Example exercise2.ipynb

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    "Now, since one should do it at least one time, try to implement a LMS algorithm. You will will define a function with the following syntax:"
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    "def lms(d,u,w,mu):\n",
    "    \"\"\" \n",
    "    Implements a single iteration of the stochastic gradient (LMS)\\n\n",
    "    :math:`w(n+1)=w(n)+\\\\mu u(n)\\\\left(d(n)-w(n)^T u(n)\\\\right)̀`\n",
    "    \n",
    "    Input:\n",
    "    ======\n",
    "        d : desired sequence at time n \n",
    "        u : input of length p\n",
    "        w : wiener filter to update \n",
    "        mu : adaptation step\n",
    "    \n",
    "    Returns:\n",
    "    =======\n",
    "        w : upated filter\n",
    "        err : d-dest\n",
    "        dest : prediction = :math:`u(n)^T w` \n",
    "    \"\"\"\n",
    "    dest=0\n",
    "    err=d-dest\n",
    "#\n",
    "# DO IT YOURSELF!\n",
    "#\n",
    "    return (w,err,dest)"
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    "You may test your function using the following validation:"
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    "np.random.seed(327)\n",
    "wout, errout, destout = lms(np.random.normal(1),np.random.normal(6),np.zeros(6),0.05)\n",
    "wtest = np.array([ 0.76063565,  0.76063565,  0.76063565,  0.76063565,  0.76063565, 0.76063565])\n",
    "#Test\n",
    "if np.shape(wout)==np.shape(wtest):\n",
    "    if np.sum(np.abs(wout-wtest))<1e-8:\n",
    "        print(\"Test validated\")\n",
    "    else:\n",
    "        print(\"There was an error in implementation\")    \n",
    "else:\n",
    "    print(\"Error in dimensions\") "
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    "A possible implementation is given now"
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    "def lms(d,u,w,mu):\n",
    "    \"\"\" \n",
    "    Implements a single iteration of the stochastic gradient (LMS)\\n\n",
    "    :math:`w(n+1)=w(n)+\\\\mu u(n)\\\\left(d(n)-w(n)^T u(n)\\\\right)̀`\n",
    "    \n",
    "    Input:\n",
    "    ======\n",
    "        d : desired sequence at time n \n",
    "        u : input of length p\n",
    "        w : wiener filter to update \n",
    "        mu : adaptation step\n",
    "    \n",
    "    Returns:\n",
    "    =======\n",
    "        w : upated filter\n",
    "        err : d-dest\n",
    "        dest : prediction = :math:`u(n)^T w` \n",
    "    \"\"\"\n",
    "    dest=u.dot(w)\n",
    "    err=d-dest\n",
    "    w=w+mu*u*err\n",
    "    return (w,err,dest)"
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   "source": [
    "## Identification procedure"
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