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    {
      "cell_type": "code",
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      "source": [
        "%matplotlib inline"
      ]
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      "cell_type": "markdown",
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      "source": [
        "\n# Time and Frequency Localization Characteristics\n\nGenerate a signal that has localized characteristics in both time and frequency\nand compute the following estimates:\n\n    * time center\n    * time duration\n    * frequency center\n    * frequency spreading\n\nExample 2.1 from the tutorial.\n"
      ]
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
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      "source": [
        "from tftb.generators import fmlin, amgauss\nfrom tftb.processing import loctime, locfreq\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# generate signal\nsignal = fmlin(256)[0] * amgauss(256)\nplt.subplot(211), plt.plot(np.real(signal))\nplt.xlim(0, 256)\nplt.xlabel('Time')\nplt.ylabel('Real part')\nplt.title('Signal')\nplt.grid()\nfsig = np.fft.fftshift(np.abs(np.fft.fft(signal)) ** 2)\nplt.subplot(212), plt.plot(np.linspace(0, 0.5, 256), fsig)\nplt.xlabel('Normalized frequency')\nplt.ylabel('Squared modulus')\nplt.title('Spectrum')\nplt.grid()\nplt.subplots_adjust(hspace=0.5)\nplt.show()\n\n\ntm, T = loctime(signal)\nprint(\"Time Center: {}\".format(tm))\nprint(\"Time Duration: {}\".format(T))\nnum, B = locfreq(signal)\nprint(\"Frequency Center: {}\".format(num))\nprint(\"Frequency Spreading: {}\".format(B))"
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