{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Building an alternating current sine wave in Python\n", "### Experimenting with wave properties amplitude, wavelength, and frequency " ] }, { "attachments": { "1200px-Types_of_current-2.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "![1200px-Types_of_current-2.png](attachment:1200px-Types_of_current-2.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Figure 1) In this lesson, we'll be seeing how sine waves represent periodic oscillations, like the green alternating current above. Today's example represents AC current, so the X coordinate is time (t), and the y coordinate is current (i) or voltage (v). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sine function is a trigonometric function of an angle. Let a line through the origin intersect the unit circle, making an angle of θ with the positive half of the x-axis. The x- and y-coordinates of this point of intersection are equal to cos(θ) and sin(θ), respectively. Remember the unit circle is a circle with a radius of one, and sine and cosine are defined in terms of periodic movement around the circle." ] }, { "attachments": { "Sine.jpg": { "image/jpeg": 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} }, "cell_type": "markdown", "metadata": {}, "source": [ "![Sine.jpg](attachment:Sine.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Look what happens if we animate our sine function at each point in the circle below. We have a sine wave! " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Given what you know about the sine function, what do you think the AMPLITUDE of the wave generated by the sine function is??" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, both cosine and sine waves are periodic, which means that after a certain time, the period, they look the same again. Also, both waves look alike, but the cosine wave appears to start at its maximum, while the sine wave starts at zero. Now in practice, how can we tell whether a wave we observe at a given time started out at its maximum, or at zero? Good question: we can’t. There’s no way to discern a sine wave and a cosine wave in practice, thus we call any wave that looks like a sine or cosine wave a “sinusoid”, which is Greek and translates to “sinus-like”. An important property of sinusoids is “frequency”, which tells us how many peaks and valleys we can count in a given period of time. High frequency means many peaks and valleys, low frequency means few peaks and valleys" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that you know what a sine function is, and how a sine wave represents, let's code one out in Python. Use the np.arange function to choose your sample size (from 0 to 10) and 0.1 your frequency. You can play around with these numbers in the binder too. Amplitude of the sine wave is sine of a variable. We'll use time, which you'll notice we just used in the [In] above. If we were making a sine wave to represent an image instead of alternating current, the x axis variable might be \"space\" for both the line above and this one. Note: Since the sine function varies from +1 to -1, the amplitude is one." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get started, we'll use an import statement to call two modules, numpy and matplotlib, that will let us build the sine wave." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "time = np.arange(0, 10, 0.1);\n", "amplitude = np.sin(time)\n", "plt.plot(time, amplitude)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An important property of sinusoids is “frequency”, which tells us how many peaks and valleys we can count in a given period of time. High frequency means many peaks and valleys, low frequency means few peaks and valleys. In the code below f is frequency:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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kqao1y7xnaxvnJnKBy/mZmTeix2qSuTtUIG4yBOys+LwDGF5j33tY4b5S1WHzbxr4AoZLzBNOm1baZnMDLHZ1tSIS1M50lv01WKZ7AqpAag2UgAqlGTD/+Fi2wGyVgRIWe7vbKJaV89PzDrTMOWr1JoBxb5+fnqdQDP4yDZvFSwXyBHBARPaKSDOGknho5U4i0gH8FPClim1tIpK03gM/AxxxpdWrcHp8rqaHLNEUZaCjJXCd6WKpzODUfNVBAwA7rKikgMk8MlNboARUKJCAuXSsa7S3FqVpWvCnAnadrTmMWq7zvq1tqMK5ACfKVotnCkRVi8B7ga8Dx4DPqOpREXmXiLyrYte3Ao+oauWd2Ad8X0SeBR4HvqKqX3Or7ZUUiiWGZ+arnli12BvAUN6R6TylstYkc1M0ws6u1sBNNp4z4/trkXlbKkE8Fgncda5H5j3dwZzfOzdhjJh2bKlubg+CO7quh/VXxHEYVX0YeHjFtg+v+Pwx4GMrtp0Crne4eZtieDqPKuysUYHs2drKQ8+s5bnzJ4NTRseyo6v6hwxgT3crp8eDZaUNTRody84t1V9nKyopaDIPTs0jAgOd669vsxpb282opIB1poNTOfpScRJNm486s9hrKc2AGUf1EGai14mVebqzBosFDOsuky8GagGeZZlrU5q7uloZmswFKpR3cCpHRKC/hs4UDANjaCpYCmRoMmeOnqrvTEWEHV2tDE4Faw5kcDJX833d0dpEKhFjcDJYMtdDqEDqxLLGax2B7DBv1iB1LoNTOaIRob+jts50x5ZWsoUimfngFBgcnMzR39FSdQivxY4tLQxNzQdOadbamYIlc3Dua4Chqfman2Uw7u2gyVwPoQKpk8HJeZqiQl+qRsvUfECDZLUMTs6zvbNlw2Vs12Kn6foaDNCDNjhV+zwXGAbGbKHIdC5II836OtOdW1oZnAyO0lwslRmZqVPmrpbAjbrqIVQgdTI4lWN7ZwvRKvMhLKzJuiBZLYNTuSUlUAuBHHVN1iuzdZ2D0bnkF0uMZvN1yzy/WApM0ujw9Dxlrd0dDcsjkKAozXoJFUidDE3m6rJYOlubaI/HAtOxQH1+YgjeqCu/WCKdLdgjc0CU5vnpeSM4pB6ZuyxDIRjX2Yo6q2/U1UJ+sRzYUvbVEiqQOjk3mVuyqGtBRALlK84tFBmfXajrIUu1xEjGY4GReajOeS5YjlgLisyDNnSm1qgrKErTMmjqnQOB4FznegkVSB3MFopM5RbrGuaDNewNhpVmtbOWOHmLoEXoLHcstcucSjTR0dIUmFGXdW0uJbfd4FSOpqiwrcb5TFhWPkG5t+slVCB1UG84q8WOLS0MBiSs1Q7LFIIVobMUaWfDdQ6KzEOTOZqjEfqStXemyUQTna1NgVlkaXAyx0Ad85kQzDnNeggVSB3Y1Znu7GplbqEUiAgdu5RmkCJ0BidzxGMRepLxuo6zc0uARl1TObZvaam6WOZKdgZodD04NV/3fd0Wj9HV1hyYkWa9hAqkDpaG+XW4cyBYQ/3BqXlamqJVVx5eSZAidKxw1mqLZa7EGoEEQ2nWF85qEbRR16Umc72ECqQOhqZytDZH6WqrvzOFYEw2Dk3l2LGlxZbOFILhKx6aztU152OxI0AROtZ1rpegJFDOL5SYmFuwVeZLgVCB1MHw9DwDnfV3pksTbwHwFY/M5OnvrP8hC5TM03n6q1w4azWWJ1j9LfP8Qomp3CIDNVYaqGRnVyuFYpmxbMGGljnH8IzR4ddS92slO7e0cn5qPpALiFVLqEDqYGQmX3M5j0pSiSaS8RgjM/5fcGh4Om9LxzJgKqGRGX9bavlFwzK1VeZpf19n65rYoTStFSuHfX5vW9fEFpk7W1golRmf87fStINQgdSB0ZnWf8OBUaRv2OeL7xSKJcZnC7Y8ZKlEjLbmKMM+70wvmB2fHaMu617xu9IcWZK5fqVpHWPE5/f20gjEhnvbMir9bijYQahAamSpM7XhIQPD8vH7CGR0xrCo7JBZROjvbPF9Z7rcsdgw0myJ0RoApWkZMnZ0pkEbgfR11BdpB8EZXdtBqEBqxOpM7RqBDHQmfH/D2WmlgWGpXQhIx2LHCETEqGDs9+tsGTLbbFCana1NJJoivh+BjMzMs7U9XlPp+pUsjUB8fm/bgacKRETeLCLHReSkiNy/yvc/LSIzIvKM+fqPm/2t01idgB0PGcC2VAvjswu+Xk95yTdu26gr4X/LdGk+4NIZaY7MzNPd1lzTokorMZRmCyMZf8s8PJO3ZQIdoKutmeZYxPfX2Q48UyAiEgU+CNwFHATuFZGDq+z6PVW9wXz9cZW/dQzr5rDrprM6ZWtk40cs14t9I5AWxmcLLBTLthzPCYZn8nTZ1JkCgRiBDE/nbTMSwJTZ7yOQ6XnbjARrpOn3OU078HIEcgtwUlVPqeoC8Gngbhd+awvDNkaqQKWv2L833cjMPJ2tTbQ029OZDnQmUIVRH1undnYsYLjC0tkCiyX/Ks2RmXnb7msIyqjLnlBtC8NQ8LfMduClAtkODFZ8HjK3reR2EXlWRL4qIldX+VtE5D4ROSwih8fGxuxoN2D4xlOJGG1xe5aVX4pW8bMCsSkfwqJ/KSrJvw+a3R3LQEcQlKY9odoWA50JRjN5ij5Vmpn8IrOFom3eBDAMQr/P79mBlwpktey7lZk3TwG7VfV64L8DX6zit8ZG1QdU9ZCqHurp6am1rRcxMjO/FG1hB5aV6+cIneEZezuW5clG/ypNI1nUPpm3+XyCNZtfJFso2hI0YLGtI0FZIe3TZEI7c0As+jsTXMjkKTV4MqGXCmQI2FnxeQcwXLmDqmZUddZ8/zDQJCJbN/NbpxmetieJ0KK1OUZHS5OvrZaRmXl7feNmJ+VXpTlXKJLJF+0dgXT6e9S1lANi5wjE5yNNO7PQLfo7WiiV1fcZ+PXipQJ5AjggIntFpBm4B3iocgcR2SZmnRARuQWjvROb+a3TGJ2pfR0L+HuCdd6sFmxnZ9oej5FMxHwr84gjHYu/E+uWckDsHF373D3rxAjEumf8PKdpB/Y48GtAVYsi8l7g60AU+KiqHhWRd5nffxj4Z8C7RaQIzAP3qFGVbdXfutV2O2sFVTLQ2eJba9wJKw0M69SvlumyNW5fx5L0edmaCw6MQJbmunx6b4/MzBMR6K2zXH8l21KGzH72KNiBZwoEltxSD6/Y9uGK9/8D+B+b/a1bXMjY37EYx0vw9LkpW49pF05YaWBYp/63TO1Vmn4uWzM8k0cE+upYlW8lS2VrfHqdh6fz9KUSxKL2OWSWRiA+vc52EWai14DlfrBzPgCMjmoqt8j8gv+SCe3OQrcwcgT8aaUNz8wjYl+yqMU2P4+6pufpTcZpsrEzFRG2+fg6G2HL9l7jjpYmWpqivr3OdhEqkBqwsqft70zNYa8PQzztrBVUSX9HCxNzC+QX/ac0R6bz9LTb25mCEcrr147F7rBli4FO/2aj27VEQSVGrTf/jq7tIlQgNWCNQOy2TP1cudTOWkGVWJafH/Mihh0IlIDlDHw/lq0ZnrE3bNnCr9noqmqEatv8LIO/5/fsIlQgNWB3eQsLP1cutWvtk5UM+DiU98JMnn4b5wIs/Fq2RlW5MJNfmgC2k/6OFsZm/ZeBP51bpFAss82BUZef3bN2ESqQGkhn8mxzoGPpTRnuIT9a46OZvK0TqxZ9pszprD9ltnuUCcsT1KM+k3m2UCS3UGKbzW5KMGRWxXd5EdY1cOJ57kslGJstNHQyYahAamA0m1/q+OyktdnIi0j7UIGkswVHZO5N+dOFNb9QIpMvLil1O+nzqaEwmjE6dycNBf/K7Mx1LpWViQZemTBUIDUwminQm7T/IQPDErJuar+wUCwzObfgiMzJuLHIkt9ktkZETsi8bUlp+kxms3PvsTEfwqLPpzJbCs2J62zJnPaZzHYSKpAqKZbKTMw6Y42DcdP5zbUxNuuclSYihsyXkGXa0dJEcyziu5GmVavKmRGI2Zn67d42ZXZmpOnP0bWdhAqkSibmFijrsuvFbnpTcUZ9NoluPQBOdCxgZAD77SGzOjonZDaUZtx34dpOXufutmaiEfFdZvZoJk9HS5PtATGw/H/023W2k1CBVInTnWlfKkE6W6Dso4k3y1J2wkoDc9Tls2H+0gjEIVdlX9Kfo6625ijtNi1RUEkkIqah4Lfr7Mx8JsDW9mZE/Oe2s5NQgVSJk64NMPzjxbIymVtw5Pi1YMns2LxPh9GZGmXO/EE6k6c5FiHV4ky1n76OhO9846PZvGMja7CMI/8pTafu61g0wtb2uO9clXYSKpAqcXLSDfwZrZLO5olGhO62ZkeO35uMUyiWycwXHTl+LViWqVkM2nb8OAIZyxRsLSi4kr6U/1yVY9mCYyNr8KfMdhIqkCpJZwuIGMNTJ+j1YeTGqNmxRCIOdaY+zItIZwuOua/A6FjmFkrMFnykNLPO5PpY+M1VWS4raYdl9mNUpZ2ECqRK0pk8W9vjtlburMSPE2+jGeddG+Cv0tdOJU5a+E1mVXV0PgAMmWfmF31T92wqt8BiSelzcNTV68MIQzsJFUiVOP2Q9bT70IXlgmsD/CezE/kQFpbbxC/+8Uy+SH6x7JhrFpbX2/DLdV6a23PSUEgmmJhbYKHorxIuduGpAhGRN4vIcRE5KSL3r/L9r4rIc+brhyJyfcV3Z0TkeRF5RkQOu9Xm0Yyzro3mWISt7c2+GvamHcq8t1jOEfCHzLmFItlC0XHXBvjHbTdmJU46eJ23LRXO9Md1Xg7Vdt44snKpGg3PFIiIRIEPAncBB4F7ReTgit1OAz+lqtcBfwI8sOL716nqDap6yPEGm6SzeUcfMjAm6P1imRaKxuqLTirNRFOUjpYm31imaYcj7aCyhIs/OhYny5hY+C2xLu1wdCH4T2a78XIEcgtwUlVPqeoC8Gng7sodVPWHqmot0fdjYIfLbXwFi6UyEw6V9KikLxX3jWWadqFjMY7vn2gVp3N9wFgPvj0eu6RktowQv8nsbBSWFRTjD5ntxksFsh0YrPg8ZG5bi98AvlrxWYFHRORJEblvrR+JyH0iclhEDo+NjdXV4PHZAqpudKYJLvik1Lc1zO9xeNTVl0pwwS/WuFXewsE5EDCrDvikY1nO9XFO5lRLjHgs4h+Zs3k6W5tsX+OmEmsU65dgCbvxUoGsFhO6aiaZiLwOQ4H8+4rNr1HVmzBcYO8RkTtW+62qPqCqh1T1UE9PT10NdjqJ0KIvlWBizh9rJ6Qdzsi26Ev5x223nHnvrMx+CvFMZ/O0x2O0OZCFbmEtbesbmR2ezwTY0tpMU1SWjJJGY9MKRETazHkLuxgCdlZ83gEMr3Le64D/BdytqhPWdlUdNv+mgS9guMQcxY1hvnV8VWPE4zXLMjutNOO+KeEymsmTaIqQSjjXmYKVF+EXpelsQp2FnxIoRx1OIgSrhIt/ZLabNRWIiERE5FdE5CsikgZeBEZE5KiI/IWIHKjz3E8AB0Rkr4g0A/cAD61owy7gQeDXVPWliu1tIpK03gM/Axypsz0bsmSZOuzaWA5r9YECyRZoigpbWp1JnLToSyXMtRO8L+FirH2ScCwL3aI3FSedKfiihMtoJu+4NQ6mzD6xxtMO5/pYWNe5EVlvBPJtYD/wfmCbqu5U1V7gtRgT2h8QkbfVemJVLQLvBb4OHAM+o6pHReRdIvIuc7f/CHQDf7siXLcP+L6IPAs8DnxFVb9Wa1s2SzpbICLQ3e68Cwv8Mdk4msnT0+5cFrpFr48mWEczeceNBDCs8YVSmencouPn2ohRF6ILYXnU5bXSLJfVKGPi0nX2w33tBOuN0e9U1YvubFWdBD4PfF5Emuo5uao+DDy8YtuHK97/JvCbq/zuFHD9yu1OM5rJ05OME3W6M/VRYp1RK8h5K60ymfCa7R2On2890pkCVw2kHD9PZdWBLQ7VGdsMqmrMB7h0nXMLJbKFIqlEXd1HXUzmFiiW1RWZt3Uk+MHL446fxwvWG4F8wXRhta21w2oKppEZdekh29pmKCk/KBCnM+8t/JRk5pY7x1p73OvrnJkvUiiW3bHGfRLW6tbcHhgGYTZfJLfgn7pndrGeAvkI8HPAaRH5vyLyC+ZcxSWL4dpwvmPx09oJrinN9ri5doK3HctsocjcQsmdjiXpj8KZow4unrUSvyxtm3ahjIlFn0+usxOsqUBU9Uuqei+wG2Mi+x3AORH5qIi80a0G+om0C1EbFn4owpZfLDEzv+iKZdoUjdDdFvd8vQinF8+qxC+uylGXgkPAP/N7l6LMTrBhGK+qzqvq/1XVt2JEO90IOD5h7TcWimUm5xZccW0A9Plgmdfl9aJdkjkV9zzhyumVCCuJx6JsaW3yvPKyW9UGYLnD9lxm8952smCmxVIy4aWoQESkT0R+R0R+AHwReAS42emG+Q2rGJobrg3jPAnPwx3dynux8IPM6aWigpeOzKMuFFK0aIvHSMZjnrtzRjN5utqaHc1Ct7DupTGfhC/byZpRWCLyW8C9wBUYLqzfU9UfuNUwv+F+ZxpnOmesnZBocv4mXw23Mu8t+lJxnhuaceVca+Hm5CoYnYvXE8rpTIFkIkZrs7OJkxZGLoj3I0033FcAqUSMRJN/SrjYyXp3zKuBDwDfVFXva2p4jJu+ceM8y1bLzq5WV865EqeX711Jb3K5hEuTQwt2bUQ6U6ClKUq7gyU9KulLxnnpQtaVc62FW3kvFn5YmTDt8PrvlYiIL2R2gvWe0j9S1UfWUh5i4Gl1XDdZLjbnnmvDOK93Vkt6KQvdnXh9P5RwGc0WHF0LfSV9qQRjswVKHpZwsTLv3cIPJVyMOlguKs0GTSZcT4H8hYh8XkTeLiJXi0iviOwSkdeLyJ8APwCucqmdnpPO5olGhG6XEr78UM4kbYYtu9eZei+z08v3rqQvFTdLuHgrs5sKxOsSLqWyMjbrrtL0UwkXO1kvjPeXgP+AMQfyQeB7wJcwMsOPA69X1W+40Ug/YPlMnS7pYeGHtRNGHV6JcCW+GHW53pl6myNgZaG75ZoF70u4TMwZIz63720/lHCxm3Udvar6AvD7LrXF17htmXa2NtEcjXhqtYxmChzobXftfJYf3qtJZVU13DkuujaWZM7mAfdLuEznFlkolV0LT4eK9eCzBU9KuLiZRGjRmzRKuMwWiiQ9LOFiN5sJ420VkT8QkQfMzwdE5Gedb5q/cNtnKiL0JOOeRuikXZ5c7W6PExHv1kafLRTJLZTctcY9zsxOL+X6XDojzaVQbZcDB4xzN5YbazOhLv8bWMCIygJjHY8/daxFPsWtaqWVeLm07fxCiUy+6KqVFo0YStOrjsWNdcFXYiWyeSezu+Hp4L171ovr7JeqA3azGQWyX1X/HFgEIzOd1VcTbFgKxRLTuUVXh/ngbbhj2sX6SJV4KrPLYctglHDZ2t7smcxLCsQjF5YXWDK7kYVu0efxXJdTbEaBLIhIC+ZysyKyH2is/8IGuFnqoRIvwx3dTiK08HL1NqtD80Jmr1yVXriwEk1ROlqaPL23t7Y3u5pr5LXbzik28x/8Txi1r3aKyD8AjwK/52irfEbaxVIPlXhZBnrZT+y20vQu3HEpcdJ1Q8E7V2U6kzczpd2tdtCX8s5VOZbN0+Pyfd0ej9HWHG24ZMLNFFP8BvCLwDuBTwGHVPU7dpxcRN4sIsdF5KSI3L/K9yIif2N+/5yI3LTZ39qJFz5T8LYMtFcjkL5Ugsm5BQrFkqvnBUPmtmb3stAtjFGXV0rT3XwICy9dlYbM7t7XYMrscQkXu9lMFNZNGCXdR4BhYJeI7BeRup4yEYli5JfcBRwE7hWRgyt2uws4YL7uAz5UxW9tw83Sz5V46StOZ/I0xyJ0tLgbcmj9j70oPGfkvXjRmcaZmC1QLLlfMcgrmXuScc+KC7q1YNhKvI6qdILNuLD+FmMN9AcwFpn6EfBp4CUR+Zk6zn0LcFJVT6nqgnnMu1fsczfwCTX4MdApIv2b/K1tLJf0cDdm3Uu/qbUSoVtZ6BZehjumM+5H2oHhMisrTMwtuH5ut5MILYwqxHnKLpdwKZWV8VnvRiBe3NeZ/CLfenGUSQfur80okDPAjap6SFVvxlgP5AhwJ/DndZx7OzBY8XnI3LaZfTbzWwBE5D4ROSwih8fGxmpqaGtTlOt3dLqWhW7hZbhjOltwff4DKkZdl5DMXhkKRuKkO6tsrqQvGWexpEzl3FWaE7MFygo9Ho00vchGPzGa5V987DDPDU3bfuzNKJArVfWo9cHMTr9RVU/Vee7VeuOV/9m19tnMb42Nqg+Yyu9QT09PlU00+J03HOBz7371xjvaTKolRjzmTTa6W2uhr8SrxDpV9VBmb2qATeUWWSy5W9LDwqvrvLxgmDcy5xfLZPLuBsU4WQh2MwrkuIh8SER+ynz9LYb7Ko6ZG1IjQ8DOis87MOZYNrPPZn4beJbLQHtgjWe8sca7WpuJRcR1mTP5IvnFsmcTyuD+CMSLJEILK9LN7UllP8js9ujayaUoNqNA3gmcBN4H/C5wyty2CLyujnM/ARwQkb0i0gzcAzy0Yp+HgLeb0Vi3ATOqOrLJ3zYEXoQ75haKZAtFTx6ySEToTcZdt0zTHoXwAnS3NSPifsfi9uJZlfR55Koc9ShBFpZHPa7f29kCsYjQ5cAc7oaRVGbm+V+ar5XM1npiVS2KyHuBrwNR4KOqelRE3mV+/2HgYeAtGAosB/z6er+ttS1+pjeV4NhIxtVzLhWb82CYD+YqfS5bpksJdR7IHItG2Nrufv7LsszeRCSB+yHq6UwBEehud7+Io1cjzXS2wNZ2ZyqJb6hAROQA8J8xwmWX7jRV3VfvyVX1YQwlUbntwxXvFXjPZn/biPQm43z3uNt+Yu+sNDBkPjMx5+o5vZbZi5GmZf27WdLDIh6LsqW1yXUXVjqbp7st7smKl0v1sDxw2zk1ytxsMcUPAUUMl9UngL93pDUhF9GXSjBbKDJbcG/ibdSjkh4WXoQ7jno86urzIJlwNFOgs7XJ9Sx0Cy+SCb1KIgRobY6RjMc8GXU55ZrdjAJpUdVHAVHVs6r6h8DrHWlNyEV44Sv2oqhgJX2pONO5RfKL7mWjp7N5o9yEy1noFt647dwt17+S3pT7NcC8lzneUNd5MwokLyIR4ISIvFdE3gr0OtKakItYzgVxz2pJZwvEYxFSLd51puBuNrpXCXUWfak447MLLLqYje5VGROLPg+CJTyX2eVRV6FYYiq36JjMm1Eg7wNagX8F3Ay8DXi7I60JuYil0D8XrRZrjWy3s9AtvJhs9Kq8hYU12nNXaXqTRGjRl0owNmssL+sGxVKZ8Vnn3Dmbwe2w/LTDNe02o0D2qOqsqg6p6q+r6j8FdjnSmpCLWHZhuWyNezjM9yKxLp31fgRitcMNymVlbNZ7mUtldaTExmpMzC2g6t08F5gurEzBtWx0pyPtNqNA3r/JbSEO0B6P0docddca96jAnoXbJVyWs9C9tUzBPZmncgtGFrrHcyDgnsxeR9qBcW8vlMpM5+rJwd48TiYRwjphvCJyF0YOxnYR+ZuKr1IYEVkhLiBiJta5PB9wxwHvOpbO1iaaoxHXwh0z80UKxbLnlim4FyyxFHXmYWdq/b8N92yH4+fzOtIOXhnKu6XN+VwUp5XmeiOQYeBJIG/+tV4PAW9ypDUhq9Lrot90zgwZ9tJKEzHWRh9zyYW1vGCYdzJ3t8WJRsQ1t93yksVeurDcDRDxapnmStxe2tbJLHRYZwSiqs8Cz4rIJ1U1HHF4SF8qwfMOVNJcDa+WdV2Jm6v0eVlgzyIaEXra3UsmXK424F1n2rNU2sO96ywCWz3IQrdw2z07minQk3QmCx3Wd2E9z/I66Bd9r6rXOdKikIvoS8b5pjnx5nRk1KjHOSAWfakEJ9I1V8qpCq+Wsl1Jb8o9V+Woh1noFk3RCFvbm90bgWSMLPSYB1noFm4vEpfO5h29r9cL9P9Zx84aUhV9qQTziyWyhSKphLMrBPpnBJLg+yfHXTmXl3WwKulNJhiayrlyrnTW2yx0i96ke8mE6ax3WegWiaYoHS1Nro40d3e3Onb8NVWxmXV+VlXPYsyDXGu+5s1tIS7R62Ior5dVaSvpTcXJ5ovkFpz3no5m8iQ9zEK36Eu5V1DR67wXC9dl9vi+Bnfrno1mnV1lczNrov8y8DjwS8AvAz8RkX/mWItCLmJ54s35m240kzey0BMed6ZJ9yYb09k8PR5bpmBc58m5BQpF50u4jHqc92LhZmLdqMf5TRZuZaPnF0tM5xYdNRQ24wz8feBVqvoOVX07xnrk/8GxFoVchHXTuzGpbAzzvctCt1gKd3Shc0lnCr6xxsGdbPQxj7PQLXqTccZnCxQdLuFSLJWZmPM2C92iJxl3xRgcW3JHe6tAIqqarvg8scnfhdhEr4vhjl4t67qSpVGXC52pkTjpvcxuXedyWX0xHwCGzGU1ssSdZHzWyEL3g8xWCZeywyVcrLBlJ0fXm1EEXxWRr4vIO0XkncBXuATW4fAT7fEY7fGYa9a4HyxTt8IdjSx0f1imS4l1Dss8mVugWFbfuHPA+evsl+hCMKIqF0vKVM5Zpbkcnu7tCOQC8EmMCfTrgAdU9d/Xc1IR6RKRb4jICfPvllX22Ski3xaRYyJyVET+dcV3fygi50XkGfP1lnraEwSsGjpO43VNKItUS4x4LOL4CCQzX2TB4yx0C7c60+UCez7oTF2qe+aX6EKjDe6MNNNLWejejkCSwP0Ycx8vAz+04bz3A4+q6gHgUfPzSorA/6uqVwG3Ae8RkYMV3/+Vqt5gvhp+RNSXdH69iFkfZKFbiIgrE6xerpG9kq7WZmIRcVxpjvog895i2VXpzgjED9d5yVXptMxmFvoWh7LQYRMKRFX/SFWvxlhadgD4roh8s87z3g183Hz/ceAXVjnviKo+Zb7PAseA7XWeN7AYoX/uWCx+sMbBnXDHUR/JHImYdc8uoevc3dZMRNyxxkWM83mNW4vEjWaMhaScykKH6ibD0xjurAnqX1CqT1VHwFAUGx1PRPYANwI/qdj8XhF5TkQ+upoLrOK394nIYRE5PDY2VmezvcOqh+VkGei0C1Eb1WAkmTndsfhMZhdWJlwqY+IDd04sGqG73fmopHS2wNZ2b7PQLZZLuDh7b49lnZ/b20weyLtF5DsYrqatwG9tpoyJiHxTRI6s8rq7mgaKSDvweeB9qpoxN38I2A/cAIwAf7nW71X1AVU9pKqHenp6qjm1r+hNxikUy2TmnUusG3XBZ1oNvW6MQJbcOf6Q2ZVRVzbPltYm4jFvs9At3Bpp+uW+jseibGl1PhvdGoE4yWayxXZjdN7PVHNgVb1zre9EZFRE+lV1RET6MUY3q+3XhKE8/kFVH6w49mjFPh8BvlxN24JIX4XftKPVmXImlmXa44NIFTBknlsoMVso0u5Qlng6UyAZj9Ha7G3ipEVvMsGPT006eo5Rn0TaWfQlE4zMON2ZFtjW4SOZUwnn57oyBW7d2+3oOTYzB3J/tcpjEzwEvMN8/w7gSyt3ECOT7e+AY6r631Z811/x8a3AEZvb5zvciNBJZ/MkmrzPQrdww1ecdrjUQ7X0peLMzC+SX3QuG90vkXYWrrjtfJL3YtGbcrYGWH6xxMz8ouMye+UQ/ADwRhE5AbzR/IyIDIiIFVH1GuDXgNevEq775yLyvIg8B7wO+F2X2+86bixtO5rxRxa6xXIuiPMy+wXLZ+1kNnraJzWhLPpScSbmFlh0KBt90cpC99Woy9lgiTGHl7K18MTUVNUJ4A2rbB/GWAURVf0+sGpPpqq/5mgDfYh1IzgZ+ueGz7Qael0I8RzN5Dm0e80YDNepHGnu7LK/imq5rMbkqo+uc18qgSqMzxbo72ix/fjjswVjLXQfjUCsbPRSWYk6ECW1vERBY45AQqqkpTlKKhFzdATiRtRGNfQ5XA9LVZdqf/kFpxPrrCz0S0nmtAsZ2dXSl4pTKisTcw7J7FJEZahAAoTTS9v6bQTSHo/R0hR1rGOZmV9koVj2dFGllThdwsVPeS8WvW7J7KMRSI/D1abdus6hAgkQToY7zhaKzC2UfGWZGtnozsk86rMcEIDO1iaaoxHHXJXLOSD+kbnX4WCJUZ/lN4Hzo+vRTIGmqLNZ6BAqkEDRl3RuHYELM/MA9Pso1BGsCB1nZB4xZR7o9I/MImKW+3ZKZqPD8pPM3W1xohFx9N6ORYSt7f4ZgThdbfrCzDzbOhKOZqFDqEACRW8qwVi24Eg2utWxODGJWQ99DoY7XpjxT32kSpwcdV2YmSci0OOjzjQaEXranZN5ZMZwzToxWV0ry9nozsm8zYX7OlQgAaIvFWehVGY6t2j7sS0F4sZNVw1WuKNTSlPEHyW+K3EyyWxkJk9P0h8lPSpxcmnbCzN5XyURAjRFI2xtb3Zu1JXJs80FY9Bfd1HIulRmo9uNZY37aaIRDJnnF0tkC/aXcLkwk2dre5zmmL8eAyerELvVsVSLkwEiF2byvhtZg1XrzX6ZVZWRmbwr7mh/PTkh6+JkuOPITJ7utmYSTf6oj2Th5ATrSMadh6xaelNxsvkiuQX7lebITJ5+n40ywbkRiNWZ+m0EAqar0gFjcCpnRBeGLqyQV+BkuONoxp8PWa+D2eijLvmJq6XPwRDPUZ92pr3JBJNzCxSK9pZwyeSLzC+W/GkoOBQUc2FpPjNUICEV9Di45KlbQ95qcTLccWRm3pcy9zokcza/SLZQ9KXM1nW2u4SL1Zn6UWn2peKMzxYo2lzC5ULGiC50Q+ZQgQSIRFOUztYmh6yWeV8+ZEurt9ks81yhSCZfpM+HMi/Pddkrs6WQLqXrbIVq+3Gk2btUwsXetdFHXFSaoQIJGE4sbZtfLDGVW/TlRGN7PEZ7PGa7zBcy7g3zq2XZhWWvzH4N1YZlmcfsvs6+HoE4U+vtwkzetVDtUIEEjF4Hlra94NMQXovelP2Jdcsy+68zTbXEiMcitk8qj7joG68WpwJE/BqqDc7K3JtMuBKqHSqQgOFEYp2fOxawMvAvHZmNEi72y+zXUG2ALa3NNEXFEZn9GKoNzq3x42bei//+qyHrYoU7lsr2JdZZk25+nA8AQ2a7V6yzSrf40bUBzshshWr7ZSnbSiIRoTeZWFJyduHXUG2A7rZmIoL9MrsYHOKJAhGRLhH5hoicMP+uuiCDiJwxF456RkQOV/v7RmSgs4WiuaaDXVyYMY7lVxfWQGcLo5m8zUrTWBfcb3kvFgOdLUsTwHbh11Bti4HOBMN2y+zTUG2AWDTCtpQDMru4fK9XI5D7gUdV9QDwqPl5LV6nqjeo6qEaf99QDHQaPvvz0/bddBdm5kklYrQ5tO54vTijNP21Kt9KBjpbuDBjr9L0a6i2xUBnC8PT9lvj/laaLQzb+Cxn84vMFoquKU2vFMjdwMfN9x8HfsHl3weW7aYCsfOmG/FpqQeL7Q4ozSB0poslZXzWTqXp/850ZGaesk1K0wrV9rvMdipNt6POvFIgfao6AmD+7V1jPwUeEZEnReS+Gn6PiNwnIodF5PDY2JhNzfcOq9OzU4Fc8L1rw36laUw0+llpGtfDLqXp51BtC7uVpp9DtS3sVppuh2o7pkBE5JsicmSV191VHOY1qnoTcBfwHhG5o9p2qOoDqnpIVQ/19PRU+3PfkUw0kUrEHBiB+Pkhs1dp5hdLTMwt+Fxme5Wm30O1wX6l6edQbYvtnQl7labL0YWOOb1V9c61vhORURHpV9UREekH0mscY9j8mxaRLwC3AI8Bm/p9ozLQ2cJ5m4a9C8Uy47P+Whd8JclEE0kblaaVU+LnztRuBeJmdnKtLMuc58Zd9R8vSDKfn563ZZXIEZdDtb1yYT0EvMN8/w7gSyt3EJE2EUla74GfAY5s9veNzHYbJ94uzORRhe1b/GulgSGzXUpzaDpnHNPHMqcSTSTjMdv845ZVb80n+RG7leb5KX+usllJpdK0g/PTOXqScddCtb1SIB8A3igiJ4A3mp8RkQERedjcpw/4vog8CzwOfEVVv7be7y8VBjpbbAv9szrTHT7uWMDeaBWrY/FzZwrWSNPmztRHS9muxFKatslsdqZ+DdUGB5Tm9Lyr97UncZuqOgG8YZXtw8BbzPengOur+f2lwkBnC9O5ReYKxbpDb5c6Ux9b42DMgzx1bsqWY1kdlJ87UzDzImzsTHtdtExrxVZDweXOtBZSCaPWm52GwtXbO2w51mYIM9EDiDWpbEei2dDUPCL+LLBXiaU07Vhk6fzUfGA6U7uy0Yem5n1vJIC9yYTnp+bZ4XOZRYSBzoQtz3K5rAxP5131JoQKJIAs50XU37mcnzY6Uz/WCqpku42+4vPTQelMW5icW2B+of5FloJgjYN9eRFWZxqU62yHzOOzBRZKZVdl9nevEbIqdvpNDSutte7jOI2dMg8FROYlpVmndVouKyPT+UDIbJfSHDM7U7/P7YF9brtB0x3t5qgrVCABpDcZJxoRexRIgCxTqF+BlMvKyMylJfOYB5ZprdilNIcCMrcHhswTcwvkF+tTmsuRdu4ZCqECCSBWEbZ6J95KVmcagIesLxknIvV3pulsgcWSBkJmuxIorc40KNY41C+z9WwEY9Rlz3X2IiAmVCABpb+j/giddDZvdKYB6Fhi0Qh9qUTd8z7nAxK2DMZ6ESL1z3UNTfk/78XCrlI9QQnVhuUAlnrnQc5P5+hoaaLdxaKooQIJKHbkCAQlhNfCkDlX1zGC5NpoikboSyaWrlOtBCGJ0GJbR4KIYIPMOTpbm3xbYbqS5aCY+u7t81Puu2ZDBRJQdna1MDKdp1gq13yMpWF+ADoWgJ1bWhicvHQ6UzCu8+BU/R1LUDrTpmiE/o6WpQnhWvGiM62VbR0JohGx5d522zAKFUhA2dXVSrGsdeUJBMkaB0PmkZl5Fop1KM2pebYEpDMF2NnVyuBknQpk2v/5EJXs7Grh3CUkc1M0wkBnoi6ZVdWTvJdQgQSUXV1tAJydqP2mG5qap6utmdbmYHSmu7rbKGt91VqDklBnsburjQuZfF0ROkMBssbBkLme+1pVTZn9P4FusburjbN1KJDp3CJzC6XQhRWyOXZ1Gw9HPVbL0FQuMFYaGCMQgLMTczUfY3Aqx44AdSy7ultQXZ4IrxajM80FIhrJYld3K+OzhZqrDkzOLZBbKAXq3t7Z1cq5Ou9rcD/qLFQgAWVbKkFzNMLZydpvurMTOXZ3t9nYKmfZbSrNWl06pbIyNDnP7q0B6kzNkWathkI6WyC/WGZPd5Bkrs84siz5PQG6zru7W5nKLZLJL9b0e2vE5rbMoQIJKNGIsGNLS82d6WKpzPnp+UB1LEb9qkjN7o2RmXkWSmX2BFBp1irzmfE58zjBkXlJgdQoszVCDZLMu22S2frfuUWoQALMru7WmjuW81PzlMoaqIdMRNjV1Vq7ZWr+r3YHSGl2tzXT2hytW+YgKs1aZT4zniMi7pb0qJedXfWNrs9M5OhLxV2fzwwVSIDZ1dXKuYkcqtWvp3xmyUoLTmcKRntr7lgCaJkuKc1aRyATc8QispTtHAQ6WowVKGtXmnP0d7T4vtpyJUsjzTpk3t3l/n0dKpAAs6urlWyhyHSuer9pEK1xMOYEzk3WpjTPTeRojkXo9/FStquxu7u19o5l0giUiEWD86iLiCFzre6cyVyg5j/AWLa5q625dpkncp48y57cVSLSJSLfEJET5t8tq+xzhYg8U/HKiMj7zO/+UETOV3z3FteF8AH1TDaencjR2hylp92dtZPtYldXC7mFEuOzC1X/9szEHLu6WolExIGWOccuMxekXK5eaZ6dmAvUiMtiVx35L0ELDrGoNecnt1AknS2wZ+ulMwK5H3hUVQ8Aj5qfX4GqHlfVG1T1BuBmIAd8oWKXv7K+V9WHV/7+UsB6SGqxTq2ORSRYnakl87kaos/OTuQCFTRgsau7jUKxTDpbqOp3qsrZ8YDK3NXG4FSOUpVKc2Z+kcm5hUDKvLurtaaoSi+9CV4pkLuBj5vvPw78wgb7vwF4WVXPOtmooLGzy5gkPDte/U13ZmJuKfIjSFiTjWfGq1OaqsrZidxSWGyQsEaaZ6rME5icWyBbKLIrgNb4rq5WFktadVFFa64oqNd5eDpfdaWFpaizS2gOpE9VRwDMv70b7H8P8KkV294rIs+JyEdXc4FZiMh9InJYRA6PjY3V12qf0doco78jwakqFUiprAwGLB/CYldXK9GIcGp8tqrfjWULzC+WAucbB9hnuiZOjVV3nZfyIQJoje/rMWWu8t62LPhAXueeNkplrXp0bY1AdjXSCEREvikiR1Z53V3lcZqBnwc+W7H5Q8B+4AZgBPjLtX6vqg+o6iFVPdTT01O9ID7nst52Tqar60yHp418iL0BtEybYxF2d7dWLbPVEQUpnNVie2cLLU3RqmU+PWZ1psGT+bLedoCaZfbCGq+XmmUen6O7rZmOliYnmrUujgUNq+qda30nIqMi0q+qIyLSD6TXOdRdwFOqOlpx7KX3IvIR4Mt2tDmI7O9p5zOHBymXddOTw9YNat2wQeOynuqV5glz/wN9wZM5EhH29bRxcqx6mZuiEkhXZXdbM52tTTVd5x1bWmhpDk4Ir8X+ntoUyIn0rGfPslcurIeAd5jv3wF8aZ1972WF+8pUOhZvBY7Y2roAcVlvO7mFEiOZzVflPZHOLv02iFzW287ZiRyLVZSyPzmapT0eY1vAQngtLutt5+UqO5aT6Sz7trYHKoTXQkS4rKd6mU+kZzkQ0Pu6LR5joCNRlQJRVU6MZj0zjLy6sz4AvFFETgBvND8jIgMishRRJSKt5vcPrvj9n4vI8yLyHPA64Hfdabb/qGXYe2J0lp5knM7WZqea5SiX9bZTLGtVRRVPpGfZ39seuKgzi8t62jk/Pc9cYfMFBr20TO3gst72qkZdpbLy8tgsB/qSDrbKWfZXKfNYtkAmX+SynktIgajqhKq+QVUPmH8nze3DqvqWiv1yqtqtqjMrfv9rqnqtql6nqj9vTchfitSkQAJspUGlzNUpkEaQebMT6fnFEucmc4FXIJNzC0zObS7nZ3Ayx0KxHHiZX07PbTrnZ9k1643SDN7YNuQVVOsrVlVOBtwytXzFL2/SUpvJLTKWLTSEAjk5lt3U/i+PzaIazDkfi/1VGkcnAj63B0bb5xc375I+MWrcD17d26ECCTjV+opHMwVmC8VAd6bV+oqtTjfInenu7jaiEdm8zJZl2htcd85lVU4qBz04BGqQeWyWVCJGT9KbihKhAmkADvQlOT6a3VR9qJdMi2V/gB8yMGR+8cLmrPGXRs2OpSe4nWlzLMLerW0c36TMJ0ZniUYkkPkQFts7W2hrjnL8QmZT+58YzdKXipNKuB/OaheWK2qzMr80angTvJrbCxVIA3DN9hQz84tLa5yvx9Fh48Y82J9yulmOcvVAihOjWQrFjZd6PTo8QzIeC1R579W4ZiC1dP024ujwDJf1tAeqIu1KIhHhYFUyZwJ/X3e1NTPQkdiUzOWycmw4w8EB72QOFUgDcPVAB2B0GhtxZHiGHVtaAhuBZXHN9g6KZeWlCxsP9Y+cNx6yoBVRXMnVAx2MzOSZmN24JtaR4QxXbw92ZwqGzC+MZDasiTW/UOJEOss12ztcaplzXL29gyPnN36Wz03myBaKXDPgncyhAmkArtyWJBoRjpzf2Go5en7G0xvOLiwZjmygNIulMsdGMg3SsRgKYSPrNJ3JM5YtNMR1vnogRW6hxOkNSpq8eCFDWZeNqSBzzUAHp8bnNgzZtu59L+/tUIE0AImmKAd62zfsTDP5Rc5M5LimASzTnV0tJBOxDS21U+NzFIrlhpD56k0qTUvBNILStGTYaHR9ZEnm4F/na7anUIVjI+sbCkeHMzRFxdPgkFCBNAhXDxjD3vUm0l8wH7KrG6BjERGuGehY6jjWwlIwjWCNd7Q0saurlaMbjDQtmb30jdvFZb3tNMciGxoKR8/P0NnaxPbOYM9zwbLS3EjmI+dnuLwv6ek8V6hAGoRrt6cYn13g/Drlr58+N23uG/zOFODaHR0cG8mQX1x7Iv3pc9O0NUfZ51Gmrt1cu72DZwan193n6cFp9ve00R53d31sJ2iKRriqP7WxzOemuXZ7R2ArDVTSm4zTk4yvK3OprDwzOM11O7x9lkMF0iC8am8XAE+cmVxzn8dPT7C/p42tAVuFcC1etaeLhWKZ54bWttQePz3JzXu6iAZ8At3iVXu2cH56nqGp1ddDKZWVJ85Mcot5PzQCt+zZwrODM2saClNzCxwfzXJrg8gsItyyp4snzkytuc/xC1my+aLn1zlUIA3CldtSJBMxHj+9ugIplZXDZ6c8v+Hs5FV7jGVgHj89ser30zmjY7llz5rLxQSOW/Z2A6x5na2O5VV7Guc637K3m4VSmWfXsMgPnzU62saSuWtdQ8EyFL2WOVQgDUI0YlgtPzl16XQsna3NXLktyU/W6EwtC66RZL5yW5JUIrbmdfZLx2Int+zpQoR1rvMkzdEI1+/sdLdhDmIZemtd58fPTDLQkWDHFm8TRUMF0kDcuq+LU+Nzqy4D+tgJYzXG2/Z1u90sR7l1bxeHz0yt6t547KUxWpqiDdWxRCLCLXu7+cHL46sGTDz20hg7trQEPmmyko7WJq7cluIHJ8dX/f6xl8a4cVcniabgJk2u5Iq+JJ2tTfzg5YtlLpbK/ODkOLft9/5ZDhVIA/H6K/sA+MYLoxd99+ixUQ72pxhogCiVSl5/VR/ziyW+f+KVD5qq8uixUf7Jga0N1bEAvOGqXoam5jk28sqyJvMLJb5/cpw7r+priMnkSt5wZS9PnJm8qDLv0FSOFy9kufOqPo9a5gyRiPC6K3r51otpiivWvXnq3DTTuUVfyBwqkAbist529ve08fWjF16xfWK2wJNnp7jzoPc3nN3cvq+bZCJ2kcxHhzMMz+R5ow8eMrsxFAQ88sIrZX7sxBiFYtkXHYvdvOnqbZQVvnnslcaRZSw14r39pqv7mM4tXjTf9cjRCzRHI9xxufdLdIcKpMG465p+fnxq4hXhvA8+dZ6yws9e17/OL4NJcyzCnVf18bWjF16Rufu5J4dojkYasmPpScZ51Z4uvvTM8CvWjfjck0NsbY9z677Gmf+wuGZ7ih1bWvjCU+eXtqkqnz08xMH+FHsDuO77RtxxeQ+tzVEefHpZ5oVimS8+c56fuqLHF2HanigQEfklETkqImURObTOfm8WkeMiclJE7q/Y3iUi3xCRE+bfxgmzqZN7btkJwCd+eAaAxVKZT/7kLDft6uTyAK/Uth5vu2032XyRzz81BMDM/CIPPjXEm67ZRldbsGt+rcXbbtvN6fE5vn08DRiLKX3rxTT/7OYdNAVwCduNEBF+9dbd/OjUxFJC7OGzU7wwkuFe855vNFqbY/zTm3bw0DPDjGWN+mcPPz/C+OyCb2T26k47Avwi8NhaO4hIFPggcBdwELhXRA6aX98PPKqqB4BHzc8hwI4trfzsdQN87IdnOJnO8tHvn+bsRI53//RlXjfNMW7a1cnNu7fw1988wVi2wF8+cpxsoci/vGOf101zjLuu2caOLS382cPHmC0U+aN/fIGmqPDOV+/xummOce8tO0nGY/zRPx4lt1DkT778Aj3JOP/05h1eN80xfv01eyir8qdfeYGZ3CJ/8fXjXLktyU9d3ut10wCQzawh4djJRb4D/FtVPbzKd7cDf6iqbzI/vx9AVf+ziBwHflpVR0SkH/iOql6x0fkOHTqkhw9fdKqGI53J8+a//h6z+SILpTJvurqPD7/t5oabWK3k+IUsd3/w+5TVGOb/+mv28J9+7mqvm+Uo3z8xzts/+hNi0QgLxTJ/8P9cxW++tnGVJsBnDw/y7z73HM0xQ+YP/epN3HVt47lmK/nrb57gr775Es2xCKrKp++7jZt3u+umFJEnVfUib5H3TrS12Q4MVnweAm413/dZ66CbSmRNdSwi9wH3AezatcuhpvqL3lSCB9/9aj7yvVNsSyX4rTv2NbTyALhiW5LP/stX8w8/OcsV25K8/fY9XjfJcf7Jga38/W/cyhefPs9t+7r5xZu2e90kx/mlQztpj8d49MU0d12zjTc0YMDASv7VGy6jNxXnqbNT/PKrdrquPNbDsRGIiHwT2LbKV7+vql8y9/kOa49Afgl4k6r+pvn514BbVPV3RGRaVTsr9p1S1Q3nQS6VEUhISEiInbg+AlHVO+s8xBBQOVO0Axg234+KSH+FCytd57lCQkJCQqrEz+EaTwAHRGSviDQD9wAPmd89BLzDfP8O4EsetC8kJCTkksarMN63isgQcDvwFRH5url9QEQeBlDVIvBe4OvAMeAzqnrUPMQHgDeKyAngjebnkJCQkBAX8TQKy23COZCQkJCQ6llrDsTPLqyQkJCQEB8TKpCQkJCQkJoIFUhISEhISE2ECiQkJCQkpCYuqUl0ERkDztb4863A6ivaeEvYruoI21UdYbuqx69tq6ddu1X1ovrxl5QCqQcRObxaFILXhO2qjrBd1RG2q3r82jYn2hW6sEJCQkJCaiJUICEhISEhNREqkM3zgNcNWIOwXdURtqs6wnZVj1/bZnu7wjmQkJCQkJCaCEcgISEhISE1ESqQkJCQkJCaCBXIJhCRN4vIcRE5KSKOr78uIh8VkbSIHKnY1iUi3xCRE+bfLRXfvd9s23EReVPF9ptF5Hnzu7+ROpYlFJGdIvJtETkmIkdF5F/7pF0JEXlcRJ412/VHfmhXxTGjIvK0iHzZL+0SkTPm8Z4RkcM+aleniHxORF4077PbfdKuK8z/lfXKiMj7vG6biPyuec8fEZFPmc+Cu21S1fC1zguIAi8D+4Bm4FngoMPnvAO4CThSse3PgfvN9/cD/8V8f9BsUxzYa7Y1an73OEbJfAG+CtxVR5v6gZvM90ngJfPcXrdLgHbzfRPwE+A2r9tV0b5/A/wf4Mt+uI7m8c4AW1ds80O7Pg78pvm+Gej0Q7tWtDEKXAB2e9k2jCW/TwMt5ufPAO90u022dXqN+jL/sV+v+Px+4P0unHcPr1Qgx4F+830/cHy19mCsn3K7uc+LFdvvBf6nje37EsZaLL5pF9AKPAXc6od2Yayi+SjwepYViB/adYaLFYin7QJSGB2i+Kldq7TzZ4AfeN02DAUyCHRhrCz7ZbNtrrYpdGFtjHWhLIbMbW7Tp6ojAObfXnP7Wu3bbr5fub1uRGQPcCOGte95u0w30TMYSxt/Q1V90S7g/wN+DyhXbPNDuxR4RESeFJH7fNKufcAY8L9Nl9//EpE2H7RrJfcAnzLfe9Y2VT0P/FfgHDACzKjqI263KVQgG7OaP9BPsc9rtc+RdotIO/B54H2qmvFDu1S1pKo3YFj8t4jINV63S0R+Fkir6pOb/Ykb7TJ5jareBNwFvEdE7vBBu2IYbtsPqeqNwByGC8brdi2f0Fha++eBz2606xptsK1t5tzG3RjuqAGgTUTe5nabQgWyMUPAzorPO4BhD9oxKiL9AObftLl9rfYNme9Xbq8ZEWnCUB7/oKoP+qVdFqo6DXwHeLMP2vUa4OdF5AzwaeD1IvJJH7QLVR02/6aBLwC3+KBdQ8CQOXoE+ByGQvG6XZXcBTylqqPmZy/bdidwWlXHVHUReBB4tdttChXIxjwBHBCRvaYFcg/wkAfteAh4h/n+HRhzENb2e0QkLiJ7gQPA4+bwNSsit5lRFW+v+E3VmMf4O+CYqv43H7WrR0Q6zfctGA/Wi163S1Xfr6o7VHUPxj3zLVV9m9ftEpE2EUla7zH85ke8bpeqXgAGReQKc9MbgBe8btcK7mXZfWW1wau2nQNuE5FW81hvAI653ia7Jpca+QW8BSPq6GXg910436cw/JqLGBbCbwDdGBOyJ8y/XRX7/77ZtuNURFAAhzA6h5eB/8GKCcoq2/RPMIa2zwHPmK+3+KBd1wFPm+06AvxHc7un7VrRxp9meRLd6//XPoxonGeBo9b97HW7zOPdABw2r+UXgS1+aJd5zFZgAuio2Ob1tfwjDGPpCPD3GBFWrrYpLGUSEhISElIToQsrJCQkJKQmQgUSEhISElIToQIJCQkJCamJUIGEhISEhNREqEBCQkJCQmoiVCAhIVUgRsXY3zbfD4jI52w89vtE5O02HOfTInLAjjaFhKxHGMYbElIFZh2wL6vqeuVSajluDKMQ5E2qWqzzWD8FvE1Vf8uWxoWErEE4AgkJqY4PAPvFWBfis2Ku2SIi7xSRL4rIP4rIaRF5r4j8G7Mw4I9FpMvcb7+IfM0sZPg9EbnSPO7rMcpkFM39viMifyUij4mxNsarRORBMdZ5+FNznzYR+YoYa6EcEZF/bh7re8CdplIKCXGMUIGEhFTH/cDLahRv/HcrvrsG+BWM2lJ/BuTUKAz4I4wSEQAPAL+jqjcD/xb4W3P7a4CVhRcXVPUO4MMY5SXeY57jnSLSjVHza1hVrzdHRF8DUNUycBK43haJQ0LWIFQgISH28W1VzarqGDAD/KO5/Xlgj1nJ+NXAZ8UoP/8/MdZjwPw7tuJ4D1X8/qiqjqhqATiFURjveYyRxn8Rkdeq6kzFb9MYVVpDQhwjHOKGhNhHoeJ9ueJzGeNZiwDT5uhlJfNAYo3jVR5r6Xiq+pKI3IxRk+w/i8gjqvrH5j4J85ghIY4RjkBCQqoji7Gkb9WosX7KaRH5JTAqHIuI5WY6BlxWzfFEZADDTfZJjMWFbqr4+nKMYokhIY4RjkBCQqpAVSdE5Afm5PmxGg7xq8CHROQPMNZw/zRGZdyvYlRUrYZrgb8QkTJG5eZ3A4hIHzCv5sp0ISFOEYbxhoT4BBH5AvB7qnqizuP8LpBR1b+zp2UhIasTurBCQvzD/SxPqtfDNPBxG44TErIu4QgkJCQkJKQmwhFISEhISEhNhAokJCQkJKQmQgUSEhISElIToQIJCQkJCamJUIGEhISEhNTE/w/mlI66w4O24wAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Fs = 8000\n", "f = 5\n", "sample = 8000\n", "x = np.arange(sample)\n", "y = np.sin(2 * np.pi * f * x / Fs)\n", "plt.plot(x, y)\n", "plt.xlabel('time(ms)')\n", "plt.ylabel('voltage(V)')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "fs = 100 # sample rate \n", "f = 6 # the frequency of the signal\n", "\n", "x = np.arange(fs) # the points on the x axis for plotting\n", "# compute the value (amplitude) of the sin wave at the for each sample\n", "y = np.sin(2*np.pi*f * (x/fs)) " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x, y)\n", "plt.xlabel('time(ms)')\n", "plt.ylabel('amplitude is current or voltage for AC')\n", "# showing the exact location of the samples\n", "plt.stem(x,y, 'r', )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }