{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "id": "aa21fb23", "metadata": { "id": "aa21fb23", "tags": [] }, "source": [ "\n", "\n", "\n", "# Using Mathematics to Make and Stream Music\n", "\n", "---\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
\n", " \n", " Dr Jon Shiach

\n", " Senior Lecturer
\n", " Department of Computing and Mathematics
\n", " Manchester Metropolitan University
\n", " Email: j.shiach@mmu.ac.uk\n", "
\n", "
\n", " \n", " \n", " \n", " Dr Stephen Lynch

\n", " Reader
\n", " Department of Computing and Mathematics
\n", " Manchester Metropolitan University
\n", " Email: s.lynch@mmu.ac.uk\n", "
\n", "
\n", " \n", " \n", " \n", " Dr Killian O\"Brien

\n", " Senior Lecturer
\n", " Department of Computing and Mathematics
\n", " Manchester Metropolitan University
\n", " Email: k.m.obrien@mmu.ac.uk\n", "
\n", "
\n", " \n", "
\n", "\n", "---\n", "\n", "## Introduction\n", "This Jupyter notebook is designed to accompany a session which introduces you to the mathematics used in the creating of digital music and also the streaming of music which is used by applications such as Spotify, YouTube and TikTok. Whilst some of the mathematics required is ordinarily taught at degree level, to follow the content of this notebook you just need an understanding of **radians**, the **sine** and **cosine** functions (which are covered in the preliminaries section below) and a little curiosity. This notebook contains some Python code to perform calculations, produce plots and play audio signals. No programming experience is necessary to follow the examples, however, readers can make changes to the code and execute to see what affects any changes has on the output." ] }, { "cell_type": "markdown", "id": "7a2c5d7a", "metadata": { "id": "7a2c5d7a", "tags": [] }, "source": [ "---\n", "\n", "## Angles and Trigonometric Ratios\n", "\n", "Here I will introduce you to the mathematical and Python concepts that you need to understand the content of this notebook.\n", "\n", "### Radians\n", "\n", "A radian is simply a measure of the size of an angle. You may be familiar with measuring angles with degrees where there are $360^\\circ$ in a circle and a right-angle is $90^\\circ$ and so on. In mathematics we prefer to measure angles in radians because it is more convenient for some applications and makes our formulas more elegant.\n", "\n", "Consider the diagram on the right. To define a radian we do the following\n", "\n", "\n", "1. Draw a circle.\n", "1. Draw a line from the centre to the edge of the circle.\n", "1. Where your line meets the edge of the circle, draw an arc around the circle which has the same length as the radius of your circle.\n", "1. Where your arc ends, draw a line to the centre of the circle\n", "\n", "The angle between the two lines that meet at the centre is 1 radian. Since the circumference of the circle can be calculated using $2\\pi r$ then length of our arc is\n", "\n", "$$r = 2 \\pi r \\left( \\dfrac{1 \\text{ rad}}{360^\\circ} \\right).$$\n", "\n", "Rearranging this gives the conversion between degrees and radians of $360^\\circ = 2\\pi \\text{ rad}$ (the unit $\\text{rad}$ is usually omitted).\n", "\n", "### The sine and cosine functions\n", "\n", "\n", "\n", "The sine and cosine functions are used in trigonometry to calculate the length of the sides of a right-angled triangle. Consider the triangle $ABC$ where the angle at point $B$ is a right-angle. The longest side of the triangle is labelled the **hypotenuse** and the two shorter sides are labelled **adjacent** and **opposite** depending on their position relative to the angle $\\theta$ (the character $\\theta$ is the Greek letter _theta_ and is commonly used to represent angles in mathematics) which in this is at the point $A$. The definition of the sine and cosine functions are related to the lengths of the sides of a right-angled triangle as follows\n", "\n", "\\begin{align*}\n", " \\sin(\\theta) &= \\frac{\\text{opposite}}{\\text{hypotenuse}}, &\n", " \\cos(\\theta) &= \\frac{\\text{adjacent}}{\\text{hypotenuse}}.\n", "\\end{align*}\n", "\n", "So if $\\theta = 0.6435$ and the length of the hypotenuse is $5$ then we can calculate the length of the opposite and adjacent sides using\n", "\n", "\\begin{align*}\n", " \\text{opposite} &= \\text{hypotenuse} \\times \\sin(\\theta) = 5\\sin(0.6435) \\approx 3, \\\\\n", " \\text{adjacent} &= \\text{hypotenuse} \\times \\cos(\\theta) = 5\\cos(0.6435) \\approx 4.\n", "\\end{align*}\n", "\n", "We can check whether these are correct using the [Pythagorean theorem](https://en.wikipedia.org/wiki/Pythagorean_theorem), i.e., $5 ^ 2 = 3 ^ 2 + 4 ^ 2 = 9 + 16 = 25$." ] }, { "cell_type": "markdown", "id": "b805bc08", "metadata": { "id": "b805bc08", "tags": [] }, "source": [ "---\n", "## Python\n", "\n", "Python is an easy to learn programming language that is has become very popular with programmers, data scientists, web developers and of course mathematicians. Python is *open source* meaning that it is free to download to any computer, we recommend downloading [**Anaconda**](https://www.anaconda.com/products/individual) which is suite of software that includes Python and Jupyter notebook.\n", "\n", "### Jupyter notebooks\n", "\n", "Jupyter notebooks are documents that combine text and Python code which allow readable documents such as this one to be created that contain executable code used to perform calculations. To run code in a notebook simply click on the code and then on the run button, or alternatively, press the **ctrl + enter** keys at the same time. Since we will be using commands to perform calculations, produce plots of audio signals, reading and playing audio files we need to import some commands to help us to do this. Run the code below to import the commands." ] }, { "cell_type": "code", "execution_count": null, "id": "ad277401", "metadata": { "id": "ad277401", "scrolled": false }, "outputs": [], "source": [ "from numpy import *\n", "import matplotlib.pyplot as plt\n", "from matplotlib.animation import FuncAnimation\n", "from IPython.display import HTML, Audio\n", "from scipy.io import wavfile\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "plt.rc('axes', labelsize=14)\n", "plt.rc('axes', titlesize=16)\n", "plt.rcParams[\"figure.figsize\"] = (12, 4)" ] }, { "cell_type": "markdown", "id": "c3cde611", "metadata": { "id": "c3cde611" }, "source": [ "Now we can perform some calculations. The Python code below calculates the length of the opposite side of the right-angled triangle from the example calculation above and prints the result. Note how the equation `opposite = 5 * sin(0.6435)` is entered in a similar way to how we write it on a piece of paper. Can you add a couple of lines of code to calculate the length of the adjacent side as well?" ] }, { "cell_type": "code", "execution_count": null, "id": "a7ceb3f6", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "a7ceb3f6", "outputId": "5f26da1c-ea9e-424a-bc6b-160e9848c366", "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.999995564825018\n" ] } ], "source": [ "opposite = 5 * sin(0.6435)\n", "print(opposite)" ] }, { "cell_type": "markdown", "id": "61dbb1cd", "metadata": { "id": "61dbb1cd" }, "source": [ "---\n", "## Co-ordinates of points on a circle\n", "\n", "\n", "\n", "We can use sine and cosine functions to calculate the co-ordinates of points on a circle. Consider the diagram on the right which shows the upper right-hand quadrant of a circle which is centred at the origin and has a radius of $r$. For every point in this quadrant of the circle we can form a right angled triangle where the length of the hypotenuse is $r$. If the angle $\\theta$ is the angle between the $x$ axes and the hypotenuse then $x$ co-ordinate of the point on the circle is equal to the length of the adjacent side of the triangle and the $y$ co-ordinate is equal to the length of the opposite side, therefore\n", "\n", "$$ (x, y) = (r \\cos(\\theta), r \\sin(\\theta)). $$\n", "\n", "We can continue this for the other quadrants in the circle, i.e., for angles $\\theta > \\dfrac{\\pi}{2}$." ] }, { "cell_type": "markdown", "id": "54ef1122", "metadata": { "id": "54ef1122" }, "source": [ "The Python code below calculates the co-ordinates of $n = 10$ points on a circle with radius $r=2$ using values of $\\theta$ from $0$ to $2\\pi$. The radius is defined by the command `r = 2` and $\\theta$ values are calculated and stored in `theta`. Then the $x$ and $y$ co-ordinates are calculated and stored in `x` and `y` which are then used to plot the points on the circle." ] }, { "cell_type": "code", "execution_count": null, "id": "3a08b759", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 588 }, "id": "3a08b759", "outputId": "5090d56f-7f1b-4f26-e5f1-dd5f56fa3195", "scrolled": false }, "outputs": [ { "data": { "image/png": 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NUmWjN1ls/34pel+4IN+i4uKYLIh8fGR+tAcflOQRHS3Jw10xYRCOHpVvTTk5Mm3CunXSJ52IZIr+NWtkUF9hoewTE7WOShtMGG7u1CmgVy/pe962rQxcuukmraMicize3jLD7cMPyzT+Dz8M/PKL1lHZHxOGG0tPlzaL9HSZRHDzZhmcR0TX8/ICvvhCqmzz84H+/aXbuTthwnBT585Jsjh5UlYjS0yUCdmIqHLe3tIZ5K67gL/+kna/s2e1jsp+mDDcUGGhFKmPHAEaNgR++AEID9c6KiLn4O8v4zQaNwaOHQMeegi4eFHrqOyDCcPNKAWMHg38+CPg5yc9Pho31joqIucSHi6fncBA6Y7+2GMy/b+rY8JwM3PmlC2p+s030nZBRJaLiJDBfT4+MhJ81CjXX4SJCcONJCQAU6bI47lzZXAeEdVc587A11/LF7DPP5eV+1wZE4abSEkBhg2Tb0BjxgBjx2odEZFrGDBAFmICgKlTpU3QVTn9XFJ0jYICWdU+Ph7Izgbq10du9xgMeWsILl70wQMPSOlCp9M6UCLX8eyzwJ49Ut07dCiw938FaPRz+c8hYmKAIUOkDstJcS6pGnDYuaQSEoARI2TItl4PGI1Qej10RiPOox6m3bwUs36L5lgLIhu4fFnWj7n5lwSs8BgBv5Kyz2Hpvl49YOlSmWPEQXAuKXeUkCDfYHJz5WejEQCg+3sfgFx8lDEQAdsrXlWQiG6Mry+wYXQC4hGDm0py5cm/P3+l+9xcmVukktU9HR1LGDXgcCWMggLp55ebW3U3DZ1OhnJnZDh1sZjIIf39OVS5udA50eeQJQx3s2qVVENVl/uVkuNWr7ZPXETu5O/PYZXJAnDqzyEThiuIj5c6UnPo9TJ3ORFZlxt8DpkwXEF2dlkdaXWMRuD8edvGQ+SO3OBzyIThCurXt+ybTWCgbeMhckdu8DlkwnAFMTGWfbMZNMim4RC5JTf4HLKXVA04ai8pY04u9HCe3hlELsXM3opKp4POgT6H7CXlbnx8sPe5pQAAIyoZwm0a2r10qUO8SYlcjo+PfL6ASqdSKP18OunnkAnDBeTnAw8vjkYM4lHgHSBPmupSTfuAAFms24FGmBK5nOho6S1lmk7hms9hLgIw1Gcd0u52zs8h55JyAdOmAampgL7JAKg9GcD3q6XL3vnz0rA2aBDwyCNO+Y2GyOkMGCDVTavLfw5LBgzCoI8ewfZdPjj/T1kS2dnmdGMbRg04UhvGzp0yxbJSwKZNQFSUpuEQURWOHZPlXQsKZFr0Rx/VOiI3a8PYvn07oqOjER4eDp1Oh/j4+GrPSUpKQrt27eDj44NmzZphwYIFtg/UBoqKgKeflmTxxBNMFkSO7vbbgRdflMeTJkl1sjNx+oRx8eJFtGnTBvPmzTPr+FOnTqF///7o0qUL9u3bh5deegnPPfcc1qxZY+NIrW/2bODgQaBBA+Ddd7WOhojM8cILQLNmQHo68NprWkdjGZeqktLpdIiLi0NMTEylx0yZMgUJCQk4fPhw6XOjR4/Gr7/+iuTkZLOu4whVUsePA61aSSnjyy9lDn4icg7ffSft47VqAQcOyHKvWnGrKilLJScnI+qaups+ffpgz549uHLlikZRWe7FFyVZ9OkjC9ATkfN46CHZiouB8eOdZy1wt0sYmZmZCAkJKfdcSEgIiouLce7cuQrPKSwsRF5eXrlNS//7H7BmjfTUmzPH+XpaEJGsfOntDfz3v/J5dgZulzAAqbq6mqlW7trnTWbNmgV/f//SrWHDhjaPsTJKAf/3f/L4qaeA1q01C4WIbkCzZmUN4BMnOkcDuNsljNDQUGRmZpZ7LisrC7Vq1UL9+vUrPGfq1KkwGAylW1pamj1CrdA33wA//wzUqQO8+qpmYRCRFUyZAjRtCvz5p9QWODq3SxiRkZFITEws99zmzZvRvn17eHp6VniOt7c3/Pz8ym1aKCgo+0YyZQoQGqpJGERkJb6+wJtvyuP33pMZ0h2Z0yeM/Px8pKSkICUlBYB0m01JSUFqaioAKR088cQTpcePHj0af/zxByZNmoTDhw/j888/x2effYbJkydrEb5F5s0DTp+W+c1M1VJE5NwGDwbatAHy8pyglKGc3NatWxWA67bY2FillFKxsbGqW7du5c7Ztm2batu2rfLy8lJNmjRRH3/8sUXXNBgMCoAyGAxW+iuqd+6cUv7+SgFKLV5st8sSkR0kJMhnu3ZtpTIz7XttS+5nLjUOw160GIfx4otSdG3TBti7F/DwsMtlicgOlAI6dQJ27QImTJDqKXvhOAwXk5MDfPSRPH7tNSYLIlej0wGvvy6PP/5YGsEdEROGE5g/H7hwAbjzThnsQ0Su54EHgK5dgcJCYOZMraOpGBOGg7t4EXj/fXk8dSoH6RG5Kp2ubG6pTz8FTp3SNp6KMGE4uE8+ka52t94KDBmidTREZEtdu8qs08XFZd1tHQkThgMrKirrZjdlikxURkSubepU2S9bJmsvORImDAe2fLlMgRweLutdEJHr69ZNekNeviw1DI6ECcNBlZTIeheADNLz9tY2HiKyD51OutYCMljXkSbRZsJwUAkJsuZFYCDwzDNaR0NE9jR0KBAcLN1r167VOpoyTBgOatEi2Y8cCdx0k7axEJF9+fgAY8bIY1MvSUfAhOGATp8GNm2SxyNHahoKEWlkzBjAywvYuVM2R8CE4YA+/VSmCnjgAelOS0TuJyQEGDZMHs+dq20sJkwYDubKFeDzz+XxqFHaxkJE2nr+edmvWgVcs4yPJpgwHMx33wFnzkiD14ABWkdDRFq6+26gY0fpNfnll1pHw4ThcEyN3U8+KfWXROTehg+X/fLl2sYBMGE4FDZ2E9G1HntMZnnYtw84eFDbWJgwHMjnn7Oxm4jKCwoCHnxQHmtdymDCcBBKAV9/LY9HjNA0FCJyMKZqqZUrAaNRuziYMBzEwYPA77/LFCDR0VpHQ0SO5KGHgIAAGfm9bZt2cTBhOIjVq2Xfpw9gp1VfichJeHsDjz4qj5ct0y4OJgwHYUoYjzyibRxE5JhM1VJr1gCXLmkTAxOGAzh8WKqkPD1ZHUVEFbvvPqBRIyA/H9iyRZsYmDAcwJo1su/dW+opiYiupdOV9ZZav16bGJgwHACro4jIHFcnDKXsf30mDI0dOwb8+qsMzBk4UOtoiMiR9eghU5+npQG//Wb/67tEwvjoo4/QtGlT+Pj4oF27dvjxxx8rPXbbtm3Q6XTXbUeOHLFjxGU2bJB9t26yWBIRUWVq1wZ69pTHWlRLOX3C+PrrrzFhwgRMmzYN+/btQ5cuXdCvXz+kpqZWed7Ro0dx5syZ0u3222+3U8Tl/fCD7KOiNLk8ETmZhx6S/Xff2f/aTp8w3n33XTz11FN4+umn0bJlS7z//vto2LAhPv744yrPCw4ORmhoaOnm4eFhp4jLFBcDSUnyuFcvu1+eiJyQqR0jORnIzrbvtZ06YRQVFWHv3r2IuubreVRUFHbs2FHluW3btkVYWBh69eqFrVu32jLMSu3dC+TlSc+ou+/WJAQicjKNGgGtW8sUIabJSu3FqRPGuXPnUFJSgpCQkHLPh4SEILOS1UbCwsKwaNEirFmzBmvXrkWLFi3Qq1cvbN++vdLrFBYWIi8vr9xmDaa+1N27AxoUcIjISZlKGfZOGLXseznb0Ol05X5WSl33nEmLFi3QokWL0p8jIyORlpaGOXPmoGvXrhWeM2vWLMyYMcN6Af/N1H7B6igiskT37sCbbwLVVKRYnVOXMIKCguDh4XFdaSIrK+u6UkdVOnXqhGPHjlX671OnToXBYCjd0tLSahyzSUEB8L//yWNTrwciInN06iT748eBrCz7XdepE4aXlxfatWuHxMTEcs8nJiaic+fOZv+effv2ISwsrNJ/9/b2hp+fX7ntRiUnS9IIDQVatrzhX0dEbiQgAGjVSh4nJ9vvuk5fJTVp0iQMHz4c7du3R2RkJBYtWoTU1FSMHj0agJQO0tPTsezvKR7ff/99NGnSBK1atUJRURFWrFiBNWvWYI1pfg47MbWz9+wpQ/6JiCwRGSlz0O3YYb9Bv06fMB577DFkZ2fj1VdfxZkzZ9C6dWts2LABjRs3BgCcOXOm3JiMoqIiTJ48Genp6fD19UWrVq2wfv169O/f365x794t+/vus+tlichFdO4MfPqpfdsxdEppMSOJc8vLy4O/vz8MBkONqqeUkqqorCwpTprqI4mIzHX0KBARIVOFGAyAl1fNfo8l9zOnbsNwVmfOSLLQ64G77tI6GiJyRs2by3RCBQVASop9rsmEoYF9+2QfESFzwxARWUqnk2opwH7VUkwYGvjlF9m3battHETk3Dp2lL3pnmJrTBgaMJUw7rlH2ziIyLndcYfsDx+2z/WYMDRgShgsYRDRjTCN4TpyxD4LKjFh2Nn588Dp0/KYCYOIbsRtt8nia/n5wJ9/2v56TBh2duCA7Js04frdRHRjPD0laQD2qZZiwrCzEydk37y5tnEQkWswVUsxYbggU3VU06aahkFELoIJw4WdOiV7JgwisgYmDBdmShhNmmgaBhG5CCYMF8YqKSKypltvlf3Zs8Dly7a9FhOGHRUWAhkZ8pgJg4iswd9fJiAEgEpWprYaJgw7+uMPGVxTuzYQFKR1NETkCnQ6mf0aYMJwKVdXR3HRJCKyFtOCoWfO2PY6TBh2ZFoKvFEjbeMgItfCEoYLysmRff362sZBRK7FlDBYwnAhubmyr1dP0zCIyMWYqqRYwnAhpoTBOaSIyJpYJeWCTFVSTBhEZE2sknJBLGEQkS34+8s+P9+212HCsCO2YRCRLZgG7nGktwthCYOIbMHXV/YFBba9Ti3b/noCIP+Lq1bhrZPxqI1stH29PvBnDDBkSNlXAyKimigoQIONq7Aa8QjOzgYG1wdiYmxyf9EpZf5KsHPnzsW4cePg4eFh1SCcTV5eHvz9/WEwGODn51f1wQkJwIgRQE4OSqCHB4xQej10RqPUTS1dCkRH2yVuInIxFdxfoNcDFtxfLLmfWVQlNXHiRLRp0waJiYmWnGZzH330EZo2bQofHx+0a9cOP/74Y5XHJyUloV27dvDx8UGzZs2wYMEC2wSWkCCZ/u+6KA8YAUCSBSDPDxwoxxERWaKS+wtseX9RFliwYIFq0KCB0uv1auDAgerEiROWnG4TX331lfL09FSffPKJOnTokHr++edVnTp11B9//FHh8SdPnlS1a9dWzz//vDp06JD65JNPlKenp1q9erXZ1zQYDAqAMhgMlR90+bJS9eoppdMpJXMOVrzpdHLc5cuW/ulE5K6seH8x6372N4sShlJK5eTkqPHjxytPT0/l4+Ojpk6dqvLz8y39NVbToUMHNXr06HLPRUREqBdffLHC41944QUVERFR7rlRo0apTp06mX1Ns17gZcuq/o+8dlu+3OzrE5Gbs+L9xZKEYXEvqYCAAHzwwQfYt28fOnfujNmzZ6N58+ZYvny59Yo9ZioqKsLevXsRFRVV7vmoqCjs2LGjwnOSk5OvO75Pnz7Ys2cPrly5UuE5hYWFyMvLK7dVKz5e6hLNodcDcXHmHUtEpNH9pcbdalu1aoUffvgBq1atgpeXF0aMGIHIyEjs3r3bKoGZ49y5cygpKUFISEi550NCQpBZyRj5zMzMCo8vLi7GuXPnKjxn1qxZ8Pf3L90aNmxYfXDZ2WV1idUxGoHz5807lohIo/vLDY/DGDx4MI4cOYLp06dj//79iIyMxJNPPlnpDdsWdNcsLqGUuu656o6v6HmTqVOnwmAwlG5ppnnKq1K/vmXfAAIDzTuWiEij+0uNE0ZJSQn27duHhQsXYsyYMfj6669RWFgIo9GIpUuXokWLFpg7d65VgqxMUFAQPDw8rktOWVlZ15UiTEJDQys8vlatWqhfybzj3t7e8PPzK7dVKybGsm8AgwaZdywRkUb3F4sSxldffYWJEyfivvvug5+fH9q3b48xY8ZgyZIlyMrKQv/+/fHGG2/giy++QIsWLTBx4kT06tULBoPBKsFey8vLC+3atbuum29iYiI6d+5c4TmRkZHXHb9582a0b98enp6e1gtuyBDpB13d0no6nRz3yCPWuzYRuTat7i+WNMzrdDql0+mUh4eHuvPOO9WoUaPU0qVL1e+//17h8R9++KHy9PRUTz75pCWXsYipW+1nn32mDh06pCZMmKDq1KmjTp8+rZRS6sUXX1TDhw8vPd7UrXbixInq0KFD6rPPPrNNt1qllEpIkG5tlXV9M/1bQkKN/nYicmNWur/YrFvt9OnT1ebNm1VeXp7Z5zz55JMqKCjIkstYbP78+apx48bKy8tL3XPPPSopKan032JjY1W3bt3KHb9t2zbVtm1b5eXlpZo0aaI+/vhji65nyQus1q2TftCAKoZeKUAZ9bJX9eoxWRBRzVVwf1EW3l8suZ9ZNDVITcyePRvTpk1DSUmJLS9jVxZNDQLIXFKrV2PL+Djocs+jZedAhI4ZJMVEziVFRDeioACn56zG3v/EIczrPDo/FChtFmbeXyy5n9k8YaSnp2Pz5s148sknbXkZu7I4YfztgQeAH34AVq4Ehg2zYYBE5FZ27ADuuw+49Vbg+HHLzrXZXFI1cfPNN7tUsrgRpmnNTSvvERFZw6VLsrd1hQXXw7AjU8IwrYtBRGQNWVmyDw627XWYMOzItNIeEwYRWZNpLW/T2t62woRhRyxhEJEtmMYih4XZ9jpMGHbENgwisgVTwmAJw4WYZisxFR+JiKyBVVIuqEkT2Z86pWkYRORiWCXlgpo2lf2ZM8Dly9rGQkSug1VSLigwELjpJnmcmqptLETkGoqKZHkMgCUMl6LTlZUyWC1FRNaQni57L6+yrvu2woRhZ0wYRGRNhw/Lvnlz89dUqikmDDtjwzcRWZMpYbRsaftrMWHYmamEcfq0pmEQkYtgwnBhphLGyZOahkFELoIJw4WZ/lMPHQKKi7WNhYicm1JMGC7t9tula+3ly8DRo1pHQ0TOLCtLphrS6aTR29aYMOxMrwfatJHH+/ZpGwsROTdT6aJJE8DX1/bXY8LQQNu2sv/lF23jICLnZs/qKIAJQxP33CN7ljCI6EakpMi+dWv7XI8JQwOmEsa+fdJoRURUEzt2yD4y0j7XY8LQwB13yDB+g4ED+IioZnJzgYMH5TEThgvz8iorQrJaiohq4uefpYbi1lvL1tqxNSYMjZjaMXbt0jYOInJOpuqozp3td02nThg5OTkYPnw4/P394e/vj+HDhyO3mgWzR4wYAZ1OV27r1KmTfQK+Spcust+61e6XJiIXYO/2C8DJE8awYcOQkpKCjRs3YuPGjUhJScHw4cOrPa9v3744c+ZM6bZhwwY7RFtez56y37tX6iKJiMxVUgLs3CmP7VnCqGW/S1nX4cOHsXHjRuzcuRMdO3YEAHzyySeIjIzE0aNH0aJFi0rP9fb2Rqitl6aqxi23yMjM338HkpKAgQM1DYeInMjBg0B+vswaYa8utYATlzCSk5Ph7+9fmiwAoFOnTvD398cOU1mtEtu2bUNwcDCaN2+OkSNHIisrq8rjCwsLkZeXV26zBlMpY8sWq/w6InITP/0k+06dAA8P+13XaRNGZmYmgoODr3s+ODgYmaYFbivQr18/rFy5Elu2bME777yD3bt3o2fPnigsLKz0nFmzZpW2k/j7+6Nhw4ZW+Rt69ZL9Dz9Y5dcRkZvYuFH23bvb97oOlzCmT59+XaP0tduePXsAADqd7rrzlVIVPm/y2GOP4cEHH0Tr1q0RHR2N77//Hr///jvWr19f6TlTp06FwWAo3dLS0m78D0XZf/bBg8Bff1nlVxKRiysoKPuS+eCD9r22w7VhjBs3DkOHDq3ymCZNmmD//v34q4K77NmzZxFiQafksLAwNG7cGMeOHav0GG9vb3h7e5v9O80VFATcfbcM79+6FajmzyYiwrZtwKVLwM03l01kai8OlzCCgoIQFBRU7XGRkZEwGAzYtWsXOnToAAD4+eefYTAY0NmCbgPZ2dlIS0tDWFhYjWO+ET17SsL44QcmDCKqnqkypH9/mdbcnhyuSspcLVu2RN++fTFy5Ejs3LkTO3fuxMiRI/HQQw+V6yEVERGBuLg4AEB+fj4mT56M5ORknD59Gtu2bUN0dDSCgoIwaNAgTf6O3r1l/913gNGoSQhE5CSUKksY9q6OApw4YQDAypUrceeddyIqKgpRUVG46667sHz58nLHHD16FAaDAQDg4eGBAwcOYODAgWjevDliY2PRvHlzJCcno27dulr8CejZE/D3BzIzywbiEBFV5PBhmX/O27us04w9OVyVlCUCAwOxYsWKKo9RV00H6+vri02bNtk6LIt4eckYjGXLgNWrgfvv1zoiInJUptJF9+4yBsPenLqE4SoeeUT2a9awWoqIKqdldRTAhOEQevcG6tYF/vyTkxESUcX++qtswB4Thhvz8QGio+Xx6tXaxkJEjunLL2UOqQ4dgGbNtImBCcNBmKqlVq/mKnxEdD1Tfx4z5le1GSYMB9G3L1CnDvDHHzKDLRGRyaFDwC+/ALVqaTteiwnDQfj6ltVLfvGFtrEQkWMxlS769ZMZIrTChOFAnnhC9suWyXwxRERGI7BypTzWsjoKYMJwKH37Ag0bAtnZwNq1WkdDRI4gKQlIS5MBvqbOMVphwnAgHh7A00/L40WLtI2FiByDqTrq0UelR6WWmDAczD//Cej18q3iyBGtoyEiLV24UNbVXuvqKIAJw+HccktZ4/cnn2gbCxFpa/FiSRotWgD33ad1NEwYDmnUKNkvWcLGbyJ3VVICfPCBPH7+eal50JoDhEDXMjV+nz/Pxm8id7V+PXDiBBAQUNaDUmtMGA7o6sbvjz7SNhYi0sb778v+mWdkUK8jYMJwUE8/LVOf/+9/ZROOEZF7+PVXWbbZwwMYO1braMowYTio8HAgNlYez5qlbSxEZF9z58p+8GCgUSNtY7kaE4YDe+EFaejasEHW/SYi15eVVTaye8IETUO5DhOGA7vtNuCxx+QxSxlE7mH+fKCoSKYx79RJ62jKY8JwcC++KPtVq4Dff9c2FiKyrezsssbuyZMBnU7TcK7DhOHg7rpL5o9RCnjrLa2jISJbmjMHyMsD2rSR9gtHw4ThBF56SfbLlskkZETkerKyygbqvfqqYwzUu5YDhkTX6tQJ6NEDuHIFePNNraMhIluYPRu4dAm4917tZ6WtDBOGk3j5ZdkvXMi2DCJXk55eNkj39dcdr+3ChAnDSXTvDjz0EFBcDEyZonU0RGRNM2cChYVAly5A795aR1M5p04YM2fOROfOnVG7dm0EBASYdY5SCtOnT0d4eDh8fX3RvXt3HDx40LaBWslbb8nIz/h4mf6ciJzfqVPAp5/KY0cuXQBOnjCKioowZMgQjBkzxuxz3nrrLbz77ruYN28edu/ejdDQUPTu3RsXLlywYaTW0bKlzCsDSJc7o1HbeIjoxr38srRP9u4NdO2qdTTVUC5g8eLFyt/fv9rjjEajCg0NVbNnzy59rqCgQPn7+6sFCxaYfT2DwaAAKIPBUJNwb8hffylVt65SgFIrVtj98kRkRdu3y2dZp1Nq925tYrDkfubUJQxLnTp1CpmZmYiKiip9ztvbG926dcOOHTsqPa+wsBB5eXnlNq0EBwNTp8rjl14CLl/WLBQiugHFxWUTC44cCbRvr2085nCrhJGZmQkACAkJKfd8SEhI6b9VZNasWfD39y/dGjZsaNM4qzNhgqzMl5paNkkZETmX+fOBAweAwEDgjTe0jsY8Dpcwpk+fDp1OV+W2Z8+eG7qG7ppWJaXUdc9dberUqTAYDKVbmsaj53x9y95gM2dyMB+Rs8nMLOsqP2sWUL++tvGYq5bWAVxr3LhxGDp0aJXHNGnSpEa/OzQ0FICUNMLCwkqfz8rKuq7UcTVvb294e3vX6Jq28o9/AAsWADt2AGPGAN9+69i9K4iozJQpMgVI+/bAU09pHY35HC5hBAUFISgoyCa/u2nTpggNDUViYiLatm0LQHpaJSUl4U0nG0Kt1wOffAK0bStLOX79NVBNniUiB/DTTzLNj04n1VIeHlpHZD6Hq5KyRGpqKlJSUpCamoqSkhKkpKQgJSUF+fn5pcdEREQgLi4OgFRFTZgwAW+88Qbi4uLw22+/YcSIEahduzaGDRum1Z9RY3fcAUybJo+fe05muiQix3V1Q/fTT8sU5k7F9p22bCc2NlYBuG7bunVr6TEA1OLFi0t/NhqN6pVXXlGhoaHK29tbde3aVR04cMCi62rZrfZahYVKtWolXfOeeELraIioKq+9Jp/VevWUOntW62iEJfcznVJKaZeunFNeXh78/f1hMBjg5+endTjYuRPo3FmmQN+cUIDeuatkOHh2trSmxcQAQ4YAPj5ah0rkHgoKZBGbqz6Hp++OQesZQ3CxxAfLlwOPP651kMKS+xkTRg04WsIApKvtybkJWKYfgQBjjjRyGI1l+3r1gKVLHXcaTCJXkZAAjBgB5JR9DpVeD53RiPOoh0Wdl2LKT9EO00nFkvuZU7dhUJlZkQmIRwz8jLnyhGneENM+NxcYOFDezERkGwkJUqLPzZWf//786f7eByAXU5IHQvetc34OWcKoAYcrYRQUAOHhULm50FX136nTAQEBQEYGq6eIrO3vzyFyc6V+uDIO9jlkCcPdrFoF5ORUnSwAeRPn5ACrV9snLiJ38vfnsMpkATj155AJwxXEx5u/nqNeD/zdzZiIrMgNPodMGK4gO9v8uc6NRuD8edvGQ+SO3OBzyIThCurXt+ybTWCgbeMhckdu8DlkwnAFMTGWfbMZNMim4RC5JTf4HLKXVA04ai+p6npnKJ0OOgfqnUHkUgoKoMKkt6Ie7CVFjsrHRwblAZVOWWuETnLJ0qUO8SYlcjk+PvjmQfkcGlHJqDzT59NJP4dMGK4iOlp6aQQEyM+mutS/97kIwECsw5JsjvQmsoXvvwf+3xfRiEE8rtQOkCev+RwiIABYt85pZ1xwuOnN6QYMGCDF3NWrpcve+fPSsDZoEOYdegTfzfLBpmeAW28FunTROlgi13HypKxRoxQQPmoAvN+v+HOIRx5xypKFCdswasDh2jDMYDTKehmrVklnjl27gGbNtI6KyPnl5AD33w8cOgR07AgkJQEOtt5aldiGQdfR64ElS2SFr+xs4KGHAINB66iInFtBgUzRduiQ9DtZvdq5koWlmDDcSO3aUn16883A4cPAY4/Jgi5EZLmSEqmG+vFHwM8P2LgRuOUWraOyLSYMNxMeLhNq1q4NbNoEjB9f/dQ3RFSeUsDzzwNr1wJeXvJF7M47tY7K9pgw3NA99wDLl0sPvwULgBdfZNIgssTs2bIet04nn6Xu3bWOyD6YMNzUww8DCxfK47feAmbO1DYeImexdCnw0kvy+L33gEcf1TYee2LCcGMjR8obHgD+85+yx0RUsQ0bgKeeksf/+pdUS7kTJgw3N2EC8Npr8njSJGDRIk3DIXJY69fLUApTY/fs2VpHZH9MGIRp04ApU+Tx6NHAihXaxkPkaBISJFkUFUl17uefmz8xrStxwz+ZrqXTAbNmAWPHSuP3iBHAmjVaR0XkGOLigMGDgStXgCFDgK++kp5R7ogJgwBI0vjgA0kWJSUyRmPZMq2jItLWqlWSJIqLgf/3/4AvvgA8PbWOSjtMGFRKrwc+/RSIjZWkERvLhnByX199JUmipAQYPly6z9Zy89n3nDphzJw5E507d0bt2rURYJqltRojRoyATqcrt3Xq1Mm2gToRDw+pn504UX6eNAn49785ToPcy4oV0rBdUiKl7sWL5bPh7pw6YRQVFWHIkCEYM2aMRef17dsXZ86cKd02bNhgowidk14PvPNO2diMmTOBZ5+VDw+RK1NKxiUNHy4Tdj79NPDZZ0wWJk5dwJoxYwYAYMmSJRad5+3tjdDQUBtE5Dp0OhmcVL8+MGaMjAg/f16K5e7a4EeurbgYGDeubEDrc89Jlaw79oaqjFu+FNu2bUNwcDCaN2+OkSNHIisrq8rjCwsLkZeXV25zF6NGSV2upyfwzTey7suFC1pHRWRdFy7Ie3vhQvmy9P77wNy5TBbXcruXo1+/fli5ciW2bNmCd955B7t370bPnj1RWFhY6TmzZs2Cv79/6dawYUM7Rqy9Rx8FvvtOJizcvBno3FkWjCFyBenpsqDYxo2Ar690o3W3EdxmUw7mlVdeUQCq3Hbv3l3unMWLFyt/f/8aXS8jI0N5enqqNWvWVHpMQUGBMhgMpVtaWpoCoAwGQ42u6ax+/lmp0FClAKUCA5X673+1jojoxqSkKHXzzfKeDg5WatcurSOyP4PBYPb9zOHaMMaNG4ehQ4dWeUyTJk2sdr2wsDA0btwYx44dq/QYb29veLvyqihm6tAB2LNHRrru2gX06QPMmSPfxnSVrHlP5KjWr5dVKPPzgZYtZZ4oK95aXJLDJYygoCAEBQXZ7XrZ2dlIS0tDWFiY3a7pzG6+WZagHD1aZu2cOBFISZFGcSdeqpjcSHEx8PLLMrsBIFOTr10L1KunaVhOwanbMFJTU5GSkoLU1FSUlJQgJSUFKSkpyM/PLz0mIiICcXFxAID8/HxMnjwZycnJOH36NLZt24bo6GgEBQVh0KBBWv0ZTsfHR/qlm3qQLF0KdOsGZGRoHRlR1TIzgd69y5LFs8/KQmJMFmayQxWZzcTGxlbYxrF169bSYwCoxYsXK6WUunTpkoqKilINGjRQnp6eqlGjRio2NlalpqZadF1L6vxcXWKiUvXqSR1wWJhSP/ygdUREFdu6VamQEHmv3nSTUl9+qXVEjsGS+5lOKY7htVReXh78/f1hMBjg5+endTiaO3ECGDgQOHhQ2jImTwZef53jNcgxGI0yFfl//iOPW7cGVq8GWrTQOjLHYMn9zKmrpMgx3Hor8PPPwDPPyEjZt98GIiOBI0e0jozcXXa2jK+YNk2SRWysvFeZLGqGCYOsok4dGfS0di0QGAj88ousHb5oEeehIm18+62UJjZskHa3zz4DliyR8URUM0wYZFWDBgEHDgAPPABcviwjxQcNAs6d0zoychfnz8tcUAMGSCN3RASwcyfwz39qHZnzY8IgqwsPl54nc+bIlCLr1gF33SWrlhHZUkIC0KqVzDar1wMvvADs2we0aaN1ZK6BCYNsQq8H/u//ZIBfy5bAmTPSMD5oEJCWpnV05Gqys4HHH5f3mKlUsWMH8OabHB9kTUwYZFN33y2jw6dMkcVn4uOBO+6QMRzFxVpHR85OKZn7qVUrYOVK+aIyZYqUKjp21Do618OEQTZXu7Z0a/zlF5m4MD9fFma6914pgRDVxOHDQL9+MlXNX39JSXbHDnmvsVRhG0wYZDd33gn8+CPwyScysjYlBejUCRg7FjAYtI6OnEVODjBhgryfNm2SdrKpU+ULCUsVtsWEQXal18sqZkeOSE8WpYCPPgKaNwfmzQOKirSOkBxVcTHw8cfA7bfLWhUlJdIT6uBB4I03WKqwByYM0kRwMLBsGfDDD5IssrKA8eOlWuHLL2WQFZHJli0yrufZZ6WB+447ZG2WdeskgZB9MGGQpnr2BH77TUoZISGyMNOwYUD79lLdwEF/7m3vXilF9Ool43vq1QM+/BD49VeZRJDsiwmDNOfpKeuGHz8OvPYaULeu9HLp21duFGwYdz+7dwMPPSRfHL79FvDwkPW2jx2TfS2HW5jBPTBhkMO46Sbg3/+WUsbEiTJ54dat0pAZEyM9YMi1/fwz0L+/LNa1fr20eQ0fLu0UH34I1K+vdYTujQmDHE5QEPDuu8Dvv8tkcTqd1FXfd59s8fFs43A1yclSouzUCfj+eylRxMZK54hlyzhZoKNgwiCH1bixTBZ38CDw1FNS4tixQ0aLt2wpExsWFGgdJdXUlSsyzXiPHjI+Z9MmSRRPPimJYskSNmg7Gq6HUQNcD0MbZ85ItcTHHwO5ufJccLDUaT/7bDXVFQUFwKpVUjzJzpaDY2KAIUPYH/NG1OB1zcyUZL9wYdkqjbVqSYnipZeAZs3sFj3BwvuZjRdzcklccU9beXlKvfeeUo0ayeppgFJeXko99phSGzcqVVx8zQnr1pUtC6jXl9/Xq6dUQoIWf4bzs+B1NRqV+vFHpYYOVcrTs+z/LThYqWnTlLJw0UuyIq64Z2MsYTgGU5XGO+9I90uTW24BRoyQ7daDCfKNF6i4j65OJ/v4eOm/SeZJMO91NSyNxxf5A7BgAbB/f9k/d+4sI/wHDwa8vW0fLlXOkvsZE0YNMGE4nn37gMWLZVrrnBx5zhsFOFsrHDcV50KHKt7mOh0QECD1I6yeql5Bgcxhn5tb5UAZI3TIRQDCkYFC+MDXV8bYjB0LtG1rv3CpalyildxO27bABx/IPf/rr4E+fYBHsQp1i3OqThaA3PRycqS4QtVbtUper2q+a+qhEIgcTG68Gu++C6SnA59+ymThzJgwyKX4+ACPPgps3Ags6BcPo87Mt7heL/NkU/Xi4+X1MoPS6/F6uzhMnCijtMm5MWGQy6p9KRt6ZeaADaMReafP48oV28bkzK5cAbZvB07uyTZ7IIzOaJQ1U8klcIA9ua769eWbsBk3txLokfhLIGLrSYNs166ydejgvs0aRqMMntyyRcZIbNkia5msRn00hh4eMCNp6PVAYKDtgyW7YMIg1xUTA6xda9ahHjBic+1BuHgRSEyUDZDBgh07SvK4/36pfw8JsV3IWlEK+PNPmcNp1y7Z79kD5OWVPy4oCMi6PQYeyea9rjAaZaQluQSn7SV1+vRpvPbaa9iyZQsyMzMRHh6Oxx9/HNOmTYOXl1el5ymlMGPGDCxatAg5OTno2LEj5s+fj1atWpl9bfaSchJm9uYx9ZIy/pmBgyd8sH27VL0kJclKbtdq0EAW77l6a9UKqFPHZn+JVV26BJw4IRP5HTpUliQyM68/1tdXSll9+sh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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculate (x, y) co-ordinates for points on a circle\n", "radius = 2 # radius of the circle\n", "n = 10 # number of points\n", "theta = arange(n) * 2 * pi / n # calculate θ values\n", "x = radius * cos(theta) # calculate x = r cos(θ)\n", "y = radius * sin(theta) # calculate y = r sin(θ)\n", "\n", "# Plot circle\n", "theta = linspace(0, 2 * pi, 100) # generate 100 values of θ in the range 0 <= θ <= 2π\n", "fig, ax = plt.subplots()\n", "plt.plot(radius * cos(theta), radius * sin(theta), \"b\") # plot the circle\n", "plt.plot(x, y, \"ro\", ms=8) # plot the points on the circle\n", "ax.set_aspect(\"equal\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7fca286d", "metadata": { "id": "7fca286d" }, "source": [ "---\n", "\n", "## Sine waves\n", "\n", "We can plot the $y$ co-ordinate of the points on the circle against the values of $\\theta$ by plotting the point with co-ordinates $(\\theta, \\sin(\\theta))$ on an axes and drawing a smooth line connecting the points. Run the Python code below to see the affect." ] }, { "cell_type": "code", "execution_count": null, "id": "b77268ff", "metadata": { "id": "b77268ff", "outputId": "fa4a8f5e-ef74-4666-83a7-12e524b69d45", "scrolled": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "
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\n", "\n", "In audio signals, we can think of the amplitude as being the volume of the sound.\n", "\n", "The code below plots the curve of $y = A\\sin(\\theta)$ for $\\theta$ values in the range $0 \\leq \\theta \\leq 4\\pi$. Try experimenting with changing the value of `A` and see what affects this has on the shape of the curve. To do this change `A = 2` to a different number, e.g., `A = 3`, and click on the run button (or press **ctrl + enter** at the same time)." ] }, { "cell_type": "code", "execution_count": null, "id": "425da62b", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 388 }, "id": "425da62b", "outputId": "5f9412d4-272a-483c-cbf4-443635f0ba81", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculate y = A sin(θ) for the range 0 <= θ <= 4π\n", "A = 2 # amplitude\n", "theta = linspace(0, 4 * pi, 100)\n", "y1 = sin(theta)\n", "y2 = A * sin(theta)\n", "\n", "# Plot the sine curves\n", "fig, ax = plt.subplots()\n", "plt.plot(theta, y1, \"b\", label=r\"$y = \\sin(\\theta)$\") # plot y = sin(θ)\n", "plt.plot(theta, y2, \"r\", label=rf\"$y = {A} \\sin(\\theta)$\") # plot y = A sin(θ)\n", "plt.xlabel(r\"$\\theta$\")\n", "plt.ylabel(\"$y$\")\n", "plt.xticks(arange(5) * pi, [\"0\", \"$\\pi$\", \"$2\\pi$\", \"$3\\pi$\", \"$4\\pi$\"])\n", "plt.legend(fontsize=12)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "06efc260", "metadata": { "id": "06efc260" }, "source": [ "---\n", "\n", "### Frequency\n", "\n", "The **frequency** of a wave is the number of times the wave repeats over an interval of $0 \\leq \\theta \\leq 2\\pi$ radians. If we consider the [points on a circle from before](#Sine-waves), if we multiply the angle $\\theta$ by 2 before calculating the $(x, y)$ co-ordinates of the points on the circle then the points will do 2 revolutions of the circle over the interval $0 \\leq \\theta \\leq 2\\pi$. The curve of $y = \\sin(2\\theta)$ will look like the diagram below\n", "\n", "

\n", "\n", "

\n", "\n", "The frequency of a sine wave is represented using $f$ so our sine function becomes\n", "\n", "$$ y = \\sin(f \\theta). $$\n", "\n", "By increasing the value of $f$ we increase the number of times we do a revolution of the circle which has the affect of reducing the spacing between the peaks and troughs of the sine wave. In audio signals we think of the frequency as the pitch of the sound. Waves with higher frequencies have a higher pitched sound and waves with lower frequencies have a lower pitched sound.\n", "\n", "The code below plots the curve of $y = \\sin(f\\theta)$ for $\\theta$ values in the range $0 \\leq \\theta \\leq 4\\pi$. Try experimenting with changing the value of the frequency `f` and see what affects this has on the shape of the wave." ] }, { "cell_type": "code", "execution_count": null, "id": "819999d6", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 392 }, "id": "819999d6", "outputId": "7d6a13fa-8a45-4e1f-a76b-b8e6dc000cb9", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculate y = sin(f θ) for the range 0 <= θ <= 4π\n", "f = 2 # frequency\n", "theta = linspace(0, 4 * pi, 10000)\n", "y1 = sin(theta)\n", "y2 = sin(f * theta)\n", "\n", "# Plot sine wave\n", "fig, ax = plt.subplots()\n", "plt.plot(theta, y1, \"b\", label=r\"$y = \\sin(\\theta)$\") # plot y = sin(θ)\n", "plt.plot(theta, y2, \"r\", label=rf\"$y = \\sin({f}\\theta)$\") # plot y = sin(fθ)\n", "plt.xlabel(r\"$\\theta$\")\n", "plt.ylabel(\"$y$\")\n", "plt.xticks(arange(5) * pi, [\"0\", \"$\\pi$\", \"$2\\pi$\", \"$3\\pi$\", \"$4\\pi$\"])\n", "plt.legend()\n", "plt.legend(fontsize=12,loc=\"upper right\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "8d7c89f0", "metadata": { "id": "8d7c89f0" }, "source": [ "---\n", "\n", "### Adding sine waves together\n", "\n", "So we have seen that we can control the shape of a sine wave by changing the amplitude ($A$) and frequency ($f$). Combining these we have the following function that describes a sine wave\n", "\n", "$$y = A \\sin(f\\theta).$$\n", "\n", "We can also add sine waves together which will form other waves. For example the diagram below shows the sum of the three sine waves with amplitudes $A = 2, \\dfrac{2}{3}, \\dfrac{2}{5}$ and frequencies $f = 1, 3, 5$ so the wave can be described by\n", "\n", "$$y = 2 \\sin(\\theta) + \\frac{2}{3}\\sin(3\\theta) + \\frac{2}{5}\\sin(5\\theta).$$\n", "\n", "

\n", " \n", "

\n", "\n", "The code below calculates the sum of 3 sine waves with different values for $A$ and $f$. Note how by adding these sine functions together we have a curve that resembles a music signal. This means that we can represent a music signal as the sum of multiple sine waves! Try experimenting with creating different waves by changing the values of the amplitudes `A` and frequencies `f`. Make sure that the that the number of values you define for each of these must be the same, e.g., if you add another value to `A` you wil also need to add another value to `f` (which could be `0`)." ] }, { "cell_type": "code", "execution_count": null, "id": "21280663", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 585 }, "id": "21280663", "outputId": "7835b82b-9d35-45ca-8b0f-72b9befa05c8", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define the amplitudes, frequences and phase angles\n", "A = [2, 2/3, 2/5] # amplitudes\n", "f = [1, 3, 5] # frequencies\n", "\n", "# Calculate the sum of the sine waves\n", "theta = linspace(0, 4 * pi, 10000)\n", "y = zeros(len(theta))\n", "for i in range(len(A)):\n", " y += A[i] * sin(f[i] * theta)\n", "\n", "# Plot sine functions\n", "fig, ax = plt.subplots(len(A) + 1, 1, figsize=(12, 2 * (len(A) + 1)))\n", "for i in range(len(A)):\n", " ax[i].plot(theta, A[i] * sin(f[i] * theta), \"b\", label=rf\"$y = {A[i]:0.2f}\\,\\sin({f[i]}\\theta)$\")\n", " ax[i].set_ylim([-1.2 * max(A), 1.2 * max(A)])\n", "\n", "plt.plot(theta, y, \"r\", label=\"sum of sines\")\n", "plt.xlabel(r\"$\\theta$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "aeb66305", "metadata": { "id": "aeb66305" }, "source": [ "---\n", "\n", "## Using sine waves to make music\n", "\n", "Now that we know how to work with sine waves we are now look at how they can be used to make audio signals of musical notes and chords. The mathematics shown here is used in electronic instruments such as keyboards to produce sounds.\n", "\n", "Here we will try to recreate piano notes using sine waves. There are 88 keys on a standard modern piano, 52 white keys and 36 black keys. When a key is pressed it causes a hammer to strike a string and the vibration of the string disturbs the air to produce the sound we hear. In a real acoustic instrument the sound of the note decreases over time. The keys to the left of the piano produce notes with a lower pitch and the keys to the right produces notes is a higher pitch.\n", "\n", "

\n", " \n", "

\n", "\n", "So if we want to recreate piano notes we need to be able to produce audio signals that have the same pitch as a piano note and we need the volume to decrease over time.\n", "\n", "\n", "### Generating a musical note\n", "\n", "An audio signal is represented over time so we need a way to convert between the angle $\\theta$ in the sine function and time $t$ in seconds. The unit of measure for frequency is **Hertz** abbreviated to Hz (named after German physicist Heinrich Rudolf Hertz, 1857 - 1894), which is defined as the number of cycles per second. So if we have a signal with a frequency of 1 Hz the one cycle of a [circle](#Sine-waves) is equivalent to 1 second in time. Since there are $2\\pi$ radians in a circle then our angle $\\theta$ is\n", "\n", "\\begin{align*}\n", " \\theta &= 2\\pi \\times \\textsf{frequency} \\times \\textsf{time}\n", " = 2 \\pi f t\n", "\\end{align*}\n", "\n", "So an audio signal with frequency $f$ Hz can be generated by the following sine function (we will ignore the phase angle from now on)\n", "\n", "\\begin{align*}\n", " \\textsf{signal} = \\textsf{amplitude} \\times \\sin(2\\pi f t).\n", "\\end{align*}\n", "\n", "The values for $t$ in an music signal are typically calculated using a **sampling rate** of 44,100 Hz which means that each second of the signal is represented by 44,100 values of $t$ so the total number of values in the signal can be calculated using\n", "\n", "$$N = \\textsf{sampling rate per second} \\times \\textsf{signal duration in seconds}.$$\n", "\n", "The sampling rate of 44.1 kHz is the standard sample rate use for music, other audio sources such as speech use a lower sampling rate of 8 kHz since they do not require as much clarity as music signals.\n", "\n", "The code below calculates a signal of 2 seconds in length with a frequency of 440 Hz which is sampled using a sampling rate of 44.1 kHz. The amplitude of the signal is reduced over time to model the decrease in volume that we would hear in an acoustic instrument. The code also plots the sine wave and creates widget which allows us to play the signal and listen to the audio.\n", "\n", "> ***NOTE:*** Make sure you turn the volume on your computer down a bit before playing the signal, especially if you are wearing headphones!" ] }, { "cell_type": "code", "execution_count": null, "id": "09f56b59", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 499 }, "id": "09f56b59", "outputId": "2332003b-ccc6-4774-8898-7b6f0164083d", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Define note parameters\n", "frequency = 440 # frequency of the note in Hz\n", "length = 2 # length of the signal in seconds\n", "samplerate = 44100 # sampling rate in Hz\n", "N = samplerate * length # number of sample values\n", "\n", "# Calculate the note signal\n", "t = arange(N) / samplerate; # calculate time values\n", "note = sin(2 * pi * frequency * t) # calculate note signal\n", "\n", "# Reduce the amplitude over time\n", "note *= ((length - t) / length) ** 2\n", "\n", "# Plot the signal\n", "fig, ax = plt.subplots()\n", "plt.plot(t, note, \"b\")\n", "plt.xlabel(\"time (seconds)\")\n", "plt.ylabel(\"$s(t)$\")\n", "plt.show()\n", "\n", "# Play the note signal\n", "Audio(note, rate=samplerate)" ] }, { "cell_type": "markdown", "id": "c03d995e", "metadata": { "id": "c03d995e" }, "source": [ "The plot above may not look much like a sine wave but if we plot the first 0.01 seconds we can see we have a sine wave which repeats approximately every 0.0023 seconds." ] }, { "cell_type": "code", "execution_count": null, "id": "bba885f3", "metadata": { "id": "bba885f3", "outputId": "68e7aa57-fe0b-44e5-bfde-b1be7e7c8f86", "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax.set_xlim(0, 0.01)\n", "display(fig)" ] }, { "cell_type": "markdown", "id": "3b83f851", "metadata": { "id": "3b83f851" }, "source": [ "The note with the frequency 440 Hz is known in music as the note **A4** or **A over middle C** (middle C is the note near the middle of the range of pitch of a piano). This note is used as the standard reference for tuning modern western instruments. Try experimenting with changing the `frequency` and `length` parameters to produce other notes which are shown below (for a full list see [wikipedia](https://en.wikipedia.org/wiki/Piano_key_frequencies)).\n", "\n", "| Note | Frequency|\n", "|:--:|:--:|\n", "| C3 | 261.6256 |\n", "| D3 | 246.9417 |\n", "| E3 | 329.6276 |\n", "| F3 | 349.2282 |\n", "| G3 | 391.9954 |\n", "| A4 | 440 | \n", "| B4 | 493.8833|\n", "\n", "\n", "---\n", "### Generating a musical chord\n", "\n", "As well as individual notes, music is also played using **chords** which are a combination of three or more different notes played at the same time. For example, the A chord consists of the notes A, C# and E.\n", "\n", "

