sp-sifting property-for github.ipynb

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    "### Signal Processing\n",
    "#### Sifting property:\n",
    "$x[n]=\\sum_{m=-\\infty}^{\\infty}x[m]\\delta[n-m]$\n",
    "<hr>\n",
    "https://github.com/ostad-ai/Signal-Processing"
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    "def delta(n):\n",
    "    if n==0:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0\n",
    "    \n",
    "def sift(n,x):\n",
    "    x_sift=0\n",
    "    for m,xm in enumerate(x):\n",
    "        x_sift+=xm*delta(n-m)\n",
    "    return x_sift"
   ]
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     "text": [
      "x[n] sift\n",
      "1    1\n",
      "2    2\n",
      "3    3\n",
      "4    4\n",
      "5    5\n"
     ]
    }
   ],
   "source": [
    "# consider x[n] as a sequence below\n",
    "# and check sifting property\n",
    "x=[1,2,3,4,5]\n",
    "print('x[n]','sift')\n",
    "for n in range(len(x)):\n",
    "    print(x[n],'  ',sift(n,x))"
   ]
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