Notebook8-NMR_processing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we are going to take the free-induction decay (FID) from an NMR and graph it as an NMR spectrum. As you can see below, I'm importing the usual packages, but I've also imported one we haven't used before. The nmrglue package is an open-source package for analyzing and graphing nmr spectra, and probably isn't preinstalled in your version of python. To install it, check out the [nmrglue install guide](https://nmrglue.readthedocs.io/en/latest/install.html).\n",
    "\n",
    "In addition, you will need to get four files that you will use to create the two NMR spectra. These four files are the D2O\\_fid, D2O\\_procpar, NoD2O\\_fid, and NoD2O\\_procpar files, and were collected on an Agilent 400 MHz NMR."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import nmrglue as ng"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The nice thing about the nmrglue package is that it lets me import data using the proprietary files created by the NMR system software. For example, I can use the read_fid() function in the nmrglue package to read Agilent NMR files, without having to turn them into an open-source data file first. I'm going to start with the NoD2O\\_fid and NoD2O\\_procpar files, which contain the necessary data to create one NMR spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dic, data = ng.fileio.agilent.read_fid(\"NoD2O_fid\", as_2d=True)\n",
    "params = ng.fileio.agilent.read_procpar(\"NoD2O_procpar\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that I've read in the fid and parameter file, I can start to work with it. First, as I'm sure you remember, the data that the NMR collects is the free induction decay, or FID. What does that look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NLc7GnQ2s3rSLFnda3BnYt4i9TU5ZSQE79jQxpKyYyv4lvFf/EWbwxgfbqCgv4bRxFSxdu40hZcWUFBawu7GZqmHlbNvdyK69zTQ1t1BRXkwfMzZ9tJey4kIcp6GpheKCPgzqV8T7m3dRUVZCYYGxcUcDQ/uXsH7bHhpbnIqy4tC+l4njhlDYw3vUDqQ9lQlArbuvBDCzR4BpgEZiFOkltu1uZMmarQAsD1cibt0VG0ki/lL590NoZMJ/v74uY/POF+eOH8acz5+S0WXsD5cUjwTWxH2uC21tzGymmdWYWU19ffvDLSIiyRxa8fEVjEcML297/42LPsEdlxzDTVPHR7q8EQNL230eWl7Sad+BfT++KXn8QYnHAuxfGtt/iLrORPaHPZVEB7zbHdNz93uBeyF2+CsbRcn+4Z7PncT/vPkhexpbOGXsECYfPZynl66nsbmFieMqeGf9Dpas2crIQX257ORRNDS2sHX3Xob1L2VQvyIKw8gEZkYfg6YWp6igDy0tjvPxyAXS+11z1mG5LiEv7A+hUgeMjvs8Clibo1okYv9+ybFccPRw6rbsZvxB/WloasHdeXvdDq6472UOrejHY9ecxs6GJh6rWcMN5xxOWXEhfSL8x3rKMSPaff7C345te3/86EF8unp0u+8PofP7cooKYnVFWZ9IPtkfQmURUGVmY4EPgOnAZ3JbkiTylUlVzDxzHI3NLQzqVwzAk0s+YPiAUiaOq6B2w07M4LDK8n2mbd39Ly0qAOC0wypYNfuitu+HAzdN/UTmV0JEutTrQ8Xdm8zsBmA+sUuK57j70hyXdcB47/9eyLIPd1BU0IfDh+0bBo3NLdRt2c2hQ/ol/Ot82gkfn/5KNL2I9C69PlQA3H0eMC/XdfRWY4eWcemJI/luF4NPxps1dTzjhpZxwdEHAfCJEQM67VtU0IexQ8siqVNE8t9+ESrZsL8dAb/u7MM458hhfLB1F+cfdRDlJYVcdNwInNjhp0/+6EXe+GDbPtPNveF0jhs1KPsFi0ivsD9cUiwp+M11p7X7fOOU8UwYO4RLThxFeUnsb4txleVt5zN+dtUpfPbUQ4BYAAE8fu1pChQR6ZL2VPYT008ZzZRjDmJnQxMfbNlNZf8Svv5Y7AmQq2ZfRHOLc+74YQzqW8TXzj8i6fyGlpdwxyXHcsclxwKxk+ytJ8lFRDqjUOnFvnpeFZ859RCWfrCdM4+o3Oeeh68/9hpnVA0FYvdDpHMnrQJFRFKhUElRPowpeM1Z4/jpnz5+ONaXz62iTx9j2PjShP1f/d/n069EYSAi2aNzKr3IP1SP5pWbJzH1mINY+G+Tkt5ANzgMUCciki3aU8ljv772NAaUFvHwy6uZdsLBjAsn0e/+3Mk5rkxEJDGFSh457xPDeObt2Iis3738eE4ZMwSAb12spyWKSO+gUEmRZfhOlVlTx3PtWYexePUWtu9p5Jwjh2V0eSIimaBQyQMjBpZybRjh9ORD9VhcEem9dKJeREQio1BJUSYvKY4fVFFEpDdTqKTIM/hor3+dfGTmZi4ikkUKlRw7rLJMD2wSkf2GQiXHfnPd3+S6BBGRyChUUpSpcyqtT0AUEdkfKFRERCQyChUREYmMQiVDRg3um7TPNWeOy0IlIiLZozvqM6DmG+fx6Z++1GWfVbMvylI1IiLZoz2VDBhaXgIZvK9FRCRfKVRERCQyCpUc+OH0E3JdgohIRihUUtTd+1Q6O/o1cdwQjfUlIvsthUrEfn3taV1+P/vS47JUiYhI9ilUItb6tMbOjBlalqVKRESyT6GSBVdMGJ3rEkREskKhkqLuDn1//KiBAFx+8ihuv/jYDFQkIpJ/dPNjhsz+1HF88YxxHDMyFi6Lv3Eeu/Y257gqEZHMUqhEZFj/EhZ8/ay2z6VFBW2BAlBRXkJFLgoTEcmijB3+MrNbzewDM1sSXhfGfXeTmdWa2TtmNjmufUpoqzWzWXHtY81soZktN7NHzaw4tJeEz7Xh+zGZWp9k+pcWMrBvUa4WLyKSFzJ9TuX77n5CeM0DMLOjgOnA0cAU4CdmVmBmBcBdwFTgKOCK0Bfg22FeVcAW4OrQfjWwxd0PB74f+omISI7k4kT9NOARd29w9/eAWmBCeNW6+0p33ws8AkwzMwPOBR4P0z8IXBw3rwfD+8eBSaF/1n15UlUuFisiklcyHSo3mNnrZjbHzAaHtpHAmrg+daGts/YKYKu7N3Vobzev8P220L8dM5tpZjVmVlNfXx/NmnWgu+RFRNIMFTN7xszeTPCaBtwNHAacAKwDvts6WYJZeQ/au5pX+wb3e9292t2rKysrk6yViIj0VFpXf7n7ean0M7P7gP8OH+uA+LsBRwFrw/tE7RuBQWZWGPZG4vu3zqvOzAqBgcDmHqyKiIhEIJNXf42I+3gJ8GZ4PxeYHq7cGgtUAa8Ai4CqcKVXMbGT+XPd3YHngMvC9DOAJ+PmNSO8vwz4Q+gvIiI5kMn7VL5jZicQOxy1CrgGwN2XmtljwFtAE3C9uzcDmNkNwHygAJjj7kvDvG4EHjGz24FXgQdC+wPAL8ysltgeyvQMro+IiCSRsVBx93/s4rs7gDsStM8D5iVoX0ns6rCO7XuAy9OrVEREoqKxvyJw+LDyXJcgIpIXFCoROHhQ31yXICKSFxQqEfi740Yk7yQicgBQqETg09V6XoqICChUREQkQgqVNI0arPMpIiKtFCppeuJLp+e6BBGRvKFQSVNl/5JclyAikjcUKiIiEhmFioiIREahIiIikVGoiIhIZBQqIiISGYVKGvqXZvLJASIivY9CJR16HJiISDsKFRERiYxCRUREIqNQERGRyChUUuQJzp+MGFSa/UJERPKYQiUND199aq5LEBHJKwqVNAwboD0VEZF4ChUREYmMQkVERCKjUBERkcgoVEREJDIavKoHxlT0Y+K4ilyXISKSdxQqPfDHfzkn1yWIiOQlHf7qpi+fe3iuSxARyVsKlW46btSgXJcgIpK3FCoiIhKZtELFzC43s6Vm1mJm1R2+u8nMas3sHTObHNc+JbTVmtmsuPaxZrbQzJab2aNmVhzaS8Ln2vD9mGTLEBGR3Eh3T+VN4FLg+fhGMzsKmA4cDUwBfmJmBWZWANwFTAWOAq4IfQG+DXzf3auALcDVof1qYIu7Hw58P/TrdBlpro+IiKQhrVBx97fd/Z0EX00DHnH3Bnd/D6gFJoRXrbuvdPe9wCPANDMz4Fzg8TD9g8DFcfN6MLx/HJgU+ne2DBERyZFMnVMZCayJ+1wX2jprrwC2untTh/Z28wrfbwv9O5vXPsxsppnVmFlNfX19GqslIiJdSXqfipk9AxyU4Kub3f3JziZL0OYkDjHvon9X8+pqmvaN7vcC9wJUV1f36MnyrgfSi4gklTRU3P28Hsy3Dhgd93kUsDa8T9S+ERhkZoVhbyS+f+u86sysEBgIbE6yjIyxRFEmIiJA5g5/zQWmhyu3xgJVwCvAIqAqXOlVTOxE+1x3d+A54LIw/Qzgybh5zQjvLwP+EPp3tgwREcmRtIZpMbNLgB8BlcDvzWyJu09296Vm9hjwFtAEXO/uzWGaG4D5QAEwx92XhtndCDxiZrcDrwIPhPYHgF+YWS2xPZTpAF0tQ0REciOtUHH3J4AnOvnuDuCOBO3zgHkJ2leS4Ootd98DXN6dZYiISG7ojnoREYmMQkVERCKjUBERkcgoVEREJDIKFRERiYxCRUREIqNQERGRyChUREQkMgoVERGJjEJFREQio1BJkWvkexGRpBQq3aSh70VEOqdQERGRyChUREQkMgoVERGJjEJFREQio1AREZHIKFRERCQyChUREYmMQkVERCKjUBERkcgoVEREJDIKFRERiYxCRUREIqNQERGRyChUUjSwbxEXHnsQleWluS5FRCRvFea6gN5izNAyfvLZk3NdhohIXtOeioiIREahIiIikVGoiIhIZBQqIiISmbRCxcwuN7OlZtZiZtVx7WPMbLeZLQmve+K+O9nM3jCzWjO70yz21HczG2JmC8xsefg5OLRb6FdrZq+b2Ulx85oR+i83sxnprIuIiKQv3T2VN4FLgecTfLfC3U8Ir2vj2u8GZgJV4TUltM8CnnX3KuDZ8BlgalzfmWF6zGwIcAtwKjABuKU1iEREJDfSChV3f9vd30m1v5mNAAa4+0vu7sBDwMXh62nAg+H9gx3aH/KYl4FBYT6TgQXuvtndtwAL+DigREQkBzJ5TmWsmb1qZn8yszNC20igLq5PXWgDGO7u6wDCz2Fx06xJME1n7fsws5lmVmNmNfX19emsk4iIdCHpzY9m9gxwUIKvbnb3JzuZbB1wiLtvMrOTgd+Z2dGAJejryUroZJqU5+Xu9wL3AphZvZmtTrLMrgwFNqYxfable32gGqOQ7/WBaoxKvtR4aCqdkoaKu5/X3SW7ewPQEN4vNrMVwBHE9iZGxXUdBawN79eb2Qh3XxcOb20I7XXA6ATT1AFnd2j/Ywq1VXZ3feKZWY27VyfvmRv5Xh+oxijke32gGqPSG2qMl5HDX2ZWaWYF4f04YifZV4bDWjvMbGK46utKoHVvZy7QegXXjA7tV4arwCYC28J85gMXmNngcIL+gtAmIiI5ktbYX2Z2CfAjoBL4vZktcffJwJnAbWbWBDQD17r75jDZdcDPgb7AU+EFMBt4zMyuBt4HLg/t84ALgVpgF3AVgLtvNrNvAYtCv9viliEiIjmQVqi4+xPAEwnafwP8ppNpaoBjErRvAiYlaHfg+k7mNQeY072q03ZvlpfXXfleH6jGKOR7faAao9IbamxjsX+zRURE0qdhWkREJDIKFRERiYxCJUVmNsXM3gljkM1KPkVkyx1tZs+Z2dthnLWvhPZbzeyDuPHVLoyb5qZQ5ztmNjkb62Bmq8KYbkvMrCa05c14bmZ2ZNy2WmJm283sq7nejmY2x8w2mNmbcW2RbTfrZKy9CGr8DzNbFup4wswGhfbIxv1Ls77Ifq9mNtbMFob6HjWz4oi24aNx9a0ysyW52oaRcne9kryAAmAFMA4oBl4DjsrSskcAJ4X3/YF3gaOAW4H/laD/UaG+EmBsqLsg0+sArAKGdmj7DjArvJ8FfDu8v5DYVX8GTAQWhvYhwMrwc3B4PzhDv88Pid3MldPtSOxKyZOANzOx3YBXgNPCNE8BUyOq8QKgMLz/dlyNY+L7dZhPwlo6W98064vs9wo8BkwP7+8BrotiG3b4/rvAN3O1DaN8aU8lNROAWndf6e57gUeIjUmWce6+zt3/Gt7vAN6mk+FogmnAI+7e4O7vEbsUewK5WYd8Hc9tErEBT7saWSEr29Hdnwc6XgofyXazrsfaS6tGd3/a3ZvCx5dpf1PzPpLU0tn69ri+LnTr9xr2BM4FHu9pfclqDMv4NPCfXc0jk9swSgqV1KQ8zlgmmdkY4ERgYWi6IRx+mBO3u5v2WGk95MDTZrbYzGaGtoyN55am6bT/HziftiNEt926GmsvSl/g4/vNILpx/9IVxe+1AtgaF6CZ2IZnAOvdfXlcW75sw25TqKSmJ2OWRVuAWTmxe3++6u7biT0C4DDgBGJjrX23tWuCybs1VloPne7uJxF7VMH1ZnZmF31zVSPhePjfA78OTfm2HbvS3ZqysT1vBpqAX4am1nH/TgS+DvzKzAZko5YOovq9ZqPuK2j/R06+bMMeUaikprPxx7LCzIqIBcov3f23AO6+3t2b3b0FuI/Y7ntXtWZ0Hdx9bfi5gdgNsRMI47mFdUh1PLdMb+epwF/dfX2oN6+2YxDVdutqrL20hQsC/g74bDgcQzistCm8X0zsPEVK4/6Fecavb49F+HvdSOwwY2GH9kiE+V4KPBpXe15sw55SqKRmEVAVrgIpJnb4ZG42FhyOtz4AvO3u34trHxHX7RJiD0wj1DXdzErMbCyxcddeyeQ6mFmZmfVvfU/sJO6b5Od4bu3+Ksyn7Rgnku3mXY+1lxYzmwLcCPy9u++Ka49y3L906ovk9xrC8jngsijri3MesMzd2w5r5cs27LFcXSHQ217Errx5l9hfDTdncbl/S2wX93VgSXhdCPwCeCO0zwVGxE1zc6jzHeKu9snUOhC7Yua18FraOm8EbeGxAAAAsklEQVRix6OfBZaHn0NCuwF3hTreAKrj5vUFYidPa4GrIt6W/YBNwMC4tpxuR2IBtw5oJPaX6NVRbjegmtg/qCuAHxNG0Yigxlpi5yBa/5u8J/T9VPhv4DXgr8Ank9XS2fqmWV9kv9fw3/crYZ1/DZREsQ1D+8+JjY0Y3zfr2zDKl4ZpERGRyOjwl4iIREahIiIikVGoiIhIZBQqIiISGYWKiIhERqEiIiKRUaiIiEhk/j96RZ0BL7Xe/wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data.real[0])\n",
    "plt.title(\"Figure 1 - FID\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's the FID. Unfortunately there are a couple of problems. The biggest is that the x-axis is wrong. To keep the FID files small the way Agilent's (and most NMR) software stores FID data is as a series of values, and so when we graph that data the x-axis is the point number. However, the x-axis should be time, not point number, so we have to create an array of points with the value of time that each data point was collected. To do this, we can use at the total acquisition time of the FID and the total number of points to find the time per point, and then use that to create an array of times. The acquisition time is stored as \"at\" in the \"params\" array that I imported, above. And no, I didn't know how to do this when I started. I had to spend a fair bit of time reading the nmrglue documentation and looking at examples on the internet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The FID acquisition took 2.6001 seconds.\n"