\n", " \n", "

\n", "\n", "We can generate an audio signal of a chord by adding together the sine waves for each of the individual notes. The frequencies of the notes in a chord are related by a **frequency ratio** which are given in the table below for the most common type of chords.\n", "\n", "| Chord | Frequency ratio |\n", "|:--|:--:|\n", "| Major | 4:5:6 |\n", "| Minor | 10:12:15 |\n", "|Diminished | 20:24:29 |\n", "| 7th | 20:25:30:36 |\n", "\n", "Since the note A4 has a frequency of 440 Hz, and the major chord has the frequency ratio 4:5:6 so the two other notes in the A4 major chord (C#5 and E5) have frequencies $\\frac{5}{4} \\times 440 = 550$ Hz and $\\frac{6}{4} \\times 440 = 660$ Hz . The first note in the chord is known as the **root note**. Therefore the signal for the A4 chord is\n", "\n", "$$s(t) = \\sin(440\\times 2 \\pi t) + \\sin(550\\times 2 \\pi t) + \\sin(660 \\times 2 \\pi t).$$\n", "\n", "The code below generates a signal of length 2 seconds of a musical chord defined by the frequency of the root note and the frequency ratio." ] }, { "cell_type": "code", "execution_count": null, "id": "fb5a65d8", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 499 }, "id": "fb5a65d8", "outputId": "330b681f-c1c4-4544-9bbf-12ba959ccd2c", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Define chord parameters\n", "frequency = 440 # frequency of the root note in Hz\n", "ratio = [4, 5, 6] # frequency ratios of the notes in the chord\n", "length = 2 # length of the signal in seconds\n", "samplerate = 44100 # sampling rate in Hz\n", "N = length * samplerate # number of sample values\n", "\n", "# Generate the chord signal\n", "t = arange(N) / samplerate;\n", "chord = zeros(t.size)\n", "for i in range(len(ratio)):\n", " chord += sin(ratio[i] / ratio[0] * frequency * 2 * pi * t)\n", "\n", "# Reduce the amplitude over time\n", "chord *= ((length - t) / length) ** 2\n", "\n", "# Plot the signal\n", "fig, ax = plt.subplots()\n", "plt.plot(t, chord, \"b\")\n", "plt.xlabel(\"time (seconds)\")\n", "plt.ylabel(\"$s(t)$\")\n", "plt.show()\n", "\n", "# Play the note signal\n", "Audio(chord, rate=samplerate)" ] }, { "cell_type": "markdown", "id": "83a43347", "metadata": { "id": "83a43347" }, "source": [ "In the plot above we can see that we have a signal similar to the one for the single note but with some spikes. A plot of the chord signal for the first 0.04 seconds is generated below." ] }, { "cell_type": "code", "execution_count": null, "id": "2b45458c", "metadata": { "id": "2b45458c", "outputId": "dbaa910f-597f-4491-df65-281aa7d05212", "scrolled": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax.set_xlim(0, 0.04)\n", "display(fig)" ] }, { "cell_type": "markdown", "id": "0dee3572", "metadata": { "id": "0dee3572" }, "source": [ "Try experimenting by changing the `frequency` of the root note, the frequency `ratio` and the `length` and listen to the affect this has on the sound of the chord." ] }, { "cell_type": "markdown", "id": "b216c749", "metadata": { "id": "b216c749" }, "source": [ "### The frequency spectrum\n", "\n", "When dealing with a signal that is the sum of lots of sine waves it is convenient to represent it as a plot of the amplitude of each of the sine wave in a signal against the freqency. This plot is know as a **frequency spectrum**. For example, the Python code below plots the frequency spectrum for an A4 chord which is the sum of three sine waves with frequencies 440 Hz, 550 Hz and 660 Hz. " ] }, { "cell_type": "code", "execution_count": null, "id": "61bd74d8", "metadata": { "id": "61bd74d8", "outputId": "2076464b-a2bc-4c29-9a41-cd09777f32bd", "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define chord parameters\n", "chord_freq = [440, 550, 660] # frequencies of the notes in the chord\n", "\n", "# Calculate the frequency and amplitude\n", "frequency = arange(1000)\n", "amplitude = zeros(1000)\n", "amplitude[chord_freq] = 1\n", "\n", "# Plot amplitude against frequency\n", "fig, ax = plt.subplots()\n", "plt.stem(frequency, amplitude, \"b\", markerfmt=\" \", basefmt=\"-b\")\n", "plt.title(\"Frequency spectrum\")\n", "plt.xlabel(\"frequency (Hz)\")\n", "plt.ylabel(\"amplitude\")\n", "plt.yticks([])\n", "plt.xlim([300, 800])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1b65c806", "metadata": { "id": "1b65c806" }, "source": [ "So here we see that the frequency spectrum shows that this signal is made up of 3 sine waves with frequences 440Hz, 500Hz and 660Hz." ] }, { "cell_type": "markdown", "id": "d454f985", "metadata": { "id": "d454f985" }, "source": [ "---\n", "## Analysing audio signals\n", "\n", "\n", "\n", "We have seen that audio signals are a collection of sine waves that are added together. We can use an amazing mathematical tool called the **Fourier transform**, named after the French mathematician Joseph Fourier (1778 - 1830), which can calculate the amplitudes and frequencies of the sine waves that form an audio signal. By analysing the sine waves in an audio signal we can remove frequencies that are inaudible to a human. Fourier discovered the Fourier series in 1822 when he was attempting to solve an equation to model the transfer of heat. It would have never had occurred to him that the Fourier transform would be used for analysing signals since the technology for recording, transmitting and analysing signals didn\"t exist until over a hundred years later. There are many examples in mathematics where a discovery has applications in other areas other than that which was the original intention, this is one of the things that makes mathematics such a fascinating subject.\n", "\n", "The following Python code reads the wave file `Fur_Elise.wav` which contains the first 12 seconds of a recording of a performance of Beethoven\"s *Fur Elise*. The code outputs the sample rate which the music was recorded, the number of sample points in the audio signal, the length of the signal in seconds and creates a widget allowing us to hear the signal." ] }, { "cell_type": "code", "execution_count": null, "id": "6fd8c125", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "6fd8c125", "outputId": "fc1b2ba0-700b-4c94-e0d9-b71871c01bbc", "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "audio file : Fur_Elise.wav\n", "sample rate : 44100 Hz\n", "no. sample points : 529201\n", "signal length : 12.0 s\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Download audio file\n", "import urllib.request\n", "urllib.request.urlretrieve(\"https://jonshiach.github.io/files/outreach/Fur_Elise.wav\", \"Fur_Elise.wav\")\n", "\n", "# Read in the audio signal and output signal information\n", "filename = \"Fur_Elise.wav\"\n", "samplerate, signal = wavfile.read(filename)\n", "N = signal.size\n", "print(f\"audio file : {filename}\")\n", "print(f\"sample rate : {samplerate} Hz\")\n", "print(f\"no. sample points : {N}\")\n", "print(f\"signal length : {N / samplerate:0.1f} s\")\n", "\n", "# Play audio signal\n", "Audio(signal, rate = samplerate)" ] }, { "cell_type": "markdown", "id": "9118a5e2", "metadata": { "id": "9118a5e2" }, "source": [ "We can see that the audio has been recorded using a sample rate of 44.1 kHz, the audio signal is made up of 529201 sample points so the length of the signal is $\\dfrac{529201}{44100} = 12$ seconds. The code below plots the ampltiude against time for all 12 seconds of the signal." ] }, { "cell_type": "code", "execution_count": null, "id": "d602c14d", "metadata": { "id": "d602c14d", "outputId": "745dd175-391e-4916-cde7-f0da4127d27d", "scrolled": true }, "outputs": [ { "data": { "image/png": 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IiIjIW3hEAmHIkCHYsGEDduzYgfLlyxuWBwcHA0CeHgA3b9409BYIDg5GRkYGkpOTrba5ceNGnv3eunXLpE3u/SQnJyMzMzNPzwQ9Pz8/BAQEmNyIiNyNPVdMmzYFdu1ybNiLI8U7vbFr+YkTakdASjIeL07kCTirE5Fn0XQCQRAEDB48GGvXrsX27dtROVf1l8qVKyM4OBhbtmwxLMvIyMCuXbvQuHFjAEB4eDh8fHxM2ly/fh0nT540tImIiEBKSgoOGl1SO3DgAFJSUkzanDx5EtevXze02bx5M/z8/BAeHq78H09E5IYePhR/qnkiP2MGUL2699QBuHhR7QhoxgzpbW0l5LZtcywWInfz9NNqR0BEStJ0AmHQoEFYvnw5Vq5ciaJFiyIpKQlJSUl4+N8RrE6nw/DhwzF58mSsW7cOJ0+eRJ8+fVCoUCH06tULABAYGIi+ffti1KhR2LZtG44dO4bXXnsNderUMczKUKtWLbRt2xYxMTHYv38/9u/fj5iYGHTs2BE1atQAAERFRSE0NBTR0dE4duwYtm3bhtGjRyMmJoY9C4jIK735ptiboGNHcVpQVxk1Cjh/HvjgA9ft093cugV8801OQoecizM2k9b8/Tcwc6baURCRFml6Gsd58+YBAJo3b26yfMmSJejTpw8A4N1338XDhw8xcOBAJCcno1GjRti8eTOKGs1v9cUXX6BAgQLo1q0bHj58iJYtW2Lp0qXInz+/oc2KFSswdOhQw2wNnTt3xuzZsw2P58+fHxs3bsTAgQPRpEkT+Pv7o1evXpg+fbqT/noiIve2ZIl4A4CNG4GPPnL+Po17Pjh7bnN31qyZ+FwcPAgYfVUREQEQe2llZ6sdBRFpkaYTCIKEPrI6nQ4TJkzAhAkTLLYpWLAgZs2ahVmzZllsU6JECSxfvtzqvipWrIiff/7ZZkxEROQc3lgDwRz987BuHRMIRJSXWskDfkYTaZ+mhzAQEZHzpacrc9DniunrNmxw/j6IHHktp6c7vv/Ll8VhKkRERK7GBAIREVn1/vvAyy87vh1XX3lyRcKCyNXu3AGeeAIoU0btSMhbPXwINGgAjBhh/7r8XCbSPiYQiIjIpnXr1I6AyHtcvWr5sbNnXRcHkTnffQccO8YijETeigkEIiJSjTcXOiSypHx5tSMgsoyf20TejQkEIiJSzaJFzts2u8oCWVlqR+CZWL2eiIi8FRMIRESkmhMnnLdtJhCAGzeUKdpHpmxMykTk0TiTApF3YwKByI1lZqodQY6MDNttjhwBtmxxfixEJN3+/WpH4Hl271Y7AiJlMeFKRFIxgUDkxg4cUDuCHElJ1h8/fRpo2BCIigI2b3ZNTKQtPEAlchyv/pIz8HVFRFIxgUBEktg6+fvxx5zfmUDQvkOHXLMfZyYVmLAgZ1HzZMv4s5bI1fbuBWJi5K9v62IEEbk/JhCI3NjHHwOXLqkdBXmj1193zX541Yu0yBWv2507zS+/eNH5+yaypEkTx9Zv3FiZOIhIPUwgELmxrVuB556Tv36bNsDJk8rE8scfymyHvNeqVa7dH3sgkJZt3Kh2BES2ffABcO+e2lEQkSsxgUDk5q5elb/u5s1ARIQyccTGSm97/74y+5RDEMQCZzdvqheDp0pLc2z9v/5SJg6p1q517f6IiLzNpEnAuHFqR0FErsQEApGHU+pk/s8/rT9uPEvDggXK7FOOjRuByEggKEi9GLQuOxs4ezbv8vbtld+XM3sJ3L3rvG27CykztTiShCT31rEjhwGRMnJ/Fv/7r/RE/LFjysdDRO6LCQQiDbh1S+0IbHOXK/7jx6sdgfZZunLPqevcz6RJttt8+qnz4/A27nLSvnGjdyTKyLUEAShZUkzEP3igdjRE5G6YQCDSgF691I7AtqNHTe+vWiVeyXalEyfyxkH2S0y0/JjSFeBtnYjFxQHff6/sPj3JkiVqR+Cd3CWBQKSUrKyc3x8/zvndGT2YHJ2JYeNG4NQpZWIhIvsxgUCkAVu3qh2B/Xr1ApYude0+69Y1va/TAY0amR4MkWO6dAGuX3f+fhITgX37gJ49gW7dgIcPnb9PIkcMGaJ2BETyLVpk+bEbN4AtW5RLnO3YIX/dQ4fEoTthYcrEQkT2YwKBiJzG0jRkrnTwILBundpReBZHp/GSomJF0+m+jGts2MNcLQciR5k7kZo9W9lpdy0NTWDvB3K1KlWAqCjrvcE++AD46ivnx2KrHhMROR8TCEQkmb09IbZscU4c9uKwBvvYOkFR8iTJ2U6cUDsC9XE6S9f56SfltuWs2Wzu3QMaNACefhpITXXOPsiz6Osg/Pqr+cePHhXrsbz1lvNjcYcLE0TejgkEIo347Te1IwBat7b8mLmDXUfHOdrDWhHHKVNcF4e3+OYbcZpQcn+nT6s7MwrJExfnnO1OnSpWzT98GBgwwDn7IO364QexN4GelB4vriq0mJYGLF/umn0RkWVMIBBpxJEjakdg3cmT6u7/xg119+9NBAHo3Rto08a1+/Rkd+4Ae/c67+/s39852/VWar4ec/cosTeWO3dyft+0yfF4yLO88gowbZraUZiX+0LF/v3qxEHk7ZhAICIih6Slue8JvrvGlduTT4q1JX75Re1IiIicS6meLxERymyHiOzDBAKRRrAYnGP++kvtCDzTqVNAkSJAvnzA6NFqR6NdKSniz59/dv2+lywBfHyA+fNdv2+tspSYunzZtXHIsXFjzu+ZmerFQZ7p5k0gPd16G/3nnZ4gWC4aSkTuhwkEIo349lv56x4+rFwcWlWjBgvqOcOMGTm/f/659PVWrrTvZOvcOeltjSUkyFvPW1y8CLz5pjjVKcfDS2cpgWDPe0AtiYk5v9+7p14c5JmCgoBq1exbZ9gwoHhxy0Uaici9MIFA5AWeflrtCNzDhAlqR+B55PaMefVV4IkngDNnpLV/9ll5+3nnHfHkmMy7ft30Pk8opcnKUjsCIvls9RAwJmcWF+MklRSzZok/33vPtEZHbq4q1khE1jGBQEQeQStj3T3N3r1qR2Dbo0dqRyCd2lMuNm+u7v61Ij5evX3/+aey22vfHpgzR9ltknv77DPpbeV+t169av86f/4JlCpluThi167yYiEiZTGBQOQlMjLUjoC0gskY7/H996b3jx7l/9/dnT+v7PZ+/RUYPFjZbZJ727VLetsdO+Tto0oVeesBOT0Scjt6VP42lbZ7N9C0qWMJPX7WklYxgUCkIY582WzYoFwcWuVOBx9kPxZ8yys52bH1Z87MuywkBDh92rHtatHZs0DnzkBUlLYO7JOT2bWblPHuu3mXyZ0CVumLFtaGNqghMhLYs0fswSPHrVviML7331c0LCKXYAKBSEMuXJC/LsfsApcuqR0BOWL7dnnrufPJ4L17wIoVjq2vtKQk4O23ld+uO3v+eaBWLeCnn4AtW+QX7VRD1apAiRJqR0GewNbQhqVL7dteYqLt45bcdVgssZRAUPvz/cYNeevNmCEW+Y2NVTYea27cEHuGfPqp6/ZJnokJBCINcYex3NOnqx2BeUpUbz51Cvj6ayA72/FtkfIEQey+/euvQHg40KeP9PXc1euvA6+9pnYUeXnbe2DnTtP77vyaMSc93fv+Z+T+Kla0PSNDSIi0bVlKar75pn0xqenRI2DNGnEaSzXer5MmiTPvfPih6/dNnoUJBCINWbtW/rr2VkW25J13lNmO0pQoLBYWBvTr59gVYXKes2eB6tXFLqNHjwLLlqkdkePWrze9LwjaO3nVOnOzdKhdzFKOuXPVjoBIugsXgC+/lN4+d5JPz95eEWoaMUIsBNm5szr754xEpBQmEIg0RG4XbkC9E39XfbmvXCmtnZRx9IcPOxaL1j18qHYE5o0YIW89LZ2Qz58PNG7snJh//135be7ZI46RvntX+W27irmeLO6SQLh8WRxOIWW2k5s3nR8PIMakpfcUuadq1YBhw9SOwrX0x0O7d6uzf75vSSlMIBBpiFpfOo544w21IzAVFKR2BO7PGwvouZP9+02vFP36q5hYcFSzZvbN/y5F06bAggXi/O1atH275R5HWVlizyY1hwZ06QLUrAk0aSJ2PVbbV1+Jhd+8rUYGudaDB47VfCIi52ICgYi8SnKyOOZcyhU9b7VqldoRKEuLV13efRc4dEg8kG7fHhgwADh2zPHtDhrk+DbM0erB/saN5pfrdMDw4cBTT9lfJf3WLYfDMoiPz/n97FnrbeUWc7PHBx+IP7/6yvn7Iu+1fr3YQ0Gns2/KSXeSmAi8+KLl+I17OfXtC/z9t/j7Tz+Jve2cMdxAi9+F5J6YQCDyIm++qc4XSEqK6/dpzYoV4hU9Xmn3Dlo8aJo5E3jmGaBXr5xlDRoAU6c6tt2vvwauXXNsG3rGM7to8TkGLA9VuH4dmD1b/N3e5/z+fcdisuSXX6w/vnCh+wy9UENysji13qJFakdCSmreXO0IrHv8WKydlJVl+pn4xhtiIsQ4fkufk4sXA23birV9OncWP/979jSfNL5/H/j3X3mxavVzmtyP5hMIu3fvRqdOnRASEgKdTof1uSpSCYKACRMmICQkBP7+/mjevDlOnTpl0iY9PR1DhgxBqVKlULhwYXTu3BlXrlwxaZOcnIzo6GgEBgYiMDAQ0dHRuJtr0GdCQgI6deqEwoULo1SpUhg6dCgylJ4Il8gBS5YoU2zQXkp0v3YGewo4SZWaKnbvtVTwiTyPMw/KfvzR9L4SQwXKlQP++ks82XJEy5Y5vztSn0VNlk64c5+0uOLqvi36hAaZun4dqFsXKFlSHOYXE6N2RKS0tDTrj9++LW07ggAcP678UK6vvwa++EKcTlX/GX35su1YjF24IM4upPfDD2LSWG/ePKBjR6BoUfG1LidRyQQCKUXzCYS0tDQ89dRTmG3hm3XatGmYMWMGZs+ejUOHDiE4OBitW7fGPaPJs4cPH45169YhLi4Oe/bswf3799GxY0dkGaUSe/Xqhfj4eGzatAmbNm1CfHw8oqOjDY9nZWWhQ4cOSEtLw549exAXF4c1a9Zg1KhRzvvjiWRQ4ovT3iuYUgscLlkiTi+0aJFrxh0vWKD8Nj/6SLwS+Pzzym9bruvXxTnuZ85UOxLPk50t1hbo2FHtSOwzZYrjNVW02rXYmNQr9nv2SN9mrmsUmiGlwKyrCjXao3Jl4MQJnhx5silTrD/evr207SxbBtSrB7Rp41g85t4H77wjXkAw12Pptdfk9xrQGzjQdMjVX385tr3z5x1bn7yc4EEACOvWrTPcz87OFoKDg4UpU6YYlj169EgIDAwU5s+fLwiCINy9e1fw8fER4uLiDG2uXr0q5MuXT9i0aZMgCIJw+vRpAYCwf/9+Q5t9+/YJAISzZ88KgiAIv/zyi5AvXz7h6tWrhjarVq0S/Pz8hJSUFEnxp6SkCAAktyfPlDORm/mbo+v/8IP8dfW3115TPu4bN0zbL1liex05sVuLy554pcThLvr2tS8muc+lu97u3HHec3vuXM5+0tPtX1/J16w9t969HX/P2tveHTVvLu35qldPEP7+WxBmzxaEhw8de+4ceS0/fqz8/01/++cf+9Z1F3KeA2/XsqX6n8v23AoUcPx1LwiC8PTTyrxGOnSwHcuTT5oue/NNQShYMOd+s2bS/na93MuPHrU/7n79ctavWtWx54A8jz3noZrvgWDNxYsXkZSUhKioKMMyPz8/REZGYu9/FdSOHDmCzMxMkzYhISEICwsztNm3bx8CAwPRqFEjQ5tnn30WgYGBJm3CwsIQEhJiaNOmTRukp6fjyJEjTv07ybvknjfe1esDzinuY9QpCIBYQM4Vqld3/MqAu1O6u6bWCIJrtu2q8ecNGzp+9V/Kc6LVYQnp6eJUmFKmrpU61Cg+XvysGDwY+OQT2+337XNOL6pZs5Tfpp6zajeoYcwYtSMgJTnjmMMRtg7rX3ghpyiiXkKC6eeuGrNqGe9fq4VvyT14dAIhKSkJABCUa962oKAgw2NJSUnw9fVF8eLFrbYpU6ZMnu2XKVPGpE3u/RQvXhy+vr6GNrmlp6cjNTXV5EZky4svqh2BZzl/XjwpIJLDmckJS44ccU1hsQMHnL8PZ1i3TjyBnz5dHE4wZAhg4WvYLvpRjVKSDo0bO2fI0HffKb9Nvbp1c2ZZ0Irjx80vnzbNtXFojaPd37XKVZ/XGza4Zj/2UuP7ijyTRycQ9HS5LgsJgpBnWW6525hrL6eNsdjYWENRxsDAQFSoUMFqTERKUKIHwqNHjm/Dlrlznb8PvVWrlLn65q5X8HjQQLl5crV+47H8Tz0lFh80KlnkMs6osSKFTic/KTppkrKxONNnn4nj2cl+iYlqR+B9tm5V9rtYiW1xJiqSy6MTCMHBwQCQpwfAzZs3Db0FgoODkZGRgeTkZKttbpgpwXzr1i2TNrn3k5ycjMzMzDw9E/TGjh2LlJQUwy2Rn+ia8/gxEBWlTGV0V7l/X3rFYksOHlQmFneSez7448elF3/Uk1KEjFxvyxbxNS8Iyncr1+qJuBKJRHfz+edApUqm1c/1vQaOHlUnJqXt2yet3Zw5zo3DHbz7rtoRkNYYn3T37Qs8fChvO3I/99WemC130qF2bSYRSB6PTiBUrlwZwcHB2LJli2FZRkYGdu3ahcaNGwMAwsPD4ePjY9Lm+vXrOHnypKFNREQEUlJScNDorOnAgQNISUkxaXPy5Elcv37d0Gbz5s3w8/NDuPG8LEb8/PwQEBBgciNt+fFH8eTE0bnZ7WX0MpOldGnHxv3LmUc+93hAd5P75L9ePeDVV4GlS9WIRlnGBztr14rzpU+b5j1XoXr2BOrUAV56CahSRf5Bozlq9u5wpCdQSopycbiL0aPFccYffpj3MUEQxyW/8ILj/7P/Sh/ZxCrn6sqdFCbPJuVz3fi9v3gxMGOG7XXOnBF79Fy9an47alq92r7hKObi9oTZdMj1NJ9AuH//PuLj4xEfHw9ALJwYHx+PhIQE6HQ6DB8+HJMnT8a6detw8uRJ9OnTB4UKFUKvXr0AAIGBgejbty9GjRqFbdu24dixY3jttddQp04dtGrVCgBQq1YttG3bFjExMdi/fz/279+PmJgYdOzYETVq1AAAREVFITQ0FNHR0Th27Bi2bduG0aNHIyYmhokBD/bFF+rsV0pxMFvsmZZMCVWrunZ/9rI0TdQbbwDbtknbhrscVFjz8stAjx5ikbHnnlM7GtdJShKvul++LP3/qYS0tLy9HrKyxP/B5587tm1/f8fW9ybJyeK45A0bHO+BJZUgSE82kPKcObVqWppYTPPkSeftg+xTqBBw9qz1Nrm/o6VcDHn6abFHT/fu8mNzhCCYT0auXy9+j/x3GiJ5W0r7+GPHv8tIg5w8I4TT7dixQwCQ59a7d29BEMSpHMePHy8EBwcLfn5+QrNmzYQTJ06YbOPhw4fC4MGDhRIlSgj+/v5Cx44dhYSEBJM2d+7cEV599VWhaNGiQtGiRYVXX31VSE5ONmlz+fJloUOHDoK/v79QokQJYfDgwcKjR48k/y2cxlF7nnhC+WmjpE5r5Oj6a9fKX9fc/h2JWRAE4cKFvO1v3lT+eZN7szb9pd6dO9L/XldZt87637V+fd51nP1cqn3bsMH8c7VypSBs327f83v2bM52MzJMH9NPTdqokenytWvVfw6k3GJjrf/tudurTerfZfy54uzncOhQ+XE6euvXTxDOn7d//1Kf49u3Hft/OUrKc7Bzp3P2PWKE+7zu5VD7s8VZt7fesv53169v2n7AAOnPlZ9fzrKyZV33N02caH55q1b2vwbNTd87d6709XNLSMjZTmam/O2Qe/CqaRybN28OQRDy3Jb+1+9Yp9NhwoQJuH79Oh49eoRdu3YhLCzMZBsFCxbErFmzcOfOHTx48AA//fRTnoKGJUqUwPLlyw2zJSxfvhzFihUzaVOxYkX8/PPPePDgAe7cuYNZs2bBz8/PmX8+qUwQ1I5Avk2b1I7AtjJlgIED1Y5CNHq07Ta5x0V+/bVzYrGHrVk7unRxSRhuxVxti7NngV69gBYt7NuWtc+AZs3En7lnM3DXYpu5GRcyFQSxS/iVK5bbT5kCfPut8+NylJY/t+2xaBFQrZrztv/ggfO2rRRnzVbiqmmGyT5Kv7f//FPZ7cnx0Ufml8upp2Du+XHkOTP+DPCWz1USaT6BQETyLFzo+n3KSVrMm6d8HHLoi7HZo18/5QsrRkcDzz7rfvNia0lcXN5l1k6MpbpwQezmeuwYcOcOcO6c+XZaKbyYmAhcvCj+/sMPYpdwa5MFjR0LvP66a2JzRKdO4pAGV7DVpZq0iSdLni87W5zFxdj06cDkyerEk9vu3Tm/yzk+UQILR3svJhCIyGFSD5L79pW3fSmFjpxNSsFBcweVSlf9X75cvKLNsdWOsXRyby/jZEDHjsB33wENGuQt6PXHH+LMHmfPqjOloFx374o/t26Vvo7alcZtOXjQ8lU9pW3ebLsXEDmf0ic6f/yR83ubNu5ZlPTePbFOw+efm87eceyYejE521dfAf/8I739vHliPQtzchdQTk8X60+NGwfcvCk7RKcoU0ZMXtu6sJCQkHeZIwlt4x5nTKp5FyYQiEiW27eBZ54RhxjUqiVtHbkzP4waBZw4IW9dJd26Zf86Slb8N8Yva8dcuGB6P/dMFYsWWT6w1Js7V3wP6BkfuOa+Uv/cc+LMHlLfK1p26pR4RSzXzMZuZfZs11UfX79efL/+8w/ft2po0gTw9RXff8bP//XrQP/+YmLPEZs3A5MmObYNZ3jnHTFRNno00LixWPT5wQMxwenJmjSxr/3s2eaX79hheR21rvhb8u+/YvI61wjtPHbuVHa/nMHBezGBQKSQS5fUjsB+J06IB1RyvgxLlxbHgbpqiIE7ZPx79rR/nWrVHDtp2LQJGDYs71XdsWNzrg47yttPai5eBP6bdAeAOFNFTAzw5pvW1xs0CEhNdW5sahMEcQrWM2ekr3PzJuDjA5QtC/z+u/Nic5SzxsebExsLPPkk8N57rtunXFI/D7TyuaHvrXX8OJDP6Kg3JARYsEBMLDjKVUNi7GHc6wAARo4EChdWJxZXspa4NPeaNVeTJjtb7O2nNXJ61q1fD3TuLG92GuP6PloZmkfKYAKByAGXL+f8XrmyenHIVbeumK2vUUP9sWy2vnwsXSVwpb//tn+d27cdi71dO+DLL8VppIzH7u/bBwwfLn+7xp580vbVdk9jfCD5xhvm23z3neX1tVII0VFt24pTsNqTCGjbNuf5fest58SlNePGiT+nTVM3DinyefiRYUqKdwwB00qCR21TpwI3bpgu27hRnVjUsHkz8NNP4kWJ3B49cn08pA0e/jVB5Frx8WpHYL99+8QTY1fMZ23tgMbWwc769YqGIoutXibm5moGlOne+tVXeXtAbNqkzEHixYvAmjWOb0er7BmacvSo2L5zZ+fF407kDNsxZk8RwdRUoGFDcTYHe9kz7tnblC9v///x119tt9mzR148aitWLGeGFDnMXal1h5N1QRCvmi9cKJ4QkjSZmXk/z7Xcs8xS3SVbx6e5e3muWQP4+wP/+5+0/b76qpiMIe/ABAKRgurXVzsC+eR0X7OXOxxkOZOl8YW5r27IYa4L+Y0blq+e28vbuh9KfS1mZACnT4uzKuzbB4SHiwWrrI2PJVO9e4tdxW2ZNQs4csT8lTBb+vWzfx1vcfWq+Jq1R/v2ttu4w7AyuXIP25s4MW+Xf0vu3cu7zJFiuVlZwLJlwF9/mS6/etW+E9mffhILtL79tnhC7A51g7Ti4EFtTEsqhb7Gxc6dwIcf5hRWXLXK+nobNuT8/vixOK0xIL2n4/ffa2OIFimjgNSGLeydHPs/Op0O27Ztk7UukRadPGm7kI0SbtwAgoLE3y9fBp54wrHtLVnicEg2ZWSIB1qe2kVWjQTJsmV5q0XLceiQeAXBU/831ljrpinn6i2Z+uYb8fbcc0Dt2pbbGf8frlwRn3uplKoHQt5p/HjxJuUz3FybJUuAV14Rh5zZa9mynBmK9Nu+fl18/et00pMThw/bv29PNXs2MHiwfesULiz2Iqxa1TkxuYq+KOjzz4s/y5UTi4VKGT61d6+YTBk50vMv+JBjJCcQdsos3anztsta5PXatZM25Z859hwEr1ghfsjv3w9ERMjbnzFb2WmlvPaaOHND2bLi2Hs9W9MPaYGWP+5mzRKvUn7wgdqRuIbx/8pa93cmD5TTuLH06e4qVOABrDfIzha/xxo3Brp1Uzsax7RvL36P5c9vvV1ampgsK1RI7CJuPCWknr44nT3vAb5fcgwZYn8CARCLQvfp41lDQOyp3XTuHDBihPNiIc8h+VpTdna2rFuWu811QuRkV67IX9eemRxGjRIreyuRPHClVauApk3FLH9CQs5Bz+LFtte1pxK8s1j7MtZyAgEQ5wv3FnKTfCSfveOKmzUTZ7og9/Tzz45v44cfxDHW3bs7vi0lGM9rL4elRLwgiFd2V68GihQBSpUSEwhVqph+9/39N/D113ln3ZGCCQTbpNSpqltX/D9p2dWrOb/fvSv9vXr0qPnlr7wiTlssxfbt4rEdeTYv7KxK5HynT7tmP++/75r9OEulSjld5i9csN3+m2+cG48U1ro3KnUAN22aOkUN794Frl1z/X7VMHCgOHd2TIzakXiXzz8Xr3DduCGOof/nH6BrV7EgaG6//y4etGp5rL2W+fhY/1zetg345BPHPveUqA+jpNdfd2z96GhxmI7xc/Lvv+J3V6NGQI8epu0vXjS9X7WqWM9DauE6Y0wgkJ7x8K9Fi4BOnaStZ2nGqB9+EJO5Uq4Jt2wpHtvJce8esHu3YzVFyDWYQCByAnNdEslxWpzlwlhWFtCqlfmulVlZYvGrZs2AMWPEkyqpvvhCuRiNh5V4updfFg+uyHVGjwZmzgSCg8UaLh07ismydu0sv7+lHLTy5Mk2e5+jx4+BatXEMfqWfPQR8MsvjsWlN3euewwZ+ugj64/beh5Pn86ZJvLoUaBkSbFbvD2Mp5m01SsiI0OcpWfyZPv24enkfCbMmKF8HGRbRoZYh6l5cyAyUpy2Ojd2aHcvOkFw7Gv30aNHOHToEK5du4b09HSzbV53NKXrJVJTUxEYGIiUlBQEBASoHQ5JYK3Lupx31vHjQL16ssPRLEEAXnoJWLfOertnn7VcKduVwwcs/W+nTRNP/i2ts2MHoK9H+8svOQW3oqPF6bdya9vW/JVZazElJgKlSwMFC4r3tT6sgtyP/rXmqtfWnj1AkybW29Svr/0Eo7MdPizOIiLn/5aQINalMLdu+/ZAiRJij7hataRvMzVVrL1iXHelYUPxREIKZ77+Ll2yfBX1779tF9obOFBMlPn6KhPPtm053x25Va5s3/BHb5L7u5rfh47JXeNDqWPg7t2B777LuR8eLn5eHT8uHtPs2SN+VsTHi0lNcg57zkMlF1E0Z86cOfjwww+RYqEqkiAI0Ol0TCCQV8rMFLuAkjRSvmz27xcPLhs21N6BwJdfAjVr5txv3z7nbzaXPACkJw/0TpwQx29Wrmy9MCCRI3Q61873/dxz7GGgBEcK1S5dKk4JZ46+B8Ly5dL/T5mZQGBg3uXuMpPAE0+IV0XNfYenpdlef+5cQMnrQKdOmU8gZGUxeWDN7t1irz5Snq33wfXrYrFsKYyTB4A4ne+xYzlTUupNmCAWEDf2zTdij505c2wXMCXlyB7CsHbtWgwZMgQVKlTA9OnTIQgCXnjhBUyePBlt27aFIAh4+eWXsVhKZTQiDySnkq3WToqVkpoqvXvaM88A06eLXUO1NE5u2DCgTRvTZQ8e5J37W67sbLGCNJAzrjYuTpltE+VmqaeNs2RmiidRlk5QmWCw7b33xDHGclgaGy3Xv/9afsxSQtXVLE3vKnXY05QpysViTnKyOBSILLtwAXj4UCxMef262tF4FluJK3PDMG/dEntc7t5te/u5kweW9O4NLFigTt0obyY7gTBz5kyUKVMG+/btw4j/zpTq1auHMWPGYOPGjVi+fDnWr1+PSnIraRBp3Jw59s9N7q0JhE8/tW/apHffFbu4tW8vnlhoVeHCQI0aymyrbNmcBAIAREUBPXsqs20itfn6AmFh4okAybNzp1jIT46bN8UTMVvOn3d8St7oaMfWV4qlpJScGRIcdedOzu+TJ4vHCiVKALdvuz4WLenbV0ze9+sHhISoHY322TOTjnEdD0EQexT06SMmCCMjcx47eFBeLFu3mh4z873gWrITCH/++Sc6d+6MQoUKGZYZT9nYq1cvtGzZEhMnTnQsQiINK16cXcml+Owzeev99pt4YmGr6JXSzp1z7f6kyF2pfssWdeIgcibOmuEYR6bCNTrcs6h6dc8Zurd9u/nlaiT6P/5YvMraoQMwbpzr969lX32ldgSeo0QJ+3rXJieLvSwHDhR7FJgruGpvUnP+fLHWSuvWpstPn86b9GPPNOeRnUDIzMxE6dKlDff9/f1xN9fl1rp16+KopUlFibyEPSVAvLUHgqM++cS1+zOuZUBERJ7nxRfd6wSkf3/lZrwgkmvmTOltS5QQe1nOn5/3sRMn5O1/wADg7Nm8y+fMAbp1A/Rl+UaOFIudWijTRw6SnUAICQnBdaMBRZUqVcKxY8dM2ly+fBkFCjhUp5FI8zilIxGRcp55Rlp3enJfWpmSjWW8iJyjbl37L5qtXGn98R9+EIe6AeL01v/8Azz1lDh1tpTipySd7ATC008/bdK7oG3btvjjjz8wZcoUnDp1CgsWLMDatWvx9NNPKxIokZZdu6Z2BKS07GyxxoU7XaEi8gaHDolDGVq0yKnIzfehe7GV4LE1utVdOq9yKBiRee7aY/bKFdP7ly+LvROKFBGnAY+JsZ2IINtkJxBeeeUVpKen49J/ZTjHjh2L8uXLY9y4cahbty4GDBiAIkWKYNq0aUrFSqRZ5cpJa+euH8iUV/78Yo2LIUPUjoTI+6xYAezYAbz2mli0L3cNEFJX7sJoggBcvZpzf8EC6+t/+qnyMcnBxBRRXrdvAzduqB2F/Ro3FmdRefVVcXrgDz4A6tQB7t9XOzLtkT2+4MUXX8SLL75ouF+6dGnEx8dj0aJF+Oeff1CpUiVER0ejnNQzJyIPl5npOcWlKMecOTlTnDEBROR6gwYBSUlqR0HGsrLE77yePYGmTcXijQsWAEuXitOu2bJundNDlMRcAoGf8+TtjErguSUpUzr+8UfOEOOSJYH0dOfG5GkULVBQvHhxvPPOO0pukshjVKtme95cIiKyz8KFakdAuUVFidMNrlljejD/1lvSEgjugskCIu3p2tW+9mpMzap1socwEJF9Ll8GbOXXeLCiTVOnisV7iIhI7IEwZkze5fYcqNetC+zeLQ5RyS0hQX5s9uDc8kTeoUMH8ViOPRGk0QmC/BFeGRkZWL9+PQ4dOoS7d+8iy0xZXZ1Oh6+//tqhIL1FamoqAgMDkZKSgoCAALXDIQnknvCfPy9OL5Pbpk1Au3aOxUTqmTYNePddtaMgInJfbduK33X2SEwEypfPuR8fD9Svr2hYkvfdvTvw3Xeu2TcRud7y5WKdBG9jz3mo7ATC5cuX0bp1a/z999+wtgmdTmc2sUB5MYGgPY70GDD3thk4EJg3T/42iYiIPE2zZsCuXTn3XZlA6NcP+OqrnPvsKUjk+XbuBJKTgS5d1I7Edew5D5VdA2HEiBG4cOECoqOj8eabb6J8+fIoUEDRkgpEXocVn4mIiEzt3g0cOACEhwMXLgB797pu36dOuW5fROQemjcXf/75pzhTA5mSfca/fft2tGzZEsuWLVMyHiKvodOJYzvz5zddRkRERKaefRYYMMD1vfT27ROT+2lp4lzyROQ96tYVp3ksXFjtSNyL7CKK2dnZqO+q/mNEHqpAAXG6Kp0u50ZERER5qTXEr0cPoGhR4ORJdfZPROopUgS4eFHtKNyL7ARCREQEzpw5o2QsRF7ppZdyfp87V704iIiIKC990cQPPlA3DiJSR79+akfgXmQnEKZMmYIdO3bgB85dRkREREQe7scf1Y6AiNSwfbtp7ZU9e4AtW8T6LN5Idg2En376Cc8//zy6d++OyMhI1K9fH4GBgXna6XQ6fPjhhw4FSURERERERKSGJk2AEyeA338XZ03TK1kS6NgR+OILoHhx9eJzJdnTOObLJ63zAqdxlI7TOGoPaxYQEREREXm3118Hli4FUlOBwEDgwQOx10JkJODjo3Z0trlkGscdO3bIXZWIiIiIiIjII3zzjXjLbdQoYPp018fjTLITCJGRkUrGQUREREREROQxPv9cnAby44/VjkQ5sosokmVz585F5cqVUbBgQYSHh+P3339XOyQiIiIiIiJysYkT1Y5AWbJ7IOyWUHYyX758CAgIQNWqVVGoUCG5u9KU1atXY/jw4Zg7dy6aNGmCBQsWoF27djh9+jQqVqyodnhEREREREREsjhURFEnsYJcvnz50Lp1a3z22WeoXbu2nN1pRqNGjdCgQQPMmzfPsKxWrVro0qULYmNjra6rlSKKd+8CKSnmH7P0arL2KrP02MmT4jQpgwaJ97Ozgb//Bi5eBO7dA/LlA15+GcifX6yKOmECcPCg2O5//wNq1gRCQ8XtCwJw6xYwbhzQty/wzDNiAcR8+cSfxrd33gE2bQL0Oa9798T1q1QBjh4FatQAzp2T8kwREREREZG3k3fG7Tr2nIfKTiBMmDABBw8exKZNm1CzZk1EREQgKCgIN27cwP79+3HmzBm0a9cOTz75JI4ePYq9e/ciMDAQBw4cQPXq1WX9Ye4uIyMDhQoVwvfff48XX3zRsHzYsGGIj4/Hrl27TNqnp6cjPT3dcD81NRUVKlRw+wTCxInA+PFqR0FEREREROT+srPde/Y2l8zC0LJlS0ydOhVLly7F66+/nufxZcuWYcCAARg7diy+/PJLrFixAtHR0fj000/xjbkSlR7g9u3byMrKQlBQkMnyoKAgJCUl5WkfGxuLjzVYUaNAAcDf3/Ljlt4c1t40uR+7f9/0fsGCwKNH0uLLzddX3L5RrsawXN87QX/Lzpa3DyIiIiIiInNSUoBixdSOQhmyeyA0b94cpUuXxvfff2+xzSuvvIJbt25h586dAIAWLVrgr7/+wpUrV2QF6+6uXbuGcuXKYe/evYiIiDAsnzRpEr799lucPXvWpL1WeyC4SmammKwwTi4Yv1ozMgA/P/H37GzxJgjisAQgZ3iCscePxSEP1pIZ6enidvLnF5MWDx6I2/bxEdcrVgxISxPneCUiIiIiIrLm3j2gSBG1o7DMnh4IsmdhOHLkCGrUqGG1TY0aNXDkyBHD/Xr16uHWrVtyd+n2SpUqhfz58+fpbXDz5s08vRIAwM/PDwEBASY3yqE/YTdmXKtAnzwAxGRBgQLiOvnzW04S5E5ImOPnJ/Z48PEBihYFgoKAsmWBUqWAkiXFbQcEAGY6lRAREREREZlw5+SBvWQnEHx9ffHnn39abRMfHw8fHx/D/aysLBQuXFjuLt2er68vwsPDsWXLFpPlW7ZsQePGjVWKipzFTE6IiIiIiIgIALB0KXDzptpRKEt2AqFVq1bYuHEjvvjiCzx+/NjkscePH2PGjBn49ddfERUVZVjuDVMZjhw5EosWLcLixYtx5swZjBgxAgkJCejfv7/aoREREREREZGCatYEevYUfx4+DBw4AMTEALdvA717A6VLqx2hsmTXQLh8+TIiIiJw48YNBAUFoWHDhihdujRu3bqFI0eOICkpCWXKlMH+/ftRqVIlJCUlISwsDAMGDMAnn3yi9N/hVubOnYtp06bh+vXrCAsLwxdffIFmzZrZXE8r0zhSDneupkpERERERM71++/Ac8+pHYVjXDKNIyAWDRwzZgx++OEHk2KAfn5+6Nq1K2JjY1G+fHm5m/c6TCBoDxMIRERERETe6cwZseeB1rksgaCXkZGBc+fOITU1FQEBAahRowZ8fX0d3azXYQJBe5hAICIiIiLyTo8emRZ21yp7zkMLKLFDX19f1KlTR4lNEXmtb74Bli0Dtm1TOxIiIiIiIjKncGHgyy+B8HDPSB7YS5EEAhHJZ9wH6PhxJhCIiIjc0ZEjwAsvAFeuqB0JEblaUJD43j9zBggL8+5eyJITCC1atIBOp8OyZctQvnx5tGjRQtJ6Op0O23hGRGTWyZOm99u3Bz7/XJ1YiIiI3FX//sDEiUCZMq7f96NH4k8/P+8+aSDyZmvWAAUKAOx0b0cCYefOndDpdHjw4IHhvhQ6ftISmbVkCVC7tumyAuwTRERElMe8eeLPV18FVqxw3X5DQ027KOeTPQE6EWnVjh1AkyZqR+E+JH8MZmdnIysrC9WrVzfcl3LLyspyWvBEWtanT95lPDAhIiJPduQIMGCAfeu88krO78uXA999p2xM1jzxhOn9yEjX7ZuI1DdsGN/3uSl+uiIIAs6fP48rHCBGZDcmELQtd48SIiIy1aAB8Prr0tsHBgJTppgu69RJ2ZisadTI9P6rr7pu30RkvzffVHZ7M2dy6FJusk9XfvzxR7z55ptITk42LLt06RLq1KmDmjVrolKlSnj11VeRnZ2tSKBEnuSrr8wv5weUtnEIChGRZfq50qV+12VnA8nJQJUqpssLFlQ2Lmu6dDG9z+9pIvf25ZeOrf/PP8ChQ2Ii4ttvlYnJ08g+3J0/fz6uXLmC4sWLG5YNHz4cp0+fRosWLXDnzh3ExcWhRYsW6Nu3ryLBEnmCW7eAUqXMP8YeCNrm7692BERE7uvTT8WfUk7CHz9W/2S9eXOgbl11YyAiaZo3BzZsEKdYlOvDD4HKlcXb118rFprHkX26curUKTzzzDOG+ykpKfjll1/QvXt3bN26FQcPHkStWrXwNZ99IhOWkgeA+gdLJM+tW+JVMh8ftSMhInJfuYcDWPLee0D+/M6NRYqXXsq7jIl+IrG4qLuJiQGKFnVsGxMnKhOLp5P9MXjr1i2ULVvWcH/Pnj14/PgxevbsCQDw8fFB69atceHCBcejJPIQ27dbf5wHJtrw1lum90uVAooV4/+PiMiacuXEn7aS5R9+6PxY5GKinwg4cULtCPLq0cOx9TdtUiYObyD7cDcgIAB37twx3N+5cyfy5cuHpk2bGpb5+PggLS3NsQiJPMTffwPPP2+9jSvHdXoKnQ743/9cu88FC4AHD4Dx48WK4nohIa6Ng4jIHX34odgr66WXgGXLxKt633yTc/Jdr5719QsVcnqIsjGBQORe74OQEGDzZscu4hw7BrRpo1xMnk52DYSaNWvip59+wqRJk5A/f37ExcWhQYMGJjURLl++jKCgIEUCJdK63EWgzGECwX4ZGWLxwmHDXLtff39gwgTTZf37A6tWuTYOIiJ3U7eu2CtrzRrzj2tluJc7DKMgcjfG06qqackS81Oiy2ErqUmmZOdqhg4dimvXrqFcuXKoUKECrl27hv79+xsez8rKwp49e/DUU08pEiiRlkVHS2vnThldrXCnmQ/8/NSOgIhIfS+8IH/d1q2Vi8NRvXrlXabm97StXoxErrB6tfrHq9HRyiUPFi5UZjveRHYC4eWXX8acOXNQu3ZtVK9eHbGxsXjTaOLNbdu24cGDB2jbtq0igRJp2bJl0tqp/YFMRETkKEd6GKxdq1wcjujVS+xFkZua39MbNpjed5crweRd1D5WXb4cWLpUue1ZK25O5jl07W7AgAEYMGCA2ceioqKQnJzsyOaJPEL9+tI/bFmEzz5Hj6odARG5g+3bgRYt1I7C/el0gCCoHYV1RYqoHYHIUo8yNU+eihQBIiKAffuA9euBs2eB779XLx7yLsuXAyVKqLf/bt2AxYsdm6bRHPYetR9PV4icbN8+6W29NYHQoQNQu7Z97f/6S0zOELkbb30fu8L8+eaXs2u3NK++6tztDx8uFgz2BO5WwuvQIfHn3r1iEuiFF9S/Ekze5dVXgXbt1Nv/6tXKJw8AFk+Ug4c5RE60fr19mU1vPRj4+WcgOFh6+4ULgWrVnBePXN76/yORfoq6yEhg0SJ1Y/EklSqJPxcvBt5+O2d5o0bqxEOWffGFtILB5jRpAljo1KoKS8MDKld2bRyA+P3YsKHr90vkyerUAR4/ZrFUOZhAIHIiewtJefMJaMuW0tqdO+e+0yW62/+vQwe1I/Aue/YAH3wAxMUBffsCiYlqR6QtlpKCx44B27YBvXuL969cEa/C/vgjEBoKfP6562LUuiZNnLPduDjx9e+IPXuAuXOViUcJlk4qKlSQv01zyRUpQzZatTK/vHlz+bEQeTL9LFkzZuQddlG5stib7c8/mTyQSycI7j4aznukpqYiMDAQKSkpCAgIUDscksDaCePly0DFivZt7+pVoHx5x2LSIkEQ5/C11Y1s7lzLV6hcefJu6VPz0CHgmWdcF4de0aLil+APPwAXLohdiJs1E7vSM4ngOuZeF+6WVFJKhw7Axo3Kbe/ePfFEytzzJfUoxVOfa6UsWSJWLnfGzDVyjiRz/7/s3Yaz/9/x8YClicTk7Pvvv8UkiT4RBgAffgiMGGF9XHmDBsCOHYC5w8J//wVKlrQ/Fm/z1lustO+oevXEZK4xue/Bli3FpDAAZGUBH38MTJxofZ3AQODuXfv2k5Qk9t7JyMjpDdy2LfDrr3aH7BXsOQ9lDwQiJ7E3eQCIH5Bk2euvqx2B+GXnblJTxQPJli3FLt7TpgEdO9qfWe/dGzh1yjkxuiNzFdalMD5oiohQJBRNmTtX2ZO3Dh3cp3CeJ+vTR/7VNl9f8ydg48YBaWkOhYX33hMTn+5G6crsISE5hT79/cWEycSJYgLYmlGjzCcPSLoFC8Srzd5m6FD72lsaFnbtGnDwoOPxAMD9+2IxRL18+cTeAr//Lh7H7NwJvPQSMGkS0LVrTlwXL9q/L/3QWF9f8Qa41zSxWuZGM6gTeQ57CicaU/MgulQp4PZt9fYvhTOK59jLXQvkKXFCN3Wq+xUOc6YOHcSrsVKnWdVr3158vzRoAJQtK//9rlVvvw388oty25s5M++yWbOAR4+AqCjl9kPy3bwpJrjfest0+aefOr7tbt2AJ590fDtK+v77nJomSipfHrh+3TQhUKAAkJICfPIJMH163nXYs8Yx+mLLdeqICZuPPlI3Hlfq2hX48kvp7S291sqWVSYeAChUyPx+n3tO/D0yUrwBwMOH4vdNs2Y5CQC5LlwAdu8Gund3bDskctNDYSJte/ZZtSOwnyPzdsvVrRtw8qS0tlr40tfygV5GhnclD55/XjxYl9P1Ol8+cQ7qoUPl92LQMlck0QoUAEaPBurWdf6+yDY1vh/UIgg5Vz6VpD8BCg7OexIVEAB89plYhNIecr5z5syxfx0t03eVB8QhI9ZqU/XpI55keitXDGrX6aQXWvX3F+t/OJo8AMTaJa++6pwhXN6ICQQihcXEqB2BPGpUQ1m9Wvr0je++69xYlOCMBELv3uYz9krq1cu7ThAAYPt2+2b+sKRVK2DgQMvTC1rjLc+58cGiuW6w2dl5l+lnXiD11azp3M8gd+3VpaQGDaT9ncOHA2PHmi6zVhvInu+cl18GzpwRP6+8SfHipvetPWcTJwJNmzo3HleSc0wyb570tvYO81m3TvzZsiXwv/+ZJndIW7zgY5vIeYxPaqdMEauCa7VQT6dO6u7f2snco0fuMXzBltwHKo4KCRGvdFtLSm3ZYvkxqQcPK1bYFZZHkXOAZTydmk4nXtEznl7QmL4rpjmWKqt7mnr1xAPFv/4Cnn5aTFauWZPzuHECYdMmIDZWLHRF6rtzRzzpNMfRpG7v3uJ45Dp1HNuOvTp1kj/VpFwNGkhva9z7IS3NeoFFe/zwg5gMIu8h58JQ//7iMdeNG0C/ftZrH9jb27ZLF/GnTif24NPXBCHtYQKByAHGMyaMGQN07qxeLADwxx/y19VPeaOW0NC8y159VZy2UV891905elCakSHOSayvqh0ba719iRLyT0L/+Ue80vLjj/LW17LRo+WvO2WKfSdO27eLhaHMjafW8pAXe06IGjUSDxSNp2msWjXnd+PCpG3aiEX15Dw3PXvavw5Z9r//WT95dbT6/9Kl4uw7zu6BkDtBumFD3toNzZsDZ8+KBd6cYepU6W0bNAC2bgXOn3d+7zNPJ3fKzS1bgB49lI1FLfq6JVJ63OmLKPr5AWXKAF99JSZ9iXJjAoHIgzRuLH9dd5wL95lngOrV1Y7CdXx8xP/DmTPAb78Br71mvX3uKZXsUbmyONZT7aSXq505I85SoWdPr5EjR8REYcGC0tfJl0/cR2KieGJsbPBg6dtRy6BB5pfn7mZtycSJYrfs3Iw/b8wNYZBj5UpltuOJ7L1S2L277QruWkmA9eqVk8DTnyDlfj62bgVq1HBeTzd7exG0bGmaZCN55M4q1KoVsGqV+ceqV1dnumY5AgLEIQlnz4ozptjy4ov2bV8rnwGkPCYQiDzE5cuOrW9rKimlvPKK9Lbe+uVUurRYfd7clTn9SejBg7anCvXW58+amjVNnxd7inPac9U9N51OnOt67Vqxov3ly0C7dvK35yqWruBJTaIMHWq+AJbx2Flvmsderanktm+3r721cfdaop8e8tgxMXGo73FVubJpO2cm0H/7zXnbZkE46+w9rpEyE9bRo+5f1Hn+fOCDD4CnnhKPI2rUkHY8YO8xA48xvBcTCEQewtbJpCXz54tXVl3RVfL558XCiefPA6mpzt+f0oyvXCupdWuxq6AUsbFAerq0boX6E15vKFImV/Hirrty7esrXuEpXVr++9XVAgLE+bflXA0tX97yAXxQkJhMfPllsdaHqwUGun6fgOvH+wNiTyN/f/vWkfL8dOwoLx5XKVIkZ3rI0qWBd94xnWnGVg8LJVy65NypSIsU0UaBYXdXrJhYIyJ3j7RevfK2LVzY9MR5/Hhp+2jZUnZ4dnv7bXFaUGNSkiP2JgQsHVscOmTfdkh7eFhJ5OX69XPsyqo9PvxQ/IKqWlXalYEaNZwfkz3eecc52928Wfw/SCV1SqOSJYGkJHGOcZKnQAFxppAZM9SORD1PPGH/SX5Ghph4sJa8+u478aBdDfZekVeCVpJGgPWp7vRq1XJ+HI64fdv645Mmid9Jx487Z/+rVrlmNhEp9RUcGe7mDaZMEZOZufXubXvdCRPERJE1b78NfPutnMiUY1wj5o03TB/r3RuIiACaNLFvm5YSDsaFhvXsOcYh98fOT0Qe4Lnn5K/rytoHUqds1Gvd2jlxaI0j3QSNr7jp1asnf3vepFs3sccM2adiRfWmqMzKAurWtT32WY2ut0uWuH6fcrljTRx7HDpku/hukSJijQ5PV6KEMp/5deuqNwTHWf76C9izB3j9dce2U6mSmDS1lNyXM81vbiEhwLVr8tf39RVnZbh7V+xhZPx5tHSpo9FZd+gQEB7u3H2Qa7EHApEHcOTqqJxpfuSyd6yzKw/ypV7VV4O+q62toopSHTigzHY8ma8vkwfG5swRu/lOn267rZrjYvPlA0aNUm//1qg1ZZnx7BeepFgxy4+ZuwLqbE2bAr//nnNfrSRabkp9t2mtW7q+YKY11aqJV+MtJcwsfZaZW+4u/29bihUT43/+ece3JeWz/soV8f3IegmehQkEIg377jux653caXY2bXLth7q1fan95eLoFQhnqlxZnJf5m2/kb0P//JYv797JEnJPYWHAnTvSTs7Vfi/36QO0b2+9ja+vesMnXE3K9G3GwsKcE4fS5FbYd5aQELE34KhRYlfwTp1ct++NG/Mui4kRi6AqNVWv1r43fvnF8W2ULm1+ec2a0rfx5puOx+EMSnxOm9tGly7izzt3xOmizU1hTNrHBAKRA9Q+UH7lFXFaOblcXWnbnYv5OXtKvZ078y7Ll0/6MA0/P8deb4cOiQe0zqwITp5N6vt30SLnxmGLTieeUA0dCqxYkffx114DQkPNj3kmsaiuFoSEAMOGqR1FjilTxJ/Tp4vd4l15wt2+fd5pYhcuBBIStDPloJIGDrR/6kxz6tUTZzPQi4sTf1auDPzxhzg9oi0jRzoeh7syd0yycKH4s0SJvLOdkOdw48N52yZNmoTGjRujUKFCKGahL1tCQgI6deqEwoULo1SpUhg6dCgyMjJM2pw4cQKRkZHw9/dHuXLlMHHiRAi5+nXv2rUL4eHhKFiwIKpUqYL5ZgY0rVmzBqGhofDz80NoaCjWrVun2N9KlNvWrWpH4FytWtnXfu5cx/b31FOOrW/N+PHiCUtuDx647oQ+PBzYsMF8HESW2HOlrUYNcYYQV1Ybt+Z//zNfRf3bb9VP/rozLV1pnjpVvMJetqzakYjFRtU0caL4ffL778DVq+rGojZrBZj1syYMHChtW598Ig71FASge/ec5Y0bO6/Qs7leC1I/s159VVo7uT1XjZmLyVKvDfIsmk4gZGRk4JVXXsGAAQPMPp6VlYUOHTogLS0Ne/bsQVxcHNasWYNRRn0wU1NT0bp1a4SEhODQoUOYNWsWpk+fjhlGg8ovXryI9u3bo2nTpjh27Bjef/99DB06FGvWrDG02bdvH7p3747o6GgcP34c0dHR6NatGw5wsLFHU/Mg1F0O0gFpXTXt7S5s74m1Iwe9uac7UlpIiDj1U26O9iogkqtPH2nt7B0nq6WTT1dq3lztCDyTnx/QubNYXM6deiOowcdHnDLyuefUmRrVnRjPOJBbvXrAw4diXRel6Y+FpMzeYI3+Kr4xKcn/mzelz/bw0UfAp58CJ07YF5sxHr94McEDLFmyRAgMDMyz/JdffhHy5csnXL161bBs1apVgp+fn5CSkiIIgiDMnTtXCAwMFB49emRoExsbK4SEhAjZ2dmCIAjCu+++K9SsWdNk22+//bbw7LPPGu5369ZNaNu2rUmbNm3aCD169JD8d6SkpAgADLGR+5s9W5+XVm6bObluy7cXXnBsfUsx27Ou8S011f595fb4cU7bBQvsf94WLZIff2am7b+/Xj1pcZhbd+FC8bFvvhEEHx9BmDdPEG7dsv9vdBW5z6MWbuasXJnz+PTp4s+4OM9+rvfutd3m9dftiz3X16TbsPYacNXzvWGD6/dp6TUv5z1ibl138+CBIHToIAhz5zp/X7mfs/r1nb9PJcl9Han1eWXPrWlT9Z7Xe/cEYf168bX47LOCUK1azvGFPc+f8fEQIAhjxwrC/fuC0LOn/PeuM3Tvrn4MpBx7zkM13QPBln379iEsLAwhRqnYNm3aID09HUf+G+S3b98+REZGws9ovp82bdrg2rVruPTfxK779u1DVFSUybbbtGmDw4cPIzMz02qbvXv3WowvPT0dqampJjfSFv349SJFXLvfQoVcuz9Xc2RaSnu99hpQQMKEto4UXNPPlx4dLU711L8/UKqU/O2RPLdu2W4zahRw/75pV1VPFBFhu43UXgpa8scfakdAzuLvD/z8M2ChU6pTPPOMWN9m1y7X7VMN+ivNatc3kULNXlBFigAvvCC+FvfuBc6ckXZ8YU1wMDB5stiLceVKceiEu8g9hGPLFnXiINfz6ARCUlISgnJNgl68eHH4+voiKSnJYhv9fVttHj9+jNu3b1tto9+GObGxsQgMDDTcKlSoIOOvJDVVry5WmXVkbl45+vVzfBtvv+34NpSkRle4Jk2kdffr3Rt48kn5+3FlQoTM27pVetLG3HATT1K8uLR2Skzz5W6kHnyXL6/sfqtXV3Z7UmzZYv9YeFcX1tWqffvEJOMPPwCRkUDRompH5Fz/XU9D376qhqEpOp3l6SGlrKsFxoU7n3nG/tpVpF1ul0CYMGECdDqd1dvhw4clb09n5l0oCILJ8txtBEHIs1xuG3P71xs7dixSUlIMt8TERFt/DrmhypVdf/CgxHzi1sYIegspV5n9/YElS5wfizvZvt3+dSZMEAs1uquAALUjcB9SDk6VqGDuLvTjkrt2lb5O9erAvXt5l//zjzijiT1++815xdasadXK/rHwthInEyaIP90tAe1qzz4rVuT3hus+yclAxYpqR0HuyN8feOkl8fd33lE3FnItt0sgDB48GGfOnLF6C5M4SXFwcHCeHgDJycnIzMw09BYw1+bmzZsAYLNNgQIFULJkSattcvdKMObn54eAgACTG5Gr6LvVK8HWCYn+C8YdLFuW87uUKsyTJmnnaoBS5MxI4e4HDw0bWn7MaAQb/ee/HLlVO3cCzZrl3K9b12nhOGTFCmD1avsSgUuXit2RjWolAxATxtZeS+bkGt3oMB8fZbdnj48+EouuOaMAHbnOypXS21qY5IzcwM2bQEyMujF8/z1w+bJ9CVrSPrdLIJQqVQo1a9a0eitYsKCkbUVERODkyZO4fv26YdnmzZvh5+eH8P8ulUVERGD37t0mUztu3rwZISEheOK/OXkiIiKwJdfAns2bN6Nhw4bw+e+b3FKbxu40WInoP7/8ApQp49g2Pvww5/ciRax31XOk+7+SNm0SrxyRd3ntNetJoE6dxF49Y8e6LiY1SUkOSBEZKY79PnYMGDrUfU8qixYFunWzr1aN/srySy8BR4+KQx9+/93+fWutp5etGXV0OiAsTH7XbHIPTZqoHQHJZXzsVrq0+sMG8uVjDxVv5GBpD3UlJCTg33//RUJCArKyshAfHw8AqFq1KooUKYKoqCiEhoYiOjoan332Gf7991+MHj0aMTExhqv9vXr1wscff4w+ffrg/fffx/nz5zF58mR89NFHhuEH/fv3x+zZszFy5EjExMRg3759+Prrr7Fq1SpDLMOGDUOzZs0wdepUvPDCC/jxxx+xdetW7Nmzx+XPC5Et7do5vo2PPxbHgeoPODt3Btatc3y7gHOu+I8bJ47vFQTxpKBYMWkHwfXrO7bfcuUcW58cV7Om9cd9fIBt21wTiyeqVw/43//UjsJ56teXX3xRTm8eV1uxImfueF7zIFKftWOg2bPFQr9Dhoj3X3lFHErg6LEKkV2cPCOEU/Xu3VsAkOe2Y8cOQ5vLly8LHTp0EPz9/YUSJUoIgwcPNpmyURAE4c8//xSaNm0q+Pn5CcHBwcKECRMMUzjq7dy5U6hfv77g6+srPPHEE8K8efPyxPP9998LNWrUEHx8fISaNWsKa9assevv4TSOJAi2p/cJDXVsfWvvenundDI2aJDltr//bvvvzsrKaX/qlO32udmaxlEK4/YvvigIdr6F82xj4EBBOH/e/m2o7fZt+6fOevBAEMLD1Z/Cy9zt00/VfkYtU+P5KFHC9r71bTyd3M8Lqc/1mTPy17V08/GR1k5q7Pfumf5Oni8hQfrrLTe1P89t3Vq1cv3zKZXUvyE7O+f34GC1oyZvYc95qKZ7ICxduhRLly612qZixYr4+eefrbapU6cOdu/ebbVNZGQkjh49arVN165d0ZWDgMjJpk1zbP0zZ5SJIzdrGfOqVR1bXw19+oi9Khzhrl26nUEQ1I7A8/zwg+VxpZMmASkpjn8ekHM8fAjcueOcHkghIeKYY6UUKQL89JP4GezqKYlJHVK/b2NjHdvP4MHiFXOyD79Pyd25XQ0EIrKubVv56wqC7e7cUtgzbeX334vzGNvD39++9oD1rrdGo40k79fR5AG5D333bK15+WXLJ6DvvgtMnQp06OCcfas5l7onKFjQecOXHJ1XvlChvMs6dnTea4ncj9QEgpSZiqyROnWukiIiXL9PqaTMoPXaa2JdgcmTxfsLFzo3JiI5mEAg0hh3KF5Vtqz0tlI75eh04gnR2LFipXN7WVtHagLj/Hkx4fH4sf3719u1S/zpyWPCLXG3XiR6/9XD1ZSnnxZ/btoEtGyZs7xqVXE8vqMnkbb8+KNzt0/ySXmfhYZafqxePcVCIY2SehxRvLhz41DS2bPAF18A77+vdiSW2Sqq+tVXwLffir+PHQukpdkubEqkBk0PYSAi96HEyeO778pf19rkLE2bSttGuXKOT0XUrBmQmen8Ezx3Y+///8UXlSu66YlmzRJ/hoUBW7cC4eHibABLlpj2tpHzvpPSi+mZZ+zfrqdo0EDtCCz79dec4mmWpKVZn5p09eqcWSamTFEuNtIOKzOMo2xZcfhURoa2pnCsUUO8aVVwMNCvn+kyc72FiNyBlx3iEpGjDh5UOwL7/PST63tteFvyQA537a3gLnKfAO7bB1y/DlSq5Pi2582z/riUmiWe7KefHFvfmTMZSEn+2DrpKF8e2LlTrIfTv78iYZHG2Pr85