DT unit step

Author: ostad-ai

README.md

@@ -1,2 +1,3 @@
 # Signal Processing
-1) Delta function and its **sifting property**.
+1) Discrete-time **unit impulse** function and its **sifting property**.
+2) Discrete-time **unit step** function and its relation to *unit impulse*.

sp-unit step fucntion-for github.ipynb

@@ -0,0 +1,99 @@
+{
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+   "cell_type": "markdown",
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+   "source": [
+    "### Signal Processing\n",
+    "#### unit impulse from the difference of  two unit steps:\n",
+    "$\\delta[n]=u[n]-u[n-1]$\n",
+    "<hr>\n",
+    "https://github.com/ostad-ai/Signal-Processing\n",
+    "<br> Explanation: https://www.pinterest.com/HamedShahHosseini/Signal-Processing"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "1dda9e30",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def delta(n):\n",
+    "    if n==0:\n",
+    "        return 1\n",
+    "    else:\n",
+    "        return 0\n",
+    "    \n",
+    "def step(n):\n",
+    "    if n<0:\n",
+    "        return 0\n",
+    "    else:\n",
+    "        return 1\n",
+    "    \n",
+    "def delta_from_step(n):\n",
+    "    return step(n)-step(n-1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "1ce18754",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "delta[n]  u[n]-u[n-1]  n\n",
+      "0             0       -2\n",
+      "0             0       -1\n",
+      "1             1       0\n",
+      "0             0       1\n",
+      "0             0       2\n",
+      "0             0       3\n"
+     ]
+    }
+   ],
+   "source": [
+    "# consider x[n] as a sequence below\n",
+    "# and check property delta[n]=u[n]-u[n-1]\n",
+    "x=[-2,-1,0,1,2,3]\n",
+    "print('delta[n] ','u[n]-u[n-1]',' n')\n",
+    "for n in x:\n",
+    "    print(delta(n),11*' ',delta_from_step(n),5*' ',n)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c6054ddb",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
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