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    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# The debug library - you can set a debug breakpoint with e.g.\n",
    "# pdb.set_trace()\n",
    "# and then examine the values of variables, types etc.\n",
    "import pdb\n",
    "\n",
    "def read_spectrum (filename): \n",
    "\n",
    " # Read in the data. It is binary format, unsigned 8 bit integers 'unit8'\n",
    " # With real value followed by imaginary value for each data point\n",
    " data = np.fromfile(filename, dtype='uint8')\n",
    "\n",
    " # This will be the number of distinct complex values, i.e. half the\n",
    " # number of total values.\n",
    " datasize = int(np.size(data)/2)\n",
    "\n",
    " # Create a numpy array (initially filled with zeros) to hold\n",
    " # the complex data \n",
    " dataz = np.zeros(datasize,dtype=complex)\n",
    "\n",
    " # Assigned the comlex values, using numpy indexing trickery.\n",
    " # real values start on 0 and step over 2\n",
    " # imag values start on 1 and step over 2\n",
    " dataz=data[0::2]+1j*data[1::2]\n",
    "\n",
    " # Calculate the mean of the data set and subtract\n",
    " offset=np.mean(dataz)\n",
    " dataz-=offset\n",
    "\n",
    " # The sampled time chunks in the data are 512 elements long\n",
    " # This will be the size of the fft we want to do\n",
    " fftsize=512;\n",
    "\n",
    " # nspec is the number of distinct time chunks in the time ordered data\n",
    " # This will also be the number of output spectra \n",
    " nspec=int(np.floor(datasize/fftsize))\n",
    " nsamp=nspec*fftsize\n",
    "\n",
    " # This makes a 2D array out of the 1-D data\n",
    " # with nspec rows and fftsize columns\n",
    "\n",
    " dataz= dataz.reshape((nspec,fftsize))\n",
    " # This calculates the fft, but only of the column axis (axis =1, fftsize long).\n",
    " fft_dataz= np.fft.fft(dataz,axis=1)\n",
    "\n",
    " # This reorders the fft data to that the 0 frequency channel is in the middle,\n",
    " # (FFT routines expect and return \"folded\" data ordering 0 to f, -f to 0)\n",
    " fft_dataz_shift= np.fft.fftshift(fft_dataz,axes=(1,))\n",
    "\n",
    " # This averages all the the individual 512 spectra together in the 2D array.\n",
    " # Notice we specify axis = 0 , the opposite axis to which the FFT was performed\n",
    " # over.\n",
    " spec = np.mean(np.abs(fft_dataz_shift),axis=0)\n",
    " \n",
    "\n",
    " # Calculate the corresponding frequency axis\n",
    " samprate=2.4e6;\n",
    " fcentre=1420.0e6;\n",
    " tau=1/samprate;\n",
    " fstep=1/(tau*fftsize);\n",
    " freq=fcentre+(fstep*(np.arange(0,fftsize)-fftsize/2));\n",
    "\n",
    " # return the freq axis and spectrum arrays\n",
    " return (freq,spec)\n",
    "\n",
    "\n"
   ]
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    "#Students enter your code here."
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