WwcRGQNhzAQeQmlTtjceb7fW7dM7z98KI7tJecTBHE6RKXwANaUr68yyQMA+G8WY4v0w3C8VUiIY+uXLq1MHM4UGcnkATlXt26O9+iT6qWXXLMfR1k7DmvUyHVxEDmKCQQiL2Gty6IS3OGKcu6CTdaGNZAyGjcGWrcWC1AuWiR9PVtVpps2Bdavdyg0TVPz/eToCbRWBQcrU7Dsrbcc34Y1ffs6d/vk3aQU+rPl0CFg+XKgdm3gyhXHtvXJJ9Yf371bHHKhZWPG2Pf9SaQ2JhCINMTZSQBP4A5FJr1F48bAnj3Ab7+JJ7zWCrfZSxDEStSOcueK3ACwbZtj63O6L+VcuwbExDi2jUmTgPbtlYnHkurVc35/7z3n7ou8z/Dhjm+jYcOcHmmOzEbSoQPwwQfW2xQq5B4XMOSKjhZrkagxYwWRXEwgEGmIUl2YncFduu3qx3cPG6ZuHFom9aT099/FAzdnHbxp+aBQquefVzsC0lPi9ebqCvAffSRWnidSipJD0Rzlab0I27TJ+f2ll4BffuE0jaRNTCAQaYgjU6sp1XvB0hf6yJHKbN9RMTFil0keVDtX//6O9RCwdbKmVE8SR2b2cAVLz4O+Sr4zlS/v/H24u1atxJ9aGEP9zjviT+PXjL+/eMWYVy/JW7nis1Ipxp+5AwcC7dp5XpKEvAMTCEQaEhwsb73ISHHqLiUEBppf7k7TDZUr5x1Xr9Vkq5K/FJGRlh8bNcrx7QNAly7KbMfVSpRw/j7+/NP5+3B3338PfPMNsHSp2pFIx2Er5M6KFlVuW9a+x0+eBPbvB8qUUW5/rsT3MWkZEwhEXmDnTm3Pj0ye6fvvLT9WsiSTQM5WvLjaEaivWDFxDLKSJz1KkvoeaNlS/MmeCKSmr78GTp2S1vbkSWDxYmltzdVRqF2bMxcQqYUJBCIP52hRMCJniIpyn7oZ7saZsyBs3eq8bXs7W9Nj6kVFSd+mrQJyevPnA7GxYvV7IrW8+ab0IQW1awNvvCGt7eHDwKpV8uMiImUxgUDkwSZMAKZPd93+nnrK9L4S3dzJsxQuDKxZA/Tr5/i29u51fBveRn+lmpRTpIhYQ+HCBWntixWTvm3jbs4dOljf5nvvAU88IX3bRO5kzhzLjwUHAz165NyvUsX58Thb2bJqR0AkXwG1AyAi5xk/3rX7274d2LED6NgRuH3bsembyDOVKyevYN2pU+IVK2Nya4K4u5kz1dv32bPq7Vur3nsPGDfOOdtu0CDnd62O9SaSwtxwndxFcJ98Evj7b+DECdfE5AybNgFXr+b9PiPSEiYQiEgxJUoAL78s/s7kAUnRpAnwxx+224WGmt4vW1Zb1beliI8Xp2q15wq10lgrxX7OLIamnyUCYM0Kcg13uDJeu7bYwyz3sKCzZ4HHj7U9c4HxVI5EWsUhDEQaIbXYkDOFhakdAbkDqUWypOja1fJjlgrIbdgAXL4MFPDAFLiayQNyDXsSDvnyia/3Vas8t8cNqeOjj/Iu27NHfk+Xb7+1/FhEhH3b0unM1xQpUEDbyQMiT8EEApFGvPii2hFYr5pPnsPWCU7u3gCuVqAA4ONju507TS0qhZS/idyPs2cL6dTJdPw3ZychJXz8cd5lTZrI354n1CUgImmYQCByc0FBwL//useVyfLl1Y6ASLrff1c7AmlGjgRefRWoVUu9GAYMABIT1ds/EWkbE1tE3sMDO4ASeZbXX7dv7Gvx4kBysnNiceZYX/IOxldSAeuvKUsHpFJfh8YF6NzZ55/LX1ep9+TTTzNBKJczT5zYK4VcpWJF522bxw5EnoU9EIjc2OrVwCef2LeOmlcxyfPJPcl84w1xLLfUee2JvN1vvwG+vmpHQd7i+HG1IwB69hR/vv++unEQkXVMIBC5sW7dAD8/taMgyrFvn7z1ihcXx3Lbc0W1bl379lG6dM7v//uffet6g/z5LT9WuLDr4vAEzz6b87u9PRCkXo1t3dq+7RI5wh2GSS5fLhbI1ScSiMg9MYFA5GGc2Z3W39952yb3Ye1k0pXd3MuVA86cAa5dk9beuMhneLhzYnI39rzfL1/Ou+zzz8WZMF56SbmYvMHw4WpHQKQccwUV7VWypOPbyJfPuUMpiEgZrIFARJJUq+aZ0+ZRXoUKAZ07i0MOjAUFyd+m3MRWzZrSt8VxtpZlZYkH57mNHOn6WDyB8Wchi8eR1rVo4fg2qleXt16xYsDdu+xxQ6Ql7IFA5KaaNpW3nrNOoipUcM52yT0995zp/TfeAHbtsr1e8+bml/PkXl3mkgck31NPOX8ffM+Qqzj6WrM1/MFaku3KFbF3VNWqjsVARK7DQwoiN8WrWuROFi8GatSw3c7eGQVef11ePCTiSaY6ypXL+b1IEfvWlfLZ3q2b5aRPy5ZibZzGje3bL5FarL3mCxfmsAUirWECgYiIFFOokH3tS5bM29uBSEvatVN+m++9Z/mxgAAgJQX4/Xfl90skFYc/EXkvjmgmIqI86tVz3b6szQ5gTtGi5pez1w6pwRnDQ8qUsf44Z+chtZUoIb0te0oReRb2QCByM/qsfmysunHkxi6G3kVuQStnnsR/+SUwcCDQpInz9uGJJk1SOwLPY/w6d8Y0jsZDJIjcEZMCRN6LPRCI3MznnwOffip/ykRnncBxXmbvU7MmcPasMttS4nU5ZIjj2/BGY8aoHYHnKVgQePllIC0NqFRJ7WiI3FtAgNoREJGSmEAgckNykwfOxCruJAWHEbgfe4eIkDQ//KB2BESO6dkTuHABiIhw7n5GjgR++825+yAi1+EpARERKcZSfQJX8MYutT16qB0BEWnVypXAwYNAARmXE+1JFqv5vUBEymMCgYgkqVZN7QhIC9gDwbVee03tCIiIiMibMIFARGYtXmx6PyREnTiIpDJOXnjLuHQmbIiIiMiVWAOBiMwqVMj0vpwujuR95JzQKnkSfOwYcPcuUL68ctskUhKTPkREpGWa7YFw6dIl9O3bF5UrV4a/vz+efPJJjB8/HhkZGSbtEhIS0KlTJxQuXBilSpXC0KFD87Q5ceIEIiMj4e/vj3LlymHixIkQcg2m3bVrF8LDw1GwYEFUqVIF8+fPzxPTmjVrEBoaCj8/P4SGhmLdunXK/+FELpK7qBIPekkL6tUDmjdXOwoiItLj8QORZ9HsNcWzZ88iOzsbCxYsQNWqVXHy5EnExMQgLS0N06dPBwBkZWWhQ4cOKF26NPbs2YM7d+6gd+/eEAQBs2bNAgCkpqaidevWeP7553Ho0CH89ddf6NOnDwoXLoxRo0YBAC5evIj27dsjJiYGy5cvxx9//IGBAweidOnSePnllwEA+/btQ/fu3fHJJ5/gxRdfxLp169CtWzfs2bMHjRo1UudJIq+k1Bd1xYrKbIeIiKSrXl3tCIiU5Y0Fbok8mWYTCG3btkXbtm0N96tUqYJz585h3rx5hgTC5s2bcfr0aSQmJiLkvwHcn3/+Ofr06YNJkyYhICAAK1aswKNHj7B06VL4+fkhLCwMf/31F2bMmIGRI0dCp9Nh/vz5qFixImbOnAkAqFWrFg4fPozp06cbEggzZ85E69atMXbsWADA2LFjsWvXLsycOROrVq1y4TNDROQezp4Fata03Y4Hl+RNbL3e/zusIHJrYWE5vwcHqxcHEbmeZocwmJOSkoISJUoY7u/btw9hYWGG5AEAtGnTBunp6Thy5IihTWRkJPz8/EzaXLt2DZcuXTK0iYqKMtlXmzZtcPjwYWRmZlpts3fvXovxpqenIzU11eRGRKRlxj1gihdXLw4irWJCjdzZ4cPAwoVA587Ajh3ikDGO2CXyLh6TQPj7778xa9Ys9O/f37AsKSkJQUFBJu2KFy8OX19fJCUlWWyjv2+rzePHj3H79m2rbfTbMCc2NhaBgYGGW4UKFez5k4kUN3iw2hEQyff002pHQGQbEwSkZeHhQEyMmCxu3lxMIkjpaaYXEAB06eKs6IjIFdwugTBhwgTodDqrt8OHD5usc+3aNbRt2xavvPIK+vXrZ/KYzsyAcEEQTJbnbqMvoKhEG3P71xs7dixSUlIMt8TERIttiVzBx0ftCEjrAgNzfg8IcN1+hwzJO3OItzDqQEdE5Nbu3AHWrlU7CiJyhNvVQBg8eDB69Ohhtc0TTzxh+P3atWt4/vnnERERgYULF5q0Cw4OxoEDB0yWJScnIzMz09BbIDg4OE8vgZs3bwKAzTYFChRAyZIlrbbJ3SvBmJ+fn8nQCSIirfPzAy5eFK+yFiyYs9zZVbh9fZ27fSJXad9e7QiInIdTQhNpn9u9jUuVKoVSpUpJanv16lU8//zzCA8Px5IlS5Avn2mHioiICEyaNAnXr19H2bJlAYiFFf38/BAeHm5o8/777yMjIwO+/x2Bbt68GSEhIYZERUREBH766SeTbW/evBkNGzaEz3+XbCMiIrBlyxaMGDHCpE3jxo3tfxKIHDB/PhAZCXzwgdqRkLcyyvGSyv776iMNsXLdgYiISHVuN4RBqmvXrqF58+aoUKECpk+fjlu3biEpKcmkF0BUVBRCQ0MRHR2NY8eOYdu2bRg9ejRiYmIQ8F/f2l69esHPzw99+vTByZMnsW7dOkyePNkwAwMA9O/fH5cvX8bIkSNx5swZLF68GF9//TVGjx5t2NewYcOwefNmTJ06FWfPnsXUqVOxdetWDB8+3KXPC1Ht2sCtWwBfeqRVcl67nGc8r27dgO3b1Y6CcrP1WmWNBCIicmdu1wNBqs2bN+PChQu4cOECypcvb/KYvj5B/vz5sXHjRgwcOBBNmjSBv78/evXqZZjmEQACAwOxZcsWDBo0CA0bNkTx4sUxcuRIjBw50tCmcuXK+OWXXzBixAjMmTMHISEh+PLLLw1TOAJA48aNERcXhw8++AAffvghnnzySaxevRqNGjVy8jNBlJdSJ1M9egBxcexS663UOJFJSgLKlHH9fj1Nr17AihVqR0FERESeRrMJhD59+qBPnz4221WsWBE///yz1TZ16tTB7t27rbaJjIzE0aNHrbbp2rUrunbtajMmIq1YtEick7xNG7UjIW/B7tv2M5cwfOkl18dB0rCHARERaZlmEwhE5HyFCwPMiXkvJYcFREYqty0yxRNSIiIichUmEIiIyGkuXwZOngTatVM7EiIiIiJyFBMIRETkNBUrijciIiIi0j7NzsJARERE5Gn+mx2aiIjILTGBQEREROQmqlRROwIiIiLLmEAgIiLN8/dXOwL1KFnskpzPWtHL2bNdFwcREZEcTCAQEZFZ3buLP2vVUjcOa2bMABo1AkaNUjsSIseVKKF2BERERNYxgUBERGaNGwesXw/s2aN2JJaNGAHs3w8EBqodCREREZHn4ywMRERklo8P8MILakdBRERERO6CPRCIyMDa2FwiIiIie9WooXYERKQkJhCIiIg0rEULtSMgIrKsRAng4kXgxg21IyEiJXAIAxERkYYtWwaULq12FKQE9gIjT/XEE2pHQERKYQ8EIiIiDStVSu0ISCmNG6sdARERkXVMIBARkap41ZVIxKu0RETk7phAICIiIiIiIiKbmEAgIiIicpE331Q7AiIiIvmYQCAiIiJykRIl1I6AiIhIPiYQiIiIPIyvr9oREBERkSdiAoGIDFjAi8gztGundgRERETkiQqoHQARuY8BA4CEBKBNG7UjIW+i06kdgWfp0wcowG93IiIicgIeYhCRga8v8PnnakdBRERERETuiEMYiIiIiIiIiMgmJhCIiIg8SKtWakdA9ujQQe0IiIiIpGMCgYiIVCUIakfgWXr1UjsCkqpWLWDmTKBcOeCLL9SOhoiIyDbWQCAiIvIQwcEsSqkle/YAJUoAiYn8vxERkTawBwIREZHG+fiIP595Rt04yD4lSog/mTwgIiKtYA8EIiIijfvzT2DJEuCdd9SOhIiIiDwZEwhEREQaV7MmMHWq2lEQERGRp+MQBiIiIiIXqVhR7QiIiIjkYw8EIiIiIhcpVw7YuRMIDFQ7EiIiIvsxgUBERETkQpGRakdAREQkD4cwEBEREREREZFNTCAQERERERERkU1MIBARERERERGRTZpOIHTu3BkVK1ZEwYIFUbZsWURHR+PatWsmbRISEtCpUycULlwYpUqVwtChQ5GRkWHS5sSJE4iMjIS/vz/KlSuHiRMnQhAEkza7du1CeHg4ChYsiCpVqmD+/Pl54lmzZg1CQ0Ph5+eH0NBQrFu3Tvk/mojIw1SqpHYERERERCSFphMIzz//PL777jucO3cOa9aswd9//42uXbsaHs/KykKHDh2QlpaGPXv2IC4uDmvWrMGoUaMMbVJTU9G6dWuEhITg0KFDmDVrFqZPn44ZM2YY2ly8eBHt27dH06ZNcezYMbz//vsYOnQo1qxZY2izb98+dO/eHdHR0Th+/Diio6PRrVs3HDhwwDVPBhGRRs2YAfTsCWzZonYkRERERGSNTsh9qV3DNmzYgC5duiA9PR0+Pj749ddf0bFjRyQmJiIkJAQAEBcXhz59+uDmzZsICAjAvHnzMHbsWNy4cQN+fn4AgClTpmDWrFm4cuUKdDodxowZgw0bNuDMmTOGffXv3x/Hjx/Hvn37AADdu3dHamoqfv31V0Obtm3bonjx4li1apWk+FNTUxEYGIiUlBQEBAQo9bQQERERERERmWXPeaimeyAY+/fff7FixQo0btwYPj4+AMReAWFhYYbkAQC0adMG6enpOHLkiKFNZGSkIXmgb3Pt2jVcunTJ0CYqKspkf23atMHhw4eRmZlptc3evXsV/1uJiIiIiIiIXE3zCYQxY8agcOHCKFmyJBISEvDjjz8aHktKSkJQUJBJ++LFi8PX1xdJSUkW2+jv22rz+PFj3L5922ob/TbMSU9PR2pqqsmNiIiIiIiIyB25XQJhwoQJ0Ol0Vm+HDx82tH/nnXdw7NgxbN68Gfnz58frr79uUgBRp9Pl2YcgCCbLc7fRr69EG3P714uNjUVgYKDhVqFCBYttiYiIiIiIiNRUQO0Achs8eDB69Ohhtc0TTzxh+L1UqVIoVaoUqlevjlq1aqFChQrYv38/IiIiEBwcnKeIYXJyMjIzMw29BYKDg/P0Erh58yYA2GxToEABlCxZ0mqb3L0SjI0dOxYjR4403E9NTWUSgYiIiIiIiNyS2yUQ9AkBOfS9AtLT0wEAERERmDRpEq5fv46yZcsCADZv3gw/Pz+Eh4cb2rz//vvIyMiAr6+voU1ISIghUREREYGffvrJZF+bN29Gw4YNDfUWIiIisGXLFowYMcKkTePGjS3G6+fnZ1J7gYiIiIiIiMhdud0QBqkOHjyI2bNnIz4+HpcvX8aOHTvQq1cvPPnkk4iIiAAAREVFITQ0FNHR0Th27Bi2bduG0aNHIyYmxlBdslevXvDz80OfPn1w8uRJrFu3DpMnT8bIkSMNww/69++Py5cvY+TIkThz5gwWL16Mr7/+GqNHjzbEM2zYMGzevBlTp07F2bNnMXXqVGzduhXDhw93+XNDREREREREpDTNJhD8/f2xdu1atGzZEjVq1MCbb76JsLAw7Nq1y3BVP3/+/Ni4cSMKFiyIJk2aoFu3bujSpQumT59u2E5gYCC2bNmCK1euoGHDhhg4cCBGjhxpMrSgcuXK+OWXX7Bz507Uq1cPn3zyCb788ku8/PLLhjaNGzdGXFwclixZgrp162Lp0qVYvXo1GjVq5LonhYiIiIiIiMhJdIJxxUFSlT3zbxIRERERERE5yp7zUM32QCAiIiIiIiIi12ECgYiIiIiIiIhsYgKBiIiIiIiIiGxyu2kcvZm+HEVqaqrKkRAREREREZE30J9/SimPyASCG7l37x4AoEKFCipHQkRERERERN7k3r17CAwMtNqGszC4kezsbFy7dg1FixaFTqdTOxyrUlNTUaFCBSQmJnLGCLKJrxeyF18zZC++ZshefM2QvfiaIXtp5TUjCALu3buHkJAQ5MtnvcoBeyC4kXz58qF8+fJqh2GXgIAAt34zkHvh64XsxdcM2YuvGbIXXzNkL75myF5aeM3Y6nmgxyKKRERERERERGQTEwhEREREREREZBMTCCSLn58fxo8fDz8/P7VDIQ3g64XsxdcM2YuvGbIXXzNkL75myF6e+JphEUUiIiIiIiIisok9EIiIiIiIiIjIJiYQiIiIiIiIiMgmJhCIiIiIiIiIyCYmEIiIiIiIiIjIJiYQyG5z585F5cqVUbBgQYSHh+P3339XOyRyU7GxsXj66adRtGhRlClTBl26dMG5c+fUDos0JDY2FjqdDsOHD1c7FHJjV69exWuvvYaSJUuiUKFCqFevHo4cOaJ2WOSmHj9+jA8++ACVK1eGv78/qlSpgokTJyI7O1vt0MhN7N69G506dUJISAh0Oh3Wr19v8rggCJgwYQJCQkLg7++P5s2b49SpU+oES27B2msmMzMTY8aMQZ06dVC4cGGEhITg9ddfx7Vr19QL2AFMIJBdVq9ejeHDh2PcuHE4duwYmjZtinbt2iEhIUHt0MgN7dq1C4MGDcL+/fuxZcsWPH78GFFRUUhLS1M7NNKAQ4cOYeHChahbt67aoZAbS05ORpMmTeDj44Nff/0Vp0+fxueff45ixYqpHRq5qalTp2L+/PmYPXs2zpw5g2nTpuGzzz7DrFmz1A6N3ERaWhqeeuopzJ492+zj06ZNw4wZMzB79mwcOnQIwcHBaN26Ne7du+fiSMldWHvNPHjwAEePHsWHH36Io0ePYu3atfjrr7/QuXNnFSJ1HKdxJLs0atQIDRo0wLx58wzLatWqhS5duiA2NlbFyEgLbt26hTJlymDXrl1o1qyZ2uGQG7t//z4aNGiAuXPn4tNPP0W9evUwc+ZMtcMiN/Tee+/hjz/+YG84kqxjx44ICgrC119/bVj28ssvo1ChQvj2229VjIzckU6nw7p169ClSxcAYu+DkJAQDB8+HGPGjAEApKenIygoCFOnTsXbb7+tYrTkDnK/Zsw5dOgQnnnmGVy+fBkVK1Z0XXAKYA8EkiwjIwNHjhxBVFSUyfKoqCjs3btXpahIS1JSUgAAJUqUUDkScneDBg1Chw4d0KpVK7VDITe3YcMGNGzYEK+88grKlCmD+vXr46uvvlI7LHJjzz33HLZt24a//voLAHD8+HHs2bMH7du3Vzky0oKLFy8iKSnJ5HjYz88PkZGRPB4myVJSUqDT6TTZW66A2gGQdty+fRtZWVkICgoyWR4UFISkpCSVoiKtEAQBI0eOxHPPPYewsDC1wyE3FhcXh6NHj+LQoUNqh0Ia8M8//2DevHkYOXIk3n//fRw8eBBDhw6Fn58fXn/9dbXDIzc0ZswYpKSkoGbNmsifPz+ysrIwadIk9OzZU+3QSAP0x7zmjocvX76sRkikMY8ePcJ7772HXr16ISAgQO1w7MYEAtlNp9OZ3BcEIc8yotwGDx6MP//8E3v27FE7FHJjiYmJGDZsGDZv3oyCBQuqHQ5pQHZ2Nho2bIjJkycDAOrXr49Tp05h3rx5TCCQWatXr8by5cuxcuVK1K5dG/Hx8Rg+fDhCQkLQu3dvtcMjjeDxMMmRmZmJHj16IDs7G3PnzlU7HFmYQCDJSpUqhfz58+fpbXDz5s08WVgiY0OGDMGGDRuwe/dulC9fXu1wyI0dOXIEN2/eRHh4uGFZVlYWdu/ejdmzZyM9PR358+dXMUJyN2XLlkVoaKjJslq1amHNmjUqRUTu7p133sF7772HHj16AADq1KmDy5cvIzY2lgkEsik4OBiA2BOhbNmyhuU8HiZbMjMz0a1bN1y8eBHbt2/XZO8DgDUQyA6+vr4IDw/Hli1bTJZv2bIFjRs3VikqcmeCIGDw4MFYu3Yttm/fjsqVK6sdErm5li1b4sSJE4iPjzfcGjZsiFdffRXx8fFMHlAeTZo0yTM97F9//YVKlSqpFBG5uwcPHiBfPtND4Pz583MaR5KkcuXKCA4ONjkezsjIwK5du3g8TBbpkwfnz5/H1q1bUbJkSbVDko09EMguI0eORHR0NBo2bIiIiAgsXLgQCQkJ6N+/v9qhkRsaNGgQVq5ciR9//BFFixY19F4JDAyEv7+/ytGROypatGieGhmFCxdGyZIlWTuDzBoxYgQaN26MyZMno1u3bjh48CAWLlyIhQsXqh0aualOnTph0qRJqFixImrXro1jx45hxowZePPNN9UOjdzE/fv3ceHCBcP9ixcvIj4+HiVKlEDFihUxfPhwTJ48GdWqVUO1atUwefJkFCpUCL169VIxalKTtddMSEgIunbtiqNHj+Lnn39GVlaW4Zi4RIkS8PX1VStseQQiO82ZM0eoVKmS4OvrKzRo0EDYtWuX2iGRmwJg9rZkyRK1QyMNiYyMFIYNG6Z2GOTGfvrpJyEsLEzw8/MTatasKSxcuFDtkMiNpaamCsOGDRMqVqwoFCxYUKhSpYowbtw4IT09Xe3QyE3s2LHD7PFL7969BUEQhOzsbGH8+PFCcHCw4OfnJzRr1kw4ceKEukGTqqy9Zi5evGjxmHjHjh1qh243nSAIgisTFkRERERERESkPayBQEREREREREQ2MYFARERERERERDYxgUBERERERERENjGBQEREREREREQ2MYFARERERERERDYxgUBERERERERENjGBQEREREREREQ2MYFARERERERERDYxgUBERORBJkyYAJ1Oh507d6odimQdO3ZEWFgYsrOz1Q7FbSxduhQ6nQ5Lly61e93Hjx+jatWq6Natm/KBERGRV2MCgYiISEN27twJnU6HCRMmqB2KIrZv346NGzdi/PjxyJePhyVKKFCgAMaNG4fvv/8ee/fuVTscIiLyIPymJiIi8iCDBw/GmTNn8Mwzz6gdiiQffvghnnjiCXTt2lXtUDxKdHQ0goKC8NFHH6kdChEReRAmEIiIiDxIqVKlULNmTRQqVEjtUGw6ceIE9u7di9deew06nU7tcDxKgQIF0KNHD2zfvh3nz59XOxwiIvIQTCAQERFpxIQJE/D8888DAD7++GPodDrD7dKlS4Y2uWsgXLp0CTqdDn369MGZM2fQsWNHFCtWDMWLF0fPnj1x+/ZtAMCBAwfQunVrBAQEoHjx4oiJiUFaWprZWHbv3o1OnTqhVKlS8PPzQ7Vq1fDBBx/gwYMHkv8e/fj+V155Jc9jKSkp+OijjxAaGooiRYogMDAQNWvWxBtvvIHExESTtoIgYPHixWjSpAkCAgJQqFAhNGzYEIsXLza7X0EQsGzZMjRr1gzFihVDoUKFUK1aNfTv3x8JCQkmbRMSEtC3b1+UK1cOvr6+KF++PPr27ZsnBgBo3rw5dDodHj9+jE8++QSVK1eGn58fqlevjrlz55qN5d9//0X//v0RFBSEQoUK4emnn8a6dessPmc7duxAu3btEBISAj8/P4SEhKB58+ZYtGhRnrbdunWDIAiy6igQERGZU0DtAIiIiEia5s2b49KlS1i2bBkiIyPRvHlzw2PFihWzuf7FixfRuHFjNGzYEP369cPhw4cRFxeHxMRETJ06Fa1bt0br1q3x1ltvYefOnYaT0q+++spkO/Pnz8fAgQNRvHhxdOrUCaVLl8ahQ4cwadIk7NixAzt27ICvr6/NeLZt24YiRYogLCzMZLkgCGjTpg0OHDiAJk2aoG3btsiXLx8uXbqEdevWoXfv3qhQoYKh7WuvvYaVK1eievXq6NWrF3x9fbFlyxb07dsXp0+fxvTp00223bNnT6xevRrlypVDz549ERAQgEuXLmH16tVo27YtKlasCAA4f/48nnvuOdy8eROdOnVC7dq1cerUKSxevBg///wz/vjjD1StWjXP39WzZ08cOHAA7dq1Q/78+fHdd99h0KBB8PHxQUxMjKHdgwcP0Lx5c5w4cQIRERGIjIxEYmIiunfvjqioqDzb3bhxIzp16oRixYrhhRdeQNmyZXHr1i3Ex8djxYoV6Nevn0n78PBw+Pr6Yvv27Tb/F0RERJIIREREpBk7duwQAAjjx483+/j48eMFAMKOHTsMyy5evCgAEAAIM2fONCzPzs4W2rdvLwAQihUrJqxfv97wWEZGhlC3bl3Bx8dHSEpKMiw/deqUUKBAAaF+/frCnTt3TPYdGxsrABCmT59u8++4d++ekC9fPqFJkyZ5Hvvzzz8FAMKLL76Y57FHjx4J9+7dM9xfuHChAEDo27evkJmZaVienp4udOrUSQAgHD582LB8zpw5AgChZcuWwoMHD0y2/eDBA5O/qUWLFgIAYcGCBSbtFixYYNiGscjISAGA0KhRIyElJcWw/OzZs0KBAgWEGjVqmLTX/69iYmJMlv/222+G/9eSJUsMy1966SUBgHD8+PE8z8vt27fzLBMEQahfv77g4+MjPHr0yOzjRERE9uAQBiIiIi9RpUoVDBkyxHBfp9OhR48eAID69evjhRdeMDzm4+ODrl27IjMzE2fOnDEsX7BgAR4/fowvv/wSJUqUMNn+u+++i9KlS2PVqlU2Y7l27Rqys7MRFBRksY2/v3+eZX5+fihSpIjh/uzZs1G4cGHMnj0bBQrkdKz09fXFpEmTAMAknjlz5iB//vyYN29enu37+/sb/qbExERs374doaGhJr0GACAmJga1atXCtm3bzA5liI2NRUBAgOF+jRo10KRJE5w7dw737t0zLP/mm2/g6+uLiRMnmqwfFRWFli1b2vW8lCxZ0mzboKAgZGZm4ubNmxa3R0REJBWHMBAREXmJp556Ks9UiWXLlgUA1KtXL097/WNXr141LNu/fz8AYNOmTdi6dWuedXx8fHD27Fmbsdy5cwcAULx48TyP1apVC3Xq1MHKlSuRmJiILl26oGnTpmjQoAHy589vaPfgwQOcOHECISEhmDJlSp7tZGZmAoAhnrS0NJw+fRpVq1ZFtWrVrMZ37NgxAEBkZGSeAo86nQ7NmjXDmTNncPz4ccNwCr0GDRrk2V758uUBAHfv3kXRokVx7949XLx4EaGhoQgODs7TvmnTpti2bZvJsm7dumHt2rVo1KgRevbsiRYtWqBp06YoU6aMxb9DnxC5fft2njiJiIjsxQQCERGRlzC+Kq6nv2pv7TH9iTggFv0DYLi6L5f+KvrDhw/N7nf79u2YMGEC1q5di1GjRgEQZ5gYMmQIxo0bh/z58yM5ORmCIODq1av4+OOPLe5LXwjy7t27AIBy5crZjC81NRUALPaQ0J/0p6Sk5HksMDDQ7N8EAFlZWSbrWTr5N7ff7t27w8fHBzNnzsSCBQswd+5c6HQ6NG/eHDNmzDCbBNI/v1qYlYOIiNwfhzAQERGRZPpEQ2pqKgRBsHizpXTp0gByEhK5lSpVCrNnz8bVq1dx+vRpzJ49GyVLlsT48eMxbdo0k1jCw8OtxrJjxw4AOSf2xj0qbP2dN27cMPu4frm5xIsU+vUsDS2wtN+XXnoJu3fvxr///otff/0V/fr1w65du9CmTRtDgsSY/vnVP99ERESOYAKBiIhIQ/Rd+PVXsl2tUaNGAHKGMsgVEhKCkiVL4vz581bb6XQ61KpVC4MGDcKWLVsAABs2bAAAFC1aFLVq1cKZM2fMnjznVqRIEYSGhuLixYs296u/mr979+48CRFBEPD777+btLNXQEAAKleujAsXLiApKSnP4/rtW1u/bdu2WLhwIfr06YObN2/iwIEDedqdO3cOISEheepVEBERycEEAhERkYboTwSvXLmiyv4HDhyIAgUKYMiQIWYLCN69e9dQP8AanU6Hpk2b4u+//87TC+HixYs4ffp0nnX0V+WNiwgOHToUDx48QExMjGGoQu5tXbp0yXB/0KBByMrKwsCBA/MMn3j06JEhlooVK+L55583TNtobPHixTh16hRatGjhUF2B6OhoZGRk4KOPPjJZvnnz5jz1DwBx2stHjx7lWa7vxZC7uGJCQgKSkpIQGRkpO0YiIiJjrIFARESkITVr1kRISAji4uJQqFAhlC9fHjqdDgMGDDA79l5pYWFhmDt3LgYMGIAaNWqgffv2ePLJJ5Gamop//vkHu3btQp8+fTB//nyb2+rSpQvWr1+PrVu3olu3boblx48fx4svvoinn34aYWFhCA4OxtWrV7F+/Xrkz5/fUBMBAN5++23s378fy5Ytwx9//IFWrVohJCQEN27cwNmzZ3HgwAGsXLkSTzzxBABgwIAB2LVrF7777jtUq1YNnTt3RkBAABISEvDbb7/h66+/RpcuXQAA8+bNw3PPPYeYmBj89NNPCA0NxenTp7FhwwaULl0a8+bNc+i5fPfdd7F27Vp89dVXOHXqFJo1a4bExER899136NChAzZu3GjSftSoUUhISEDz5s3xxBNPQKfTYc+ePTh48CAaN26MJk2amLTX99jQ/z1ERESOYgKBiIhIQ/Lnz4+1a9dizJgx+Pbbbw3TAvbo0cMlCQRAnMawXr16mDFjBnbv3o0NGzYgMDAQFStWxIgRI9C7d29J2+nWrRuGDx+O5cuXmyQQGjZsiPfeew87d+7Exo0bcffuXQQHByMqKgrvvPMOnnnmGUNbnU6HpUuXon379vjqq6/w888/4/79+yhTpgyqVauG6dOno1WrVibt4+LiEBUVhUWLFuGbb76BIAgoV64cunXrhvDwcEPbGjVq4PDhw/j444+xadMmbNy4EaVLl0afPn0wfvx4VKpUyaHnsXDhwti1axfGjh2LdevW4ejRo6hduzZWr16NlJSUPAmEsWPHYu3atThy5Ah+++03+Pj4oHLlypg2bRoGDhxoMkMFACxfvhxlypRhAoGIiBSjE6RUOiIiIiJygvfffx/Tp0/HP//8Y5jqkBx34cIF1KhRA+PHj88zRIKIiEguJhCIiIhINampqXjyySfxyiuvYO7cuWqH4zF69+6NLVu24Pz58yhcuLDa4RARkYdgEUUiIiJSTUBAAJYvX44KFSogOztb7XA8wuPHj1GtWjV8++23TB4QEZGi2AOBiIiIiIiIiGxiDwQiIiIiIiIisokJBCIiIiIiIiKyiQkEIiIiIiIiIrKJCQQiIiIiIiIisokJBCIiIiIiIiKyiQkEIiIiIiIiIrKJCQQiIiIiIiIisokJBCIiIiIiIiKyiQkEIiIiIiIiIrLp/wktPEJxBwcuAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot audio signal\n", "time = arange(signal.size) / samplerate\n", "fig, ax = plt.subplots()\n", "plot = plt.plot(time, signal, \"b\")\n", "plt.xlabel(\"time (seconds)\")\n", "plt.ylabel(\"signal\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0010e129", "metadata": { "id": "0010e129" }, "source": [ "We can see that the first second is silent since the amplitude is zero before we see some spikes in the amplitude. These correspond to the notes that we can hear are being played. It may be difficult to see how this signal can be made up of sine waves but if we plot the signal over a period of 0.02 seconds we can see the similarities between the audio signal and the [sum of the sine waves from before](#Adding-sine-waves-together)." ] }, { "cell_type": "code", "execution_count": null, "id": "e8a664a9", "metadata": { "id": "e8a664a9", "outputId": "a666f52b-2c2f-4561-ff6f-0558b5670466", "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax.set_xlim(4, 4.02)\n", "display(fig)" ] }, { "cell_type": "markdown", "id": "76803815", "metadata": { "id": "76803815" }, "source": [ "The Fourier transform converts a signal expressed over time (known as the **time domain**) to the amplitudes and frequencies of the sine waves that form the signal (known as the **frequency domain**). The following code calculates the Fourier transform for our audio signal and plots the [frequency spectrum](#Frequency-spectrum). The frequencies with the largest amplitudes are the dominant sine waves in a signal." ] }, { "cell_type": "code", "execution_count": null, "id": "9ea42075", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 350 }, "id": "9ea42075", "outputId": "0f747f29-d596-4a3c-b77e-273f4dbfcfaf", "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculate the Fourier transform of the audio signal\n", "fourier = fft.rfft(signal)\n", "\n", "# Calculate the amplitude and frequencies using the Fourier transform\n", "amplitude = abs(fourier)\n", "frequency = fft.rfftfreq(N, d=1.0 / samplerate)\n", "\n", "# Plot amplitude against frequency\n", "fig, ax = plt.subplots()\n", "plt.stem(frequency, amplitude, \"b\", markerfmt=\" \", basefmt=\"-b\")\n", "plt.title(\"Frequency spectrum\")\n", "plt.xlabel(\"frequency (Hz)\")\n", "plt.ylabel(\"amplitude\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e493191d", "metadata": { "id": "e493191d" }, "source": [ "Here the sine waves with lower frequencies have the larger amplitudes and the higher frequencies have almost zero amplitude. This makes sense because this signal is of a piece of piano music and the highest note on a piano is C8 which has the frequency 4186 Hz. Let's plot the frequency spectrum for frequences less than 1000 Hz." ] }, { "cell_type": "code", "execution_count": null, "id": "4f6bd82c", "metadata": { "id": "4f6bd82c", "outputId": "c2686c50-e723-460d-de25-e5b4204d6ee8", "scrolled": true }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax.set_xlim(0, 1000)\n", "display(fig)" ] }, { "cell_type": "markdown", "id": "bbf4e182", "metadata": { "id": "bbf4e182" }, "source": [ "Looking at the frequency spectrum for the first 1000 Hz we see that we have spikes at certain frequencies. These are the frequencies of the individual notes that are being played in the sample of music.\n", "\n", "---\n", "## Compressing audio signals\n", "\n", "Looking at the plots of the frequency spectrum for the audio signal we saw that the higher freqency sine waves had very small amplitudes. This means we should be able to remove these and not notice much difference in the audio signal. This is called **compressing** the audio signal and means it will require less memory and therefore easier to store on a computer and stream over the internet.\n", "\n", "The code below removes all of the sine waves with frequencies higher than 10000 kHz and reconstructs the compressed audio signal using the remaining sine waves." ] }, { "cell_type": "code", "execution_count": null, "id": "addd2c5d", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 480 }, "id": "addd2c5d", "outputId": "a0b15b12-2215-4713-e046-09b5fad08b23", "scrolled": true }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Size of the original signal : 529201\n", "Size of the compressed signal : 120001\n", "Compression rate (percentage) : 77.32%\n" ] }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Remove frequencies higher than 4 kHz\n", "threshold = 10000 # cut off threshold\n", "compressed_fourier = fourier[frequency < threshold]\n", "\n", "# Reconstruct compressed signal\n", "compressed_signal = real(fft.ifft(compressed_fourier))\n", "t = arange(compressed_signal.size) / threshold\n", "\n", "# Plot compressed signal\n", "time = arange(compressed_signal.size) / samplerate\n", "fig, ax = plt.subplots(figsize=(12, 4))\n", "plot = plt.plot(time, compressed_signal, \"b\")\n", "plt.xlabel(\"time (seconds)\")\n", "plt.ylabel(\"signal\")\n", "plt.show()\n", "\n", "# Output signal sizes\n", "print(f\"Size of the original signal : {N}\")\n", "print(f\"Size of the compressed signal : {compressed_signal.size}\")\n", "print(f\"Compression rate (percentage) : {(N - compressed_signal.size) / N * 100:0.2f}%\")\n", "\n", "# Create play widget\n", "Audio(compressed_signal, rate=threshold)" ] }, { "cell_type": "markdown", "id": "b194e42a", "metadata": { "id": "b194e42a" }, "source": [ "Looking at the plots of the compressed signal they look very similar to the original signal above. Of course we have changed the original signal so we should play it to see (or more appropriately hear) whether the compressed signal sounds the same. You may hear some differences between the original signal and the reconstructed signal.\n", "\n", "The compressed audio signal uses much less memory than the original signal so is easier to stream over the internet. The fewer sine waves that are removed the closer the reconstructed signal will be to the original, but of course this would require more memory. Try experimenting with the `threshold` value to see the affects it has on the audio compression." ] }, { "cell_type": "markdown", "id": "432b0a54", "metadata": { "id": "432b0a54" }, "source": [ "---\n", "\n", "## Streaming music to your device\n", "\n", "The steps involved for going from the recording of a piece of music to you listening to it on your device are summarised in the flow chart below.\n", "

\n", " \n", "

\n", "\n", "1. The music is recorded, digitised and stored as on a computer.\n", "1. The Fourier transform is calculated so that we can analyse the amplitudes and frequencies of the sine waves in the signal.\n", "1. The frequencies that are inaudible to us are discarded (and some other techniques to reduce the memory needed to store the signal are also applied)\n", "1. The inverse Fourier transform is calculated and the compressed sound signal is reconstructed.\n", "1. The compressed sound signal is streamed over the internet to your device allowing you to enjoy the music.\n", "\n", "A similar method can be used to help reduce the memory required to store and transmit video signals and are used by applications such as YouTube, TikTok, Netflix etc. to make video streaming possible. Just think, without mathematics and the work of Joseph Fourier 200 years ago, this would not be possible!" ] }, { "cell_type": "markdown", "id": "1bd070a5", "metadata": { "id": "1bd070a5" }, "source": [ "---\n", "## Useful Links\n", "\n", "If you would like to further explore Python and fractals you may find the following links useful:\n", "\n", "- [Anaconda](https://www.anaconda.com/products/distribution) - a suite of software tools that includes Jupyter Notebook and Python. Download and install on your computer to write and run Jupyter notebooks\n", "- [Google Colab](https://colab.research.google.com/) - run Jupyter notebooks in the cloud using Google Colab (you will need to have a Google account to do this)\n", "- [Radian](https://en.wikipedia.org/wiki/Radian)\n", "- [Sine wave](https://en.wikipedia.org/wiki/Sine_wave)\n", "- [Amplitude](https://en.wikipedia.org/wiki/Amplitude)\n", "- [Frequency](https://en.wikipedia.org/wiki/Frequency)\n", "- [Fourier transform](https://en.wikipedia.org/wiki/Fourier_transform)\n", "\n", "© Dr Jon Shiach 2024" ] } ], "metadata": { "colab": { "include_colab_link": true, "provenance": [] }, "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": "3.11.3" } }, "nbformat": 4, "nbformat_minor": 5 }