOlyXej76lvSeV0XM2sHuS70rZvXM7C12+PoZtYWcl3oUBt2GT57iQjvYGRm+Zb7Qq9WioxdvsH5yetpRzEza6r8F3q5toORx9HNLO9yX+gP7Ohhw7oOhs9MpB3FzKypcl/o6wod7O0vcmTEV+hmlm+5L3SojaOfODfFjRlPMDKz/GqbQp+enePE+am0o5iZNU2bFPr8jdGJdIOYmTVRWxT69t4N9Bc3+kkXM8u1tih0gH0Vr7xoZvnWNoU+WClxbuIa7015gpGZ5VPbFPr8Dka+SjezvGqbQn9oZy9dhQ4/j25mudU2hb6+s8BD/b0c8YxRM8uptil0qK3rcvzcBDdn59KOYmaWuPYq9EqR6zfnOPnu5bSjmJklrq0KfXCgNsFo2M+jm1kOtVWh79yygY/1rPeTLmaWS21V6JKoVoqeMWpmudRWhQ61CUY/uPABF67cSDuKmVmi2q7Q5xfqOjoykW4QM7OEtV2hf7J/C50d8ji6meVO2xX6xq4CD+7o9ZMuZpY7DRW6pEclnZR0StLTy5zzGUlHJZ2Q9L+SjZmsaqXIsZEJZuci7ShmZolZsdAlFYBngP3AHuAJSXsWnVMEfhP4XEQ8BPzd5KMmp1opcnV6lu+PeYKRmeVHI1fojwCnIuJ0REwDLwCPLTrn7wHfjoizABExlmzMZFXL3sHIzPKnkULvB0YWvB6tH1voPqAk6U8lvSLp80t9kKQnJR2WdHh8fHxtiRMwsLWbuzZ1MXzG4+hmlh+NFLqWOLZ48LkT+CvATwM/CfxzSfd95IciDkbEUEQM9fX1rTpsUiRRLRc54kcXzSxHGin0UaC84PUu4PwS53wnIq5GxPvAd4GHk4nYHNVKkVNjV5i8djPtKGZmiWik0F8G7pV0t6Qu4HHgxUXn/Bfgr0vqlNQNfAp4I9moyRr0BCMzy5kVCz0iZoCngJeolfQ3IuKEpAOSDtTPeQP4DnAc+HPguYh4rXmxb9/echEJr+tiZrnR2chJEXEIOLTo2LOLXv8q8KvJRWuuzes7uX97j590MbPcaLuZogtVKyWOnL3EnCcYmVkOtHmhF5m6PsPp96+mHcXM7La1daEPVoqAx9HNLB/autDv2baZ3g2dDHsc3cxyoK0LvaND7KuPo5uZZV1bFzpAtVzkrfcuc+XGTNpRzMxuS9sX+uBAibmA455gZGYZ1/aFvm9XEcDruphZ5rV9oW/pXsfH+zZ5HN3MMq/tCx3mJxhNEOEJRmaWXS50agt1Xbg6zdmLH6QdxcxszVzo1GaMgncwMrNsc6ED923vYVNXwePoZpZpLnSg0CEeLhc9Y9TMMs2FXletFHnjnSmuTc+mHcXMbE1c6HXVcomZueC185NpRzEzWxMXet38jdHhMx5HN7NscqHXbd28noGt3X7Sxcwyy4W+QLVcZPjsJU8wMrNMcqEvMDhQYuzyDc5PXk87ipnZqrnQF6iWS4B3MDKzbHKhL/DAjh42rOvwOLqZZZILfYF1hQ729hd9hW5mmeRCX6RaKfLauSluzHiCkZlliwt9kWqlyPTsHK+fn0o7ipnZqrjQF6lW5m+MTqQbxMxslVzoi2zv3UB/cSPDHkc3s4xxoS9hX6XoK3QzyxwX+hKq5SLnJq4xNuUJRmaWHS70JQwO1MbRvT66mWWJC30JD+3spavQwZERj6ObWXY0VOiSHpV0UtIpSU/f4ry/KmlW0s8lF/HOW99ZYM/OXo+jm1mmrFjokgrAM8B+YA/whKQ9y5z3b4GXkg6ZhsFKieOjE9ycnUs7iplZQxq5Qn8EOBURpyNiGngBeGyJ834J+BYwlmC+1FQrRa7fnOPku5fTjmJm1pBGCr0fGFnwerR+7EOS+oGfBZ691QdJelLSYUmHx8fHV5v1jprfwcjruphZVjRS6Fri2OIdIH4N+EpE3HIBlIg4GBFDETHU19fXYMR09Bc38rGe9R5HN7PM6GzgnFGgvOD1LuD8onOGgBckAWwDfkrSTET8QRIh0yCJaqXoGaNmlhmNXKG/DNwr6W5JXcDjwIsLT4iIuyNid0TsBr4J/GKWy3xetVLiBxc+4OLV6bSjmJmtaMVCj4gZ4ClqT6+8AXwjIk5IOiDpQLMDpmmwvlDXUT+PbmYZ0MiQCxFxCDi06NiSN0Aj4h/efqzW8Mn+LRQ6xPCZCX78ge1pxzEzuyXPFL2FjV0FHtzR4xmjZpYJLvQVDFZKHBuZZHZu8YM9ZmatxYW+gmqlyJUbM3x/zBOMzKy1udBXUC17ByMzywYX+goGtnZz16Yuzxg1s5bnQl+BJKrlotdGN7OW50JvQLVS5NTYFSav3Uw7ipnZslzoDajWJxgdG5lIN4iZ2S240BvwcLmIhNd1MbOW5kJvwOb1ndy/vcdPuphZS3OhN6haKXJ0ZII5TzAysxblQm9QtVJi8tpN3r5wNe0oZmZLcqE3aLC+g9HwGY+jm1lrcqE36J5tm+nd0MkRP+liZi3Khd6gjg6xr1LyjVEza1ku9FWoloucfHeKKzdm0o5iZvYRLvRVqFaKzAUcH51IO4qZ2Ue40FfBKy+aWStzoa/Clu51fLxvk1deNLOW5EJfpWr9xmiEJxiZWWtxoa9StVLkwtVpRi5eSzuKmdkPcaGv0mB95UUv1GVmrcaFvkr3be+hu6vgcXQzazku9FUqdIiHdxU9Y9TMWo4LfQ0GB4q8fn6K6zdn045iZvYhF/oaVMslZuaCV89Nph3FzOxDLvQ12FdfedHj6GbWSlzoa7Bt83oGtnZ7xqiZtRQX+hpVy0WGz17yBCMzaxku9DWqVkq8N3WDdyavpx3FzAxosNAlPSrppKRTkp5e4v2/L+l4/evPJD2cfNTWMj/ByMMuZtYqVix0SQXgGWA/sAd4QtKeRae9DfyNiNgL/ApwMOmgreaBHT2s7+zwjFEzaxmNXKE/ApyKiNMRMQ28ADy28ISI+LOImG+27wG7ko3ZetYVOti7a4ufdDGzltFIofcDIwtej9aPLeeLwB8t9YakJyUdlnR4fHy88ZQtarBS4rXzU9yY8QQjM0tfI4WuJY4t+WiHpL9JrdC/stT7EXEwIoYiYqivr6/xlC2qWikyPTPH6+en0o5iZtZQoY8C5QWvdwHnF58kaS/wHPBYRFxIJl5rq/rGqJm1kEYK/WXgXkl3S+oCHgdeXHiCpArwbeDnI+Kt5GO2pu29G9i5ZYMX6jKzltC50gkRMSPpKeAloAA8HxEnJB2ov/8s8C+ArcBvSgKYiYih5sVuHdWBEsNnfGPUzNK3YqEDRMQh4NCiY88u+P4XgF9INlo2VMtF/tvxdxibus7HejekHcfM2phnit6mD8fRPexiZilzod+mT/T30lXo8I1RM0udC/02re8ssGdnr2eMmlnqXOgJqFaKHB+dYGZ2Lu0oZtbGXOgJGKyUuH5zjjffvZx2FDNrYy70BFS9g5GZtQAXegL6ixvp61nvG6NmlioXegIkMVgp+tFFM0uVCz0h1UqJt9+/ysWr02lHMbM25UJPSLVcBODoiMfRzSwdLvSE7N1VpNAhj6ObWWpc6AnZ2FXgwR09nmBkZqlxoSeoWi5xbGSS2bkl9/8wM2sqF3qCBgeKXLkxw6mxK2lHMbM25EJPULU8v4ORh13M7M5zoSdoYGs3pe51Hkc3s1S40BMkiWql5CddzCwVLvSEDVaKfH/sCpPXbqYdxczajAs9YfM7GB3zMgBmdoe50BO2d9cWJDzsYmZ3nAs9YT0b1nH/9h6OeAkAM7vDXOhNUK0UOXJ2gjlPMDKzO8iF3gTVconJazd5+8LVtKOYWRtxoTfB4EAR8Di6md1ZLvQmuGfbZno2dHqCkZndUS70JujoEPvKRV+hm9kd5UJvksFKiZPvTnH1xkzaUcysTbjQm6RaKTIXcHx0Mu0oZtYmXOhNMr/yosfRzexOcaE3yZbudXy8b5PH0c3sjnGhN1G1UuLoyCUiPMHIzJqvoUKX9Kikk5JOSXp6ifcl6dfr7