ryanvolz/ambiguity.ipynb

## ambiguity.ipynb
{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ambiguity(code, nfreq=1):\n",
      "    \"\"\"Calculate the ambiguity function of code for nfreq frequencies.\n",
      "    \n",
      "    The ambiguity function is the square of the autocorrelation,\n",
      "    normalized so the peak value is 1.\n",
      "    \n",
      "    For correct results, we require that nfreq >= len(code).\n",
      "    \n",
      "    The result is a 2-D array with the first index corresponding\n",
      "    to frequency shift. The code is frequency shifted by \n",
      "    normalized frequencies of range(nfreq)/nfreq and correlated\n",
      "    with the baseband code. The result amb[0] gives the \n",
      "    ambiguity with 0 frequency shift, amb[1] with 1/nfreq\n",
      "    frequency shift, etc. These frequencies are the same as (and \n",
      "    are in the same order as) the FFT frequencies for an nfreq-\n",
      "    length FFT.\n",
      "    ****Thus, the peak value is at amb[0, len(code) - 1]****\n",
      "    \n",
      "    To relocate the peak to the middle of the result, use\n",
      "        np.fft.fftshift(amb, axes=0)\n",
      "    To relocate the peak to the [0, 0] entry, use\n",
      "        np.fft.ifftshift(amb, axes=1)\n",
      "    \n",
      "    \"\"\"\n",
      "    inlen = len(code)\n",
      "    outlen = 2*inlen - 1\n",
      "    \n",
      "    # Doppler shift the code to form a correlation bank in the form of a matrix\n",
      "    doppleridx = np.arange(nfreq)[:, np.newaxis]*np.arange(inlen)\n",
      "    dopplermat = np.exp(2*np.pi*1j*doppleridx/nfreq)\n",
      "    # code is conjugated to form matched correlation\n",
      "    codebank = code.conj()*dopplermat\n",
      "    \n",
      "    # initialize the output autocorrelation array\n",
      "    acorr = np.zeros((nfreq, outlen), np.complex_)\n",
      "    \n",
      "    # correlate the Doppler-shifted codes with the original code\n",
      "    # to get autocorrelation\n",
      "    for k, shifted_code in enumerate(codebank):\n",
      "        acorr[k] = np.correlate(code, shifted_code, mode='full')\n",
      "    \n",
      "    # calculate ambiguity function as normalized square magnitude of autocorrelation\n",
      "    # (index of peak value is [0, inlen - 1])\n",
      "    amb = np.abs(acorr / acorr[0, inlen - 1])**2\n",
      "    \n",
      "    return amb"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "barker13 = np.asarray([1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1], np.float_)\n",
      "L = len(barker13)\n",
      "N = 256\n",
      "b13amb = ambiguity(barker13, N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.imshow(np.fft.fftshift(b13amb, axes=0).T, extent=(-N/2, N/2, -L, L),\n",
      "           aspect='auto', interpolation='none', origin='lower')\n",
      "plt.xlabel('Frequency Index')\n",
      "plt.ylabel('Delay Index')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.text.Text at 0x7f88f39ba490>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XLbq3iQ4ePGj/vGbNGtTV1RWwNUREZ4aiu5toyZIl2LVrFyRJwsiRI/Hkk08W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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f88f460e210>"
       ]
      }
     ],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}
	{
	"metadata": {
	"name": ""
	},
	"nbformat": 3,
	"nbformat_minor": 0,
	"worksheets": [
	{
	"cells": [
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"import numpy as np\n",
	"import matplotlib.pyplot as plt"
	],
	"language": "python",
	"metadata": {},
	"outputs": [],
	"prompt_number": 1
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"def ambiguity(code, nfreq=1):\n",
	" \"\"\"Calculate the ambiguity function of code for nfreq frequencies.\n",
	" \n",
	" The ambiguity function is the square of the autocorrelation,\n",
	" normalized so the peak value is 1.\n",
	" \n",
	" For correct results, we require that nfreq >= len(code).\n",
	" \n",
	" The result is a 2-D array with the first index corresponding\n",
	" to frequency shift. The code is frequency shifted by \n",
	" normalized frequencies of range(nfreq)/nfreq and correlated\n",
	" with the baseband code. The result amb[0] gives the \n",
	" ambiguity with 0 frequency shift, amb[1] with 1/nfreq\n",
	" frequency shift, etc. These frequencies are the same as (and \n",
	" are in the same order as) the FFT frequencies for an nfreq-\n",
	" length FFT.\n",
	" **Thus, the peak value is at amb[0, len(code) - 1]**\n",
	" \n",
	" To relocate the peak to the middle of the result, use\n",
	" np.fft.fftshift(amb, axes=0)\n",
	" To relocate the peak to the [0, 0] entry, use\n",
	" np.fft.ifftshift(amb, axes=1)\n",
	" \n",
	" \"\"\"\n",
	" inlen = len(code)\n",
	" outlen = 2*inlen - 1\n",
	" \n",
	" # Doppler shift the code to form a correlation bank in the form of a matrix\n",
	" doppleridx = np.arange(nfreq)[:, np.newaxis]*np.arange(inlen)\n",
	" dopplermat = np.exp(2np.pi1j*doppleridx/nfreq)\n",
	" # code is conjugated to form matched correlation\n",
	" codebank = code.conj()*dopplermat\n",
	" \n",
	" # initialize the output autocorrelation array\n",
	" acorr = np.zeros((nfreq, outlen), np.complex_)\n",
	" \n",
	" # correlate the Doppler-shifted codes with the original code\n",
	" # to get autocorrelation\n",
	" for k, shifted_code in enumerate(codebank):\n",
	" acorr[k] = np.correlate(code, shifted_code, mode='full')\n",
	" \n",
	" # calculate ambiguity function as normalized square magnitude of autocorrelation\n",
	" # (index of peak value is [0, inlen - 1])\n",
	" amb = np.abs(acorr / acorr[0, inlen - 1])**2\n",
	" \n",
	" return amb"
	],
	"language": "python",
	"metadata": {},
	"outputs": [],
	"prompt_number": 2
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"barker13 = np.asarray([1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1], np.float_)\n",
	"L = len(barker13)\n",
	"N = 256\n",
	"b13amb = ambiguity(barker13, N)"
	],
	"language": "python",
	"metadata": {},
	"outputs": [],
	"prompt_number": 3
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"plt.imshow(np.fft.fftshift(b13amb, axes=0).T, extent=(-N/2, N/2, -L, L),\n",
	" aspect='auto', interpolation='none', origin='lower')\n",
	"plt.xlabel('Frequency Index')\n",
	"plt.ylabel('Delay Index')"
	],
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"metadata": {},
	"output_type": "pyout",
	"prompt_number": 4,
	"text": [
	"<matplotlib.text.Text at 0x7f88f39ba490>"
	]
	},
	{
	"metadata": {},
	"output_type": "display_data",
	"png": 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	"text": [
	"<matplotlib.figure.Figure at 0x7f88f460e210>"
	]
	}
	],
	"prompt_number": 4
	}
	],
	"metadata": {}
	}
	]
	}