From f0ac9294681f08ffc872e69594d80083c6a3ac91 Mon Sep 17 00:00:00 2001
From: Kees van Kempen <k.vankempen@student.science.ru.nl>
Date: Tue, 15 Feb 2022 14:17:31 +0100
Subject: [PATCH] 05: Task 3 is done, and runs quite quickly.

---
 ...Discrete and Fast Fourier Transforms.ipynb | 57 +++++++++++++++++--
 1 file changed, 52 insertions(+), 5 deletions(-)

diff --git a/Week 2/5 Discrete and Fast Fourier Transforms.ipynb b/Week 2/5 Discrete and Fast Fourier Transforms.ipynb
index c7e604a..d8945f4 100644
--- a/Week 2/5 Discrete and Fast Fourier Transforms.ipynb	
+++ b/Week 2/5 Discrete and Fast Fourier Transforms.ipynb	
@@ -84,7 +84,8 @@
    "outputs": [],
    "source": [
     "import numpy as np\n",
-    "from matplotlib import pyplot as plt"
+    "from matplotlib import pyplot as plt\n",
+    "import timeit"
    ]
   },
   {
@@ -229,6 +230,10 @@
     "ax[1].plot(np.abs(np.fft.fft(yk1)), label=\"numpy.fft.fft\")\n",
     "ax[1].legend(loc=\"upper right\")\n",
     "\n",
+    "# TODO: So the graphs overlap completely. Is this good enough?\n",
+    "#       To make it more clear, we could mirror one of the graphs (multiply by -1),\n",
+    "#       like what is often done in spectroscopy, or we could add the difference.\n",
+    "\n",
     "fig.show()"
    ]
   },
@@ -266,7 +271,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -281,10 +286,52 @@
      "task": false
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "M = 2 gives\n",
+      "tOut = [0.0010804971680045128, 0.0005500782281160355, 0.0005198698490858078, 0.0005232971161603928, 0.0006225360557436943]\n",
+      "\n",
+      "M = 3 gives\n",
+      "tOut = [0.0005145492032170296, 0.00047505367547273636, 0.000535009428858757, 0.0003488045185804367, 0.00028009340167045593]\n",
+      "\n",
+      "M = 4 gives\n",
+      "tOut = [0.0002853143960237503, 0.00024075806140899658, 0.00021690316498279572, 0.00021761376410722733, 0.00023322459310293198]\n",
+      "\n",
+      "M = 5 gives\n",
+      "tOut = [0.000910954549908638, 0.0005088187754154205, 0.0005268435925245285, 0.0005177054554224014, 0.0005334652960300446]\n",
+      "\n",
+      "M = 6 gives\n",
+      "tOut = [0.002634277567267418, 0.0023930883035063744, 0.0024030981585383415, 0.002396835945546627, 0.0023911641910672188]\n",
+      "\n",
+      "M = 7 gives\n",
+      "tOut = [0.0092502785846591, 0.008834738284349442, 0.00884521659463644, 0.008864735253155231, 0.008844294585287571]\n",
+      "\n",
+      "M = 8 gives\n",
+      "tOut = [0.034397597424685955, 0.03395726904273033, 0.03396071586757898, 0.03401851560920477, 0.03401240427047014]\n",
+      "\n",
+      "M = 9 gives\n",
+      "tOut = [0.14702877961099148, 0.148259031586349, 0.14664556831121445, 0.14639647398144007, 0.14646969363093376]\n",
+      "\n",
+      "M = 10 gives\n",
+      "tOut = [0.5762987565249205, 0.5738314474001527, 0.5741532389074564, 0.5737893972545862, 0.574077476747334]\n",
+      "\n"
+     ]
+    }
+   ],
    "source": [
-    "# YOUR CODE HERE\n",
-    "raise NotImplementedError()"
+    "for M in range(2, 10+1):\n",
+    "    N = 2**M\n",
+    "    xk  = 2*np.pi*np.arange(N)/N\n",
+    "    # Using the first equation for yk from the previous exercise.\n",
+    "    yk = np.exp(20j*xk) + np.exp(40j*xk)\n",
+    "    tOut = timeit.repeat(stmt=lambda: DFT(yk), number=10, repeat=5)\n",
+    "    tMean = np.mean(tOut)\n",
+    "    print(\"M =\", M, \"gives\")\n",
+    "    print(\"tOut =\", tOut)\n",
+    "    print()"
    ]
   },
   {