{
 "metadata": {
  "name": "",
  "signature": "sha256:cf8a8fc13ae83e9b831f55806e2fdb9830b47be1f45e666171b0ee04cc86a17a"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import print_function\n",
      "from deltasigma import *\n",
      "from IPython.core.display import Image"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# skip this, this is just to display nice tables.\n",
      "from itertools import izip_longest\n",
      "class Table(list):\n",
      "    def _repr_html_(self):\n",
      "        html = [\"<table>\"]\n",
      "        for row in self:\n",
      "            html.append(\"<tr>\")\n",
      "            for col in row:\n",
      "                try:\n",
      "                    float(col)\n",
      "                    html.append(\"<td>%.6f</td>\" % col)\n",
      "                except(ValueError):\n",
      "                    html.append(\"<td><b>%s</b></td>\" % col)\n",
      "            html.append(\"</tr>\")\n",
      "        html.append(\"</table>\")\n",
      "        return ''.join(html)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Modulator realization and dynamic range scaling - # demo3"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this ipython notebook, the following is demonstrated:\n",
      "\n",
      " * A 5th order delta sigma modulator is synthesized, with optimized zeros and an OSR equal to 42.\n",
      "\n",
      " * We then convert the synthesized NTF into `a`, `g`, `b`, `c` coefficients for the `CRFB` modulator structure.\n",
      " \n",
      " * The maxima for each state are evaluated.\n",
      " \n",
      " * The `ABCD` matrix is scaled so that the state maxima are less than the specified limit.\n",
      "\n",
      " * The state maxima are re-evaluated and limit compliance is checked.\n",
      "\n",
      "**NOTE:** This is an ipython port of `dsdemo3.m`, from the **[MATLAB Delta Sigma Toolbox](http://www.mathworks.com/matlabcentral/fileexchange/19-delta-sigma-toolbox)**, written by Richard Schreier."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Delta sigma modulator synthesis"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "order = 5\n",
      "R = 42\n",
      "opt = 1\n",
      "H = synthesizeNTF(order, R, opt)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's inspect the NTF, printing out the transfer function and plotting poles and zeros with respect to the unit circle."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(pretty_lti(H))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "        (z^2 - 1.995z + 1) (z^2 - 1.998z + 1) (z - 1)         \n",
        "--------------------------------------------------------------\n",
        " (z^2 - 1.614z + 0.6657) (z^2 - 1.797z + 0.8552) (z - 0.7783) \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(10, 5))\n",
      "plotPZ(H, showlist=True)\n",
      "title('NTF');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Y5+TJkxg1alS789bS784PPvgAhoaGrXbBatj2ccyYMejfvz/E4odPxDz77LNI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\n3iWk83IqysuJlBPv0h5zCAoLC+OC7CQmDujNvI0lPPD+enK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       "text": [
        "<matplotlib.figure.Figure at 0x10aff4150>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Evaluation of the coefficients for a CRFB topology\n",
      "The CRFB topology is depicted in the following diagram."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Image(url='http://python-deltasigma.readthedocs.org/en/latest/_images/CRFB.png', retina=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<img src=\"http://python-deltasigma.readthedocs.org/en/latest/_images/CRFB.png\"/>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<IPython.core.display.Image at 0x1007342d0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since the modulator order is 5, we're interested in the topology for odd order modulators."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Unscaled modulator"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Calculate the coefficients"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a, g, b, c = realizeNTF(H)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Feed-in selection\n",
      "We'll use a single feed-in for the input, to have a maximally flat STF.\n",
      "\n",
      "This means setting $\\ b_n = 0, \\ \\forall n > 1$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = np.concatenate((b[0].reshape((1, )), np.zeros((b.shape[0] - 1, ))), axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = Table()\n",
      "ilabels = ['#1', '#2', '#3', '#4', '#5', '#6']\n",
      "t.append(['Coefficients', 'DAC feedback', 'Resonator feedback', \n",
      "          'Feed-in', 'Interstage'])\n",
      "t.append(['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'])\n",
      "[t.append(x) for x in izip_longest(ilabels, a.tolist(), g.tolist(), b.tolist(), c.tolist(), fillvalue=\"\")]\n",
