From efaa2b8a7ade1957040b646700e6e4a6a6c90b6b Mon Sep 17 00:00:00 2001
From: Cumhur Erkut <cumhur.erkut@gmail.com>
Date: Sat, 3 Aug 2024 08:42:11 +0200
Subject: [PATCH] LaTeX format using Colab

---
 03-Fourier-Transform/SPIS03.ipynb | 48 +++++++++++++++++--------------
 1 file changed, 26 insertions(+), 22 deletions(-)

diff --git a/03-Fourier-Transform/SPIS03.ipynb b/03-Fourier-Transform/SPIS03.ipynb
index 68a3931..3051bbf 100644
--- a/03-Fourier-Transform/SPIS03.ipynb
+++ b/03-Fourier-Transform/SPIS03.ipynb
@@ -7,7 +7,7 @@
         "colab_type": "text"
       },
       "source": [
-        "<a href=\"https://colab.research.google.com/github/SMC-AAU-CPH/SPIS/blob/main/03-Fourier-Transfom/SPIS03.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+        "<a href=\"https://colab.research.google.com/github/SMC-AAU-CPH/SPIS/blob/main/03-Fourier-Transform/SPIS03.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
       ]
     },
     {
@@ -55,7 +55,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 1,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -136,7 +136,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 2,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -232,7 +232,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 3,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -283,7 +283,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 4,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -354,7 +354,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 5,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -443,7 +443,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 6,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -535,7 +535,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 7,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -711,10 +711,14 @@
       "source": [
         "#### Example: DTFT of a window phasor\n",
         "Let us look at the phasor\n",
+        "\n",
+        "\n",
+        "\\\n",
         "$$\n",
         "    x_n = \\mathrm{e}^{j\\omega_0 n}\n",
         "$$\n",
-        "which we observe for $n=0,1,\\ldots,N-1$.\n",
+        "\n",
+        "which we observe for \\$n=0,1,\\ldots,N-1$.\n",
         "\n",
         "The DTFT of this windowed phasor is (note that subscript $N$ in $X_N(\\omega)$ indicates the window length)\n",
         "\\begin{align}\n",
@@ -727,7 +731,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 8,
+      "execution_count": null,
       "metadata": {
         "id": "8RRX9z1yJszQ"
       },
@@ -756,7 +760,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 10,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -808,7 +812,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 13,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -870,7 +874,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 14,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -958,7 +962,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 16,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -1032,7 +1036,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 17,
+      "execution_count": null,
       "metadata": {
         "id": "vmZ2ombiJszT"
       },
@@ -1057,7 +1061,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 18,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -1088,7 +1092,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 19,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -1183,7 +1187,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 20,
+      "execution_count": null,
       "metadata": {
         "id": "sYzH1FYeJszU"
       },
@@ -1206,7 +1210,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 21,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -1347,7 +1351,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 22,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -1398,7 +1402,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 23,
+      "execution_count": null,
       "metadata": {
         "id": "-OzqVKTHJszW"
       },
@@ -1414,7 +1418,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 24,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",