     ]
    }
   ],
   "source": [
    "acq_time = float(params['at']['values'][0])\n",
    "time_per_point = acq_time/(data.shape[1])\n",
    "time=np.arange(0,acq_time,time_per_point)\n",
    "print(\"The FID acquisition took \" + \"{:1.5}\".format(acq_time) + \" seconds.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's look at the FID with the correct x-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(time,data.real[0])\n",
    "plt.title(\"Figure 2 - FID\")\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel('Measured signal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Turns out, in FT-NMRs there are two reciever antennaes, one along the x-axis of the NMR and one along the y-axis of the NMR, and each antennae collects an FID. One is stored as \"real\" and the other is stored as \"imaginary\", but these names are just mathematical convenience. The FID above is the one stored as the real. What does the one stored as imaginary look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(time,data.imag[0])\n",
    "plt.title(\"Figure 3 - Imaginary FID\")\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel('Measured signal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I don't really see any difference between the two, but rest assured, they are different. To turn the FID into a useful spectrum that we can analyze by eye, we have to Fourier transform it. Luckily, the numpy package has a Fourier transform function called fft() (for Fast Fourier Transform)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fftdata = np.fft.fft(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at our NMR spectrum!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zgcfDQMuvlH0AHwJ+n2P5RGBV1vvV6bKcJF0saaGkhRs3bixh8cysP3BFoHy6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\nqf8PSvZLh8W+InwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c64da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fftdata.real[0])\n",
    "plt.title(\"Figure 4 - NMR spectrum\")\n",
    "plt.xlabel(\"Chemical shift (ppm)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, that doesn't seem quite right. For a proton NMR we typically expect chemical shifts between 0 and 10, not 17,500. And the peaks are mostly pointing down and have weird edge effects. What went wrong? Nothing, actually, we're just not done yet. First, when we Fourier transform the FID, our x-axis goes from time (s) to frequency (s$^{-1}$), and we have to do an extra step to turn it into chemical shift (ppm). Also, we need to remember that our data is stored as points without time, so we need to also use the fft() function on our time array to create the correct x-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NMR_freq = 400\n",
    "freq = np.fft.fftfreq(time.shape[0],time_per_point)\n",
    "chem_shift = -(freq - 1986)/NMR_freq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After multiple tries I was able to figure out that the TMS peak was at a frequency value of 1986, and so I subtracted that from the frequency to get the TMS peak at zero. So, what does the spectrum look like now?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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St1VfJ9o7omsSu33tnTy3s4112/Yya+Iotu/dT51Ec0Mda7buYevufQxrrGdfeyfD05r5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\nRjkAmJnVKAcAM7Ma5QBgZlaj/g93MgrM5sj5iwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112ebd8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(chem_shift,fftdata.real[0])\n",
    "plt.title(\"Figure 5 - NMR spectrum\")\n",
    "plt.xlabel(\"Chemical shift (ppm)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's starting to look better, but we still have two issues. The first, which is minor, is that standard NMR spectra convention is to have the positive chemical shifts to the left, rather than the right, so we'll need to fix our axis. The seconds, which is a bigger issue, is that the peaks still look odd. This is where the real vs. imaginary FIDs become important. Right now we are only graphing the Fourier transformed real FID, and the result is that our peaks are out of phase with the detector. So we need to combine the real and imaginary data to get everything in phase. If you've messed with the phase setting on the NMR, this is what you are changing. Here, we need to change the phase by hand. Mathematically, this works out to be the real data times $\\cos{\\theta}$ + imaginary data times times $\\sin{\\theta}$, where we need to find theta. After multiple tries I found that a good value for $\\theta$ is 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZcHYqm9nw++r1s7no9qeZvWR1U8+TTDhHV8t325CNCF5Z3dbn9rU+Z0e02dDx9QPbWr+p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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c3b0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = np.degrees(10)\n",
    "plt.plot(chem_shift,fftdata.real[0]*np.cos(np.radians(theta)) + fftdata.imag[0]*np.sin(np.radians(theta)))\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(-3,10)\n",
    "ax.set_xlim(ax.get_xlim()[::-1])\n",
    "ax.axes.yaxis.set_ticklabels([])\n",
    "ax.axes.yaxis.set_ticks([])\n",
    "plt.title(\"Figure 6 - NMR spectrum\")\n",
    "plt.xlabel(\"Chemical shift (ppm)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And there we have it, the NMR spectrum. If you want, play around with different $\\theta$ values to see how that affects the graph. Now, your job is to use the D2O\\_fid and D2O\\_procpar files to create an NMR spectrum, and compare it to the spectrum above. The spectrum you are graphing is for the same material as above, but *after* some D$_{2}$O has been added to the NMR tube."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the differences between the two spectra? What can you say about the material, knowing that the change was due to the addition of D$_{2}$O?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer here**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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