      "t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><td><b>Coefficients</b></td><td><b>DAC feedback</b></td><td><b>Resonator feedback</b></td><td><b>Feed-in</b></td><td><b>Interstage</b></td></tr><tr><td><b></b></td><td><b>a(n)</b></td><td><b>g(n)</b></td><td><b> b(n)</b></td><td><b> c(n)</b></td></tr><tr><td><b>#1</b></td><td>0.000667</td><td>0.001622</td><td>0.000667</td><td>1.000000</td></tr><tr><td><b>#2</b></td><td>0.008583</td><td>0.004593</td><td>0.000000</td><td>1.000000</td></tr><tr><td><b>#3</b></td><td>0.055201</td><td><b></b></td><td>0.000000</td><td>1.000000</td></tr><tr><td><b>#4</b></td><td>0.247607</td><td><b></b></td><td>0.000000</td><td>1.000000</td></tr><tr><td><b>#5</b></td><td>0.556935</td><td><b></b></td><td>0.000000</td><td>1.000000</td></tr><tr><td><b>#6</b></td><td><b></b></td><td><b></b></td><td>0.000000</td><td><b></b></td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "[['Coefficients',\n",
        "  'DAC feedback',\n",
        "  'Resonator feedback',\n",
        "  'Feed-in',\n",
        "  'Interstage'],\n",
        " ['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'],\n",
        " ('#1',\n",
        "  0.0006670795813848786,\n",
        "  0.001622050471799641,\n",
        "  0.0006670795813848786,\n",
        "  1.0),\n",
        " ('#2', 0.00858263528791771, 0.004592653480622877, 0.0, 1.0),\n",
        " ('#3', 0.05520145164491604, '', 0.0, 1.0),\n",
        " ('#4', 0.2476072516506828, '', 0.0, 1.0),\n",
        " ('#5', 0.5569351152496502, '', 0.0, 1.0),\n",
        " ('#6', '', '', 0.0, '')]"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Calculate the state maxima"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ABCD = stuffABCD(a, g, b, c);\n",
      "u = np.linspace(0, 0.6, 30);\n",
      "N = 1e4; \n",
      "T = np.ones((1, N))\n",
      "maxima = np.zeros((order, len(u)))\n",
      "for i in range(len(u)):\n",
      "    ui = u[i]\n",
      "    v, xn, xmax, _ = simulateDSM(ui*T, ABCD);\n",
      "    maxima[:, i] = np.squeeze(xmax)\n",
      "    if any(xmax > 1e2):\n",
      "        umax = ui;\n",
      "        u = u[:i+1];\n",
      "        maxima = maxima[:, :i]\n",
      "        break;\n",
      "# save the maxima\n",
      "prescale_maxima = np.copy(maxima)\n",
      "print('The state maxima have been evaluated through simulation.')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The state maxima have been evaluated through simulation.\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot of the state maxima"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(order):\n",
      "    semilogy(u, maxima[i, :],'o-')\n",
      "    if not i:\n",
      "        hold(True)\n",
      "grid(True)\n",
      "xlabel('DC input')\n",
      "ylabel('Peak value')\n",
      "title('Simulated State Maxima')\n",
      "xlim([0, 0.6]) \n",
      "ylim([1e-4, 10]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5rY5muFti6Dtivq4jsN86kWTs0c9YMCXCgYBmXJ9+6WFcBSBJJkySCUkyIUkS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\nP4JjD+jEE38eTL+8dCRJ4mA19oR2oqfKpnpcVui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       "text": [
        "<matplotlib.figure.Figure at 0x10cbea050>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Scaled modulator\n",
      "### Calculate the scaled coefficients"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ABCDs, umax, _ = scaleABCD(ABCD, N_sim=1e5)\n",
      "as_, gs, bs, cs = mapABCD(ABCDs)\n",
      "print('\\nScaled modulator, umax = %.2f\\n' % umax)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Scaled modulator, umax = 0.58\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = Table()\n",
      "ilabels = ['#1', '#2', '#3', '#4', '#5', '#6']\n",
      "t.append(['Coefficients', 'DAC feedback', 'Resonator feedback', \n",
      "          'Feed-in', 'Interstage'])\n",
      "t.append(['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'])\n",
      "[t.append(x) for x in izip_longest(ilabels, as_.tolist(), gs.tolist(), bs.tolist(), cs.tolist(), fillvalue=\"\")]\n",
      "t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><td><b>Coefficients</b></td><td><b>DAC feedback</b></td><td><b>Resonator feedback</b></td><td><b>Feed-in</b></td><td><b>Interstage</b></td></tr><tr><td><b></b></td><td><b>a(n)</b></td><td><b>g(n)</b></td><td><b> b(n)</b></td><td><b> c(n)</b></td></tr><tr><td><b>#1</b></td><td>0.100298</td><td>0.008508</td><td>0.100298</td><td>0.135347</td></tr><tr><td><b>#2</b></td><td>0.174656</td><td>0.010817</td><td>0.000000</td><td>0.190649</td></tr><tr><td><b>#3</b></td><td>0.214165</td><td><b></b></td><td>0.000000</td><td>0.380271</td></tr><tr><td><b>#4</b></td><td>0.365304</td><td><b></b></td><td>0.000000</td><td>0.424567</td></tr><tr><td><b>#5</b></td><td>0.348852</td><td><b></b></td><td>0.000000</td><td>1.596478</td></tr><tr><td><b>#6</b></td><td><b></b></td><td><b></b></td><td>0.000000</td><td><b></b></td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[['Coefficients',\n",