x+XNJh81OypVoq8f2WakYvX0o5iZm1gxUKXVACeAfYDe4AnJO1ZdNp+4N7615PAVxPOmUkf7mDkdV3M7A7obOCcR4BTEXEaQNILwGPA6wvOeQz4naiNLXxPUlHSjoh4J/HEf/Q0vPtq4h/bDA8SfGP9JTr+AI79oUe3zKymsHMvn/hi8te9jRR6PzCy4PUo8KkGzukHfqjQJT1J7QqeSqWy2qyZI0Tlrm6mrnuzCzP7S4V1haZ8biOFriWOLb7L18g5RMRB4CDA0NDQ2u4U7v83a/qxtPxI/cvMrNkaGQcYBcoLXu8Czq/hHDMza6JGCv1l4F5Jd0vqAh4HXlx0zovA5+tPu/woMNmU8XMzM1vWikMuETEj6SngJaAAPB8RJyQdqL//LHAI+CngFPAB8IXmRTYzs6U0MoZORByiVtoLjz274PsAvpRsNDMzWw0/S2dmlhMudDOznHChm5nlhAvdzCwnlNZKgJLGgTNr/PFtwPsJxmm2LOXNUlbIVt4sZYVs5c1SVri9vAMR0bfUG6kV+u2QdDgihtLO0ags5c1SVshW3ixlhWzlzVJWaF5eD7mYmeWEC93MLCeyWugH0w6wSlnKm6WskK28WcoK2cqbpazQpLyZHEM3M7OPyuoVupmZLeJCNzPLicwV+kobVrcSSc9LGpP0WtpZViKpLOlPJL0h6YSkL6edaTmSNkj6c0nH6ln/VdqZGiGpIOmIpP+adpZbkfQDSa9KOirpcNp5VlLf8vKbkt6s///719LOtBRJ99f/TOe/piT9cqK/I0tj6PUNq98C/ja1TTVeBp6IiNdv+YMpkfRjwBVq+61+Iu08tyJpB7AjIoYl9QCvAH+nFf9sJQnYFBFXJK0D/g/w5Yj4XsrRbknSPwaGgN6I+Jm08yxH0g+AoYjIxEQdSb8N/O+IeK6+Z0N3REykHOuW6l12DvhURKx1guVHZO0K/cMNqyNiGpjfsLolRcR3gYtp52hERLwTEcP17y8Db1DbF7blRM2V+st19a+WvjKRtAv4aeC5tLPkiaRe4MeArwFExHSrl3ndZ4G/SLLMIXuFvtxm1JYgSbuBKvD/Uo6yrPrwxVFgDPgfEdGyWet+DfgnwFzKORoRwH+X9Ep9Y/dWdg8wDvzH+nDWc5I2pR2qAY8DX0/6Q7NW6A1tRm1rJ2kz8C3glyNiKu08y4mI2YjYR23/2kckteyQlqSfAcYi4pW0szTo0xExCOwHvlQfOmxVncAg8NWIqAJXgVa/t9YFfA74vaQ/O2uF7s2om6g+Hv0t4Hcj4ttp52lE/Z/Xfwo8mm6SW/o08Ln62PQLwI9L+k/pRlpeRJyv/3cM+H1qQ52tahQYXfAvtG9SK/hWth8Yjoj3kv7grBV6IxtW2xrUbzR+DXgjIv592nluRVKfpGL9+43A3wLeTDXULUTEP42IXRGxm9r/s38cEf8g5VhLkrSpflOc+tDFTwAt+5RWRLwLjEi6v37os0DL3chf5AmaMNwCDe4p2iqW27A65VjLkvR14DPANkmjwL+MiK+lm2pZnwZ+Hni1PjYN8M/q+8m2mh3Ab9efFOgAvhERLf0oYIZsB36/9vc7ncB/jojvpBtpRb8E/G79Iu80LbxJvaRuak/p/aOmfH6WHls0M7PlZW3IxczMluFCNzPLCRe6mVlOuNDNzHLChW5mlhMudDOznHChm5nlxP8Hpgy61uq0KiQAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(i_tabs.real)\n",
+    "plt.plot(i_tabs.imag)\n",
+    "plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "92311556",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.9.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}