05: Implement DFT(yk) with an example

Week 2/5 Discrete and Fast Fourier Transforms.ipynb

@@ -39,7 +39,7 @@
    "cell_type": "raw",
    "metadata": {},
    "source": [
-    "team_members = \"\""
+    "team_members = \"Koen Vendrig, Kees van Kempen\""
    ]
   },
   {
@@ -66,7 +66,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -83,10 +83,7 @@
    },
    "outputs": [],
    "source": [
-    "# Import packages here ...\n",
-    "\n",
-    "# YOUR CODE HERE\n",
-    "raise NotImplementedError()"
+    "import numpy as np"
    ]
   },
   {
@@ -121,7 +118,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -139,8 +136,31 @@
    "outputs": [],
    "source": [
     "def DFT(yk):\n",
-    "    # YOUR CODE HERE\n",
-    "    raise NotImplementedError()"
+    "    N = len(yk)\n",
+    "    x = 2*np.pi*np.arange(N)/N\n",
+    "    beta = yk.T * np.exp(-np.dot(np.arange(N), x)*1j)\n",
+    "    return beta"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([-1.-8.57252759e-16j, -2.-1.71450552e-15j, -7.-6.00076932e-15j,\n",
+       "       -6.-5.14351656e-15j])"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "DFT(np.array([1,2,7,6]))"
    ]
   },
   {
@@ -419,7 +439,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "Python 3",
    "language": "python",
    "name": "python3"
   },