        "  'DAC feedback',\n",
        "  'Resonator feedback',\n",
        "  'Feed-in',\n",
        "  'Interstage'],\n",
        " ['', 'a(n)', 'g(n)', ' b(n)', ' c(n)'],\n",
        " ('#1',\n",
        "  0.1002977628115526,\n",
        "  0.008508036472714772,\n",
        "  0.1002977628115526,\n",
        "  0.1353470899398978),\n",
        " ('#2', 0.17465586699409, 0.01081726217175677, 0.0, 0.19064921465740636),\n",
        " ('#3', 0.21416477448557475, '', 0.0, 0.3802708889041198),\n",
        " ('#4', 0.3653036244427978, '', 0.0, 0.4245670861721391),\n",
        " ('#5', 0.348852264230054, '', 0.0, 1.5964784304291457),\n",
        " ('#6', '', '', 0.0, '')]"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Calculate the state maxima"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u = np.linspace(0, umax, 30)\n",
      "N = 1e4\n",
      "T = np.ones((N,))\n",
      "maxima = np.zeros((order, len(u)))\n",
      "for i in range(len(u)):\n",
      "    ui = u[i]\n",
      "    v, xn, xmax, _ = simulateDSM(ui*T, ABCDs)\n",
      "    maxima[:, i] = xmax.squeeze()\n",
      "    if any(xmax > 1e2):\n",
      "        umax = ui;\n",
      "        u = u[:i]\n",
      "        maxima = maxima[:, :i]\n",
      "        break\n",
      "print('The state maxima have been re-evaluated through simulation.')\n",
      "print(\"The maximum input was found to be %.6f\" % umax)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The state maxima have been re-evaluated through simulation.\n",
        "The maximum input was found to be 0.583333\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot of the state maxima after scaling"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(order):\n",
      "    semilogy(u, maxima[i, :], 'o-')\n",
      "    if not i:\n",
      "        hold(True)\n",
      "grid(True)\n",
      "ylabel('Peak value')\n",
      "xlabel('DC input')\n",
      "xlim([0, 0.6])\n",
      "ylim([4e-2, 4]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fAB5e9EntQ43uvLWmva7R48b97X0UJ/YF9xODzC5aN3eXs7T3H666jq2e+bQ4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\n5G1Xck73KIzHE5unNwTq/Vp1ic976Tk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       "text": [
        "<matplotlib.figure.Figure at 0x10d00e090>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### System version information"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#%install_ext http://raw.github.com/jrjohansson/version_information/master/version_information.py\n",
      "%load_ext version_information\n",
      "%reload_ext version_information\n",
      "\n",
      "%version_information numpy, scipy, matplotlib, deltasigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>2.7.8 |Anaconda 2.1.0 (x86_64)| (default, Aug 21 2014, 15:21:46) [GCC 4.2.1 (Apple Inc. build 5577)]</td></tr><tr><td>IPython</td><td>2.2.0</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td>numpy</td><td>1.9.1</td></tr><tr><td>scipy</td><td>0.14.0</td></tr><tr><td>matplotlib</td><td>1.4.2</td></tr><tr><td>deltasigma</td><td>0.1-9</td></tr><tr><td colspan='2'>Tue Nov 11 11:44:19 2014 CET</td></tr></table>"
       ],
       "json": [
        "{\"Software versions\": [{\"version\": \"2.7.8 |Anaconda 2.1.0 (x86_64)| (default, Aug 21 2014, 15:21:46) [GCC 4.2.1 (Apple Inc. build 5577)]\", \"module\": \"Python\"}, {\"version\": \"2.2.0\", \"module\": \"IPython\"}, {\"version\": \"posix [darwin]\", \"module\": \"OS\"}, {\"version\": \"1.9.1\", \"module\": \"numpy\"}, {\"version\": \"0.14.0\", \"module\": \"scipy\"}, {\"version\": \"1.4.2\", \"module\": \"matplotlib\"}, {\"version\": \"0.1-9\", \"module\": \"deltasigma\"}]}"
       ],
       "latex": [
        "\\begin{tabular}{|l|l|}\\hline\n",
        "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
        "Python & 2.7.8 |Anaconda 2.1.0 (x86\\letterunderscore{}64)| (default, Aug 21 2014, 15:21:46) [GCC 4.2.1 (Apple Inc. build 5577)] \\\\ \\hline\n",
        "IPython & 2.2.0 \\\\ \\hline\n",
        "OS & posix [darwin] \\\\ \\hline\n",
        "numpy & 1.9.1 \\\\ \\hline\n",
        "scipy & 0.14.0 \\\\ \\hline\n",
        "matplotlib & 1.4.2 \\\\ \\hline\n",
        "deltasigma & 0.1-9 \\\\ \\hline\n",
        "\\hline \\multicolumn{2}{|l|}{Tue Nov 11 11:44:19 2014 CET} \\\\ \\hline\n",
        "\\end{tabular}\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "Software versions\n",
        "Python 2.7.8 |Anaconda 2.1.0 (x86_64)| (default, Aug 21 2014, 15:21:46) [GCC 4.2.1 (Apple Inc. build 5577)]\n",
        "IPython 2.2.0\n",
        "OS posix [darwin]\n",
        "numpy 1.9.1\n",
        "scipy 0.14.0\n",
        "matplotlib 1.4.2\n",
        "deltasigma 0.1-9\n",
        "<tr><td colspan='2'>Tue Nov 11 11:44:19 2014 CET</td></tr>"
       ]
      }
     ],
     "prompt_number": 17
    }
   ],
   "metadata": {}
  }
 